Geophysical and Astrophysical Internal Waves

Conference in Les Houches (France), 6-11 February 2011
Organized by Thierry Dauxois (ENS Lyon) and Thomas Peacock (MIT)

The school is open from Sunday 6th February until February 11th in the afternoon. The conference will end just after Friday's lunch, i.e. around 2pm.

	Monday February 7th	Tuesday February 8th	Wednesday February 9th	Thursday February 10th	Friday February 11th
Chairman	Camassa	Staquet	Linden	Akylas	Helfrich
9h	MacKinnon	Wake	Rieutord	Carr	Linden
9h30	Lund	Turck-Chieze	Vanderhoff	Buhler	Simmons
10h00	Maas	Sommeria	Fringer	Boegman	Rogers
10h20	Coffee Break	Coffee Break	Coffee Break	Coffee Break	Coffee Break
Chairman	Legal	Alford	Paluszkiewicz	Zeitlin	Pinkel
10h45	Achatz	Llewellyn-Smith	Alford	Paluszkiewicz	Zeitlin
11h05	Helfrich	Diamessis	Akylas	Nycander	Dalaudier
11h25	Holmes-Cerfon	Camassa	Sutherland	Staquet	Van Grootel
11h45	Snively	Le Bars	Voisin	St Laurent	Weidman
12h05	Grue	Pinkel	Free Afternoon	Le Dizes	Farmer
	Free Afternoon	Free Afternoon	Free Afternoon	Free Afternoon
17h30	Marcus	Chomaz	Free Afternoon	Lund
18h00 - 19h15	Poster Session	Questions Session hosted by Buhler & MacKinnon	Free Afternoon	Questions Session hosted by Carr & Sutherland
19h30	Dinner	Dinner	Dinner	Dinner

Afternoons will be free to enjoy Nature wilderness (Hiking, Walking or Skiing) and to stimulate scientific discussions.

Posters Session

O. Aubert & M. Le Bars, P. Le Gal, P.S. Marcus A universal scaling law for pancake vortices in a rotating stratified fluid
G. Bordes , T. Dauxois & JB. Flor Pancake-like vortices in non rotating stratified fluids
S. Falahat The Calculation of Maximum Spring tide total velocity
U. Harlander & S. Koch, R. Hollerbach, C. Egbers Laboratory experiments of inertial waves in containers rotating with time modulation
S. Joubaud, B. Voisin & T. Dauxois Tangential oscillations of a disk in a stratified fluid
S. M. Kelly & J. D. Nash, K. I. Martini, M. H. Alford, E. Kunze Internal-tide generation and scattering on a continental slope
H. J. Lee & JH Park, M. Wimbush Tidal effects on the intermediate waters of the East/Japan Sea
K. I. Martini Near-inertial internal wave observations in the Beaufort Sea
B. Maurer & Paul Linden Intrusion-generated internal waves in a constantly stratified fluid
J. Munroe Parametric Instability Growth Rates of Mode-1 Internal Waves
D. J. Muraki & Y. Bao Unravelling the Resonant Instabilities of a Stratified Gravity Wave
E. Parau Gravity-capillary and gravity interfacial waves with a free surface
F. Senf & U. Achatz On the impact of middle-atmosphere thermal tides on the propagation and dissipation of gravity waves
E. Shroyer Observations of Large-amplitude, Mode-2 waves over the New Jersey Shelf
K. Slaoui & J. Lambrechts, V. Legat, J.-F. Remacle High-order efficient discontinuous Galerkin stereographic method
V. Teeluck Internal tide generation by Kelvin waves at the continental shelf
P. Williams Internal Waves Emitted from Balanced Flow: Observations, Properties, and Consequences
E. Stoylen Internal Kelvin waves in a jet-type Arctic fjord

Abstracts

Ulrich Achatz & Mark Fruman
Inertia-Gravity-Wave Breaking: Primary and Secondary Instabilities
The three-dimensionalization of turbulence in the breaking of nearly vertically propagating inertia-gravity waves is investigated using singular vector analysis applied to the Boussinesq equations linearized about two-dimensional time-dependent basic states obtained from nonlinear simulations of breaking waves. The singular vectors are compared to integrations of the linear model using random initial conditions, and the leading few singular vectors are found to be representative of the structures that emerge in the randomly initialized integrations. A main result is that the length scales of the leading secondary instabilities are an order of magnitude smaller than the wavelengths of both the initial wave and the primary perturbation, suggesting that the essential dynamics of the breaking might be captured by tractable nonlinear three-dimensional simulations in a relatively small triply-periodic domain. A sub-grid-scale scheme is tested as to whether it is able to treat turbulence in such cases via parameterization, with encouraging results.

Triantaphyllos R. Akylas & R. Grimshaw, A. Tabaei, S. Clarke
Theoretical model for local generation of solitary waves by reflecting wave beams in the ocean thermocline
It is generally accepted that ocean internal solitary waves can arise from the interaction of the barotropic tide with the continental shelf, which generates an internal tide that in turn steepens and forms solitary waves as it propagates shorewards. Some field observations, however, reveal large-amplitude internal solitary waves in deep water, hundreds of kilometers away from the continental shelf, suggesting an alternative generation mechanism: tidal flow over steep topography forces a propagating beam of internal tidal wave energy which impacts the thermocline at a considerable distance from the forcing site and gives rise to internal solitary waves there. Motivated by this possibility, a simple nonlinear long-wave model is proposed for the interaction of a tidal wave beam with the thermocline and the ensuing local generation of solitary waves. Theoretical predictions are consistent with field observations and earlier fully numerical simulations, suggesting that this generation mechanism is quite robust for typical oceanic conditions.

Matthew Alford
Observations of internal tides and dissipation in Luzon Strait: a tale of two ridges
Luzon Strait is a two-ridge system with strong mixed semidiurnal/diurnal barotropic tides flowing past it, situated between Taiwan and Luzon, Philippines. We show recently collected data from the region documenting some of the strongest and most dissipative internal waves in the world oceans, with currents exceeding 1 meter per second and vertical displacements exceeding 500 m. Part of the waves' vigor may s tem from the phenomenon of resonance, wherein waves generated at the two ridges interact constructively when their spacing is comparable to a horizontal internal tide wavelength. We investigated these c oncepts observationally in summer 2010 by measuring internal tide energy, energy flux and dissipation along two cross-ridge lines. Dissipation on the northern line, where the spacing between the ridges was close to the mode-1 semidiurnal wavelength, was extremely strong, exceeding 10^{-5} W kg^{-1} near the western ridge. Dissipation on the southern line, where the spacing was half that of the northern line, was much weaker. Net energy flux was small between the ridges on the northern line, consistent with interference between waves generated at the two ridges. This was not observed at the southern line. The data are presented and implications for resonance are discussed.

Oriane Aubert & M. Le Bars, P. Le Gal, P.S. Marcus
A universal scaling law for pancake vortices in a rotating stratified fluid
The Great Red Spot of Jupiter and the Meddies in the Atlantic Ocean are the most famous examples of long-lived anticyclones in a rotating and stably stratified medium. To reproduce and study these vortices in the laboratory, we inject a volume of isodensity dyed fluid in a rotating linearly stratified layer of salt water. Due to the Coriolis force, the injected fluid rapidly forms a pancake vortex whose long term evolution is quantified using PIV measurements and image processing. Three different phases take place: a fast geostrophic adjustment, an axisymmetrization by viscous coupling with the outside and finally a slow decrease of the motion while preserving the self-similar shape of the vortex. This last regime is described using a simplified system of equations based on a cyclo-geostrophic equilibrium, where the energy source maintaining the long-lived vortex is the density anomaly with the outside, maintained by internal recirculations. It gives an analytical solution for the self-similar shape of the vortex and the evolution law for the aspect ratio. These theoretical predictions are verified experimentally and also agree with published measurements for the Meddies and Jupiter's Great Red Spot.

Leon Boegman & Payam Aghsaee
Breaking of and resuspension beneath shoaling internal solitary waves
The breaking of shoaling internal solitary waves upon uniformly sloping bottom topography has been investigated in the laboratory and through two-dimensional (2D) direct numerical simulations (DNS). Over steep slopes, three distinct breaking mechanisms were observed: surging, plunging and collapsing breakers, associated with reflection, convective instability and boundary-layer separation, respectively. To correctly simulate the breaking mechanism, it was necessary to resolve the separated boundary layer flow beneath the shoaling wave, which is an inverse function of the Reynolds number. The 2D DNS overestimates the buoyancy flux (b) and underestimates the dissipation (e), during breaking, resulting in accurate simulation of the reflection coefficient (b+e), but not mixing efficiency (b/(b+e)). During flow separation, wave-induced near-bottom vortices suspend bed material. The resuspension is directly attributed to the near-bed viscous stress and to near-bed patches of elevated positive Reynolds stress.

Guilhem Bordes, T. Dauxois & JB. Flor
Pancake-like vortices in non rotating stratified fluids
Pancake-like vortices in non rotating fluid cannot represent the behaviour of large meddies in the ocean, because Coriolis force has to be taken into account. However, studying one single vortex is a good starting point for the understanding of vortices resulting from decaying turbulence in a stratified fluid. Here we present the method to produce such quasi-2D vortices in laboratory and some experimental results compared to an analytical model."

Oliver Buhler
Energy dynamics of waves and vortices
Waves and vortices can exchange energy in a variety of ways, some of which are significant for geophysical flows. In this talk recent theoretical and numerical work is described on the energy dynamics of a spectrum of waves that interacts with simple vortex flows. For once, no ray-tracing assumptions are made in this kind of investigation. The conservation (or lack thereof) of pseudoenergy and pseudomomentum will be seen to play a crucial role for the total wave energy budget.

Roberto Camassa
Spectral analysis of internal wave self-induced shears
Internal waves moving in stratified fluids generate their own shear flows that can become unstable to Kelvin-Helmholtz roll-ups. This talk will present a combined theoretical and numerical study of this instability starting with the spectral analysis of the corresponding non-self adjoint Taylor-Goldstein equation for parallel shears. Mode evolution in this set-up, and in particular non-normal mode growth and/or decay in addition to true spectral instability, helps explain some of the features observed in a numerical study of internal wave propagation.

Magda Carr
Shear-Induced Instabilities in Internal Solitary Waves
 Numerical simulation of shear-induced instabilities in internal solitary waves (ISWs) are presented. It is shown that both the critical Richardson number and the critical amplitude required for instability vary with the ratio of the undisturbed layer depths. It is found that a Richardson number less than 0.09 is required for instability when the non-dimensional depth of the lowest layer is large and hence the critical bound given in Barad & Fringer (2010) is not a sufficient bound for instability in ISWs. It is also shown that an instability bound based on the length of the region in a wave in which the Richardson number is less than one quarter is sensitive to the ratio of the undisturbed layer depths. Therefore, the alternative criterion for instability, presented in Fructus et al. (2009), is shown to be valid only for a limited parameter range. Preliminary laboratory observations of shear-induced billows in ISWs and their associated Thorpe scales will also be presented.

Jean-Marc Chomaz & M. Ahmed
Absolute and convective instability of internal gravity wave.
Even though all finite amplitude internal gravity waves in uniformly stratified fluid are known to be unstable, they are currently observed in many field or lab experiments as for example in the lee of topography. We explore here an explanation for this paradox by hypothesizing that the instability of these waves is convective and not absolute. Hence, in the frame of reference of a mountain, a localized initial perturbation should give rise to a wavepacket that grows but is advected downstream, eventually leaving the flow undisturbed.
The evolution of an initially localized perturbation was computed using direct numerical simulation of the Navier-Stokes equations under the Boussinesq approximation linearized around a 2-D uniform finite-amplitude planar gravity wave. The shape of the localized perturbation impulse was chosen so that perturbation energy was concentrated in higher wavenumber modes. This minimized the spreading of the perturbation impulse due to fast-propagating long neutral waves.
The edge velocity of the wavepacket resulting from the evolution of the impulse was determined by analyzing the amplitude of its energy on spatio-temporal rays. This generic technique allowed discrimination between the absolute and convective nature of the instability. Results showed that the wavepacket that develops from the initial perturbation impulse splits into different wavepackets corresponding to different instability modes. but all wavepackets are convectively unstable for the wave amplitude considered.

Francis Dalaudier
Pertinence of spectral modeling for gravity waves
Observation of the mesoscale dynamics in the atmosphere, and also in the ocean, show that gravity waves are the dominant fluctuations between large scales organized motions (general circulation and meteorological processes) and small scale turbulence providing the final dissipation. The reasons and mechanisms for this role will be discussed as well as the importance of this scale domain for the atmosphere dynamics. These fluctuations are described through spectral (statistical) modeling. The applications, the validity and the limitations of such description will be discussed for the simulation, the statistical prediction and the parameterization of the gravity waves effects.

Peter J. Diamessis & Ammar M. Abdilghanie
The internal wave field radiated by a stratified turbulent wake
The internal wave (IW) field radiated by a stratified turbulent wake with non-zero net momentum is investigated numerically over a broad range of body-based Reynolds number and Froude numbers. At higher Reynolds numbers, secondary Kelvin-Helmholtz instabilities and turbulence in the wake core drive persistent IW radiation up to . Through two-dimensional wavelet analysis the wavelengths, group/phase velocities and orientation angle of the wake-emitted IW field are estimated. At the higher Reynolds number value, IW beams propagate at an angle closer to the horizontal plane suggesting that the wave-generation mechanism is no longer viscously controlled but serves to efficiently extract momentum from the mean wake flow. Finally, the steepness of the near-field waves increases with Reynolds and Froude number, indicating potential for enhanced remote breaking in geophysical/naval environments.

Saeed Falahat
The Calculation of Maximum Spring tide total velocity
Internal tides, internal gravity waves generated in stratified ocean by the interaction of barotropic tidal currents with bottom topography, play a role in vertical mixing in the deep ocean. Analytical model, developed to calculated energy conversion from barotropic tide to baroclinic tide, is now used to compute calculate and map total (barotropic+baroclinic) spring tidal velocities near the seafloor for a given region in the ocean. The idea behind this study is that tides maybe affect sediment dynamic in the deep ocean. Therefore, in this study, we try to shed more light on deep sea phenomena affected by internal tides.

David Farmer & Li Qiang
Evolution of large amplitude internal waves in the deep basin of the South China Sea
Several months of measurements from inverted echo-sounders deployed on the floor of the South China Sea allow us to observe the transformation of large amplitude internal tides generated over ridges in Luzon Strait as they propagate westwards across the deep basin. A fully nonlinear model coupled to a wave generation solution provides a framework for explaining the competing effects of nonlinearity, rotation and non-hydrostatic dispersion on the evolving wave structure for different representative forcing conditions. The results allow comparison of the fully and weakly nonlinear descriptions and explain the intermittent character of short period nonlinear internal wave formation.

Oliver B. Fringer & Sean Vitousek
Physical vs numerical dispersion in nonhydrostatic internal wave modeling
Most flows in the ocean are hydrostatic and so hydrostatic models are satisfactory for most applications of interest. However, when the vertical scales are on the same order as the horizontal scales, such as in weakly nonlinear internal gravity waves, solution of the nonhydrostatic pressure may be required. Because solution of the nonhydrostatic pressure can incur substantial computational overhead, it is important to understand minimum grid resolution requirements that are sufficient to resolve the nonhydrostatic internal waves while incurring as little computational overhead as possible. The primary physical effect of the nonhydrostatic pressure in internal gravity waves is frequency dispersion, which causes waves of different frequencies to travel at different speeds. However, errors in computing the hydrostatic pressure gradient can lead to erroneous numerical dispersion that mimics the effect of the nonhydrostatic pressure. We show that in order for this numerical dispersion to be smaller than the physical nonhydrostatic dispersion, the grid resolution, Dx, must satisfy Dx/h < O(1), where h is the relevant depth scale. This constraint poses a significant computational requirement for simulation of nonhydrostatic internal gravity waves in the ocean.

David Fritts
Gravity Wave Interactions and Instabilities Accompanying Multiscale Superpositions
This talk will examine the role of gravity wave superpositions in driving spectral evolution, instabilities, and fine structure. Such superpositions, and the interactions that arise, lead to turbulence in several ways that have interesting implications for spectral energy transfers and transport processes.

John Grue
Finite amplitude internal waves over topography by successive Fourier transform
We consider nonlinear interfacial motion in three dimensions under the effect of gravity. The interface separates two horizontal homogeneous layers of different density and finite different thickness. The lowerlayer is bounded below by a variable bottom and the upper layer by a rigid lid. Integral equations over the nonlinear interface and bottom topography representing the motion are inverted by successive Fourier transform and used in the forward time integration of the interface. Nonlinear interaction with topography will be illustrated. Analysis in relation to internal run-up across a slope measured in laboratory will be commented on.

Uwe Harlander & Sandy Koch, Rainer Hollerbach, Christoph Egbers
Laboratory experiments of inertial waves in containers rotating with time modulation
Inertial waves occur in rotating homogeneous fluids. Such waves are important for the motion of the Earth's outer fluid core and the oceans. We experimentally investigate such waves for spherical shell geometry. For this geometry theoretical understanding is hampered by the occurrence of singularities and a complicated Ekman layer structure. In our experiments and simulations, the waves are excited by modulating the rotation rate of the inner sphere. Preliminary results show the generation of higher harmonics in the equatorial region of the shell. We also find a vertical layer, touching the inner sphere's equator. The layer is reminiscent of a Stewartson layer but shows a different spatial structure. Finally, we suggest similar experiments for cylindrical geometry.

Karl Helfrich
Models of large-amplitude internal solitary waves with trapped cores
Large-amplitude internal solitary waves in continuously stratified systems can be found by solution of the Dubreil-Jacotin-Long (DJL) equation. For large wave amplitudes these solutions may have trapped cores with densities outside the ambient range. The cores may be statically unstable and are physically questionable. To address these issues a new model for trapped-core waves is formulated. A finite core of uniform density and velocity equal to the phase speed, but unknown shape, is assumed. The exterior flow satisfies the DJL equation and pressure continuity is imposed at the core boundary. Numerical solutions of the DJL equation with the core condition are discussed. Two-dimensional numerical solutions of time-dependent non-hydrostatic equations with the theoretical solutions as initial conditions show that these solutions are stable, but have a leaky, rather than completely isolated core. Above a critical amplitude, shear instability destroys the initial wave. Three-dimensional numerical solutions indicate that the two-dimensional trapped core solutions below the shear instability limit are stable to transverse perturbations.

Miranda Holmes-Cerfon
Scattering of the internal tide over random topography
We consider how the internal tide is modified as it propagates over subcritical random topography in a finite-depth ocean. The intent is to model the decay of low-mode internal waves as they propagate away from the large topographic features where they were generated, and the role that bottom topography might play in this. Numerical results show a peculiar focusing effect, where the streamfunction becomes concentrated on narrow rays in real space. Analytic results show that when the amplitude of the topography is small, the streamfunction can be described as a superposition of linear modes whose evolution is governed by a system of stochastic differential equations. Analyzing this system yields an estimate for the decay rate of the mode-1 internal tide, which suggests a possible parametrization for the scattering of the internal tide due to bottom topography.

Sylvain Joubaud, B. Voisin & T. Dauxois
Tangential oscillations of a disk in a stratified fluid
We present an experimental study of the generation of internal waves by the horizontal oscillations of a disk in a stratified fluid. Viscosity is the motor of the generation mechanism through the no-slip condition at the surface of the disk. Velocity fields are measured by particle image velocimetry and show that the waves form steady cross-shaped wave beams. Comparison with the theory of Davis & Llewellyn Smith (J. Fluid. Mech. 2010) exhibits good prediction of the wave profile but also a surprising underestimation of the wave amplitude at small amplitude of oscillation.

Sam M. Kelly & J. D. Nash, K. I. Martini, M. H. Alford, E. Kunze
Internal-tide generation and scattering on a continental slope
Observations and numerical simulations indicate that the tidal dynamics on Oregon continental slope are influenced by locally-generated and shoaling internal tides. Here, we develop a methodology to separate these influences and identify energy pathways from large to small scales. First, by approximating tides as predominantly propagating in the across-slope direction, we simultaneously estimate onshore and off_shore energy fluxes. Then, using an expression for inter-modal energy conversion, we estimate internal-tide generation and scattering. Our results suggest locally-generated internal tides propagate offshore while shoaling internal tides scatter to small scales and drive local mixing.

Michael Le Bars & P. Le Gal, D. Guimbard, S. Le Diz�s, S. Leblanc.
Experimental studies of the strato-elliptical and strato-rotational instabilities.
In this talk, I present the main results of two investigations of fluid instabilities driven by coupling of gravito-inertial waves, of direct interest for geophysical and astrophysical flows.
The first study is dedicated to the so-called strato-elliptical instability (SEI). SEI takes place in any rotating and stratified flow whose streamlines are elliptically deformed. It could generically affect any vortex in the atmosphere and in the ocean. We have analysed the characteristics of SEI in a finite and elliptically deformed cylinder, in the presence of both background rotation and axial stratification. A general formula for the linear growth rate of the stationary sinuous modes has been derived including viscous and detuning effects in the limit of small eccentricity. This formula is discussed and compared to experimental results which are obtained in a cylinder filled with salted water for two different eccentricities by varying the stratification, the background rotation and the cylinder rotation. A good agreement with the theory concerning the domain of instability of the sinuous modes is demonstrated. Other elliptic instability modes, oscillating at the cylinder angular frequency are also evidenced. The nonlinear regime of the elliptic instability is documented. In contrast with the homogeneous case, no cycle involving growth, breakdown and re-laminarization is observed in the presence of strong stratification. The elliptic instability in a stratified fluid seems to yield either a persistent turbulent state or a weakly nonlinear regime.
The second study is dedicated to the so-called strato-rotational instability (SRI). SRI affects rotating shear flows when the fluid is stably stratified in the axial direction. This instability may be relevant for accretion disks, where it provides an alternative explanation for the destabilisation of the Keplerian flow, in addition to the so-called magneto-rotational instability (MRI). In agreement with recent theoretical and numerical analyses, we describe in detail the destabilization of the stratified cylindrical Couette flow below the Rayleigh line (i.e. the stability threshold without stratification). We confirm that the unstable modes of the SRI are non axisymmetric, oscillatory, and take place (in the limit of our experimental set-up) as soon as the azimuthal linear velocity decreases along the radial direction. The analytical analysis of this instability as well as an additional and more general experiment in an unbounded domain will be presented in the companion talk by Le Diz�s et al.

Stephane Le Diz�s & X. Riedinger, J. Candelier, P. Meunier, C. Millet
Radiative instability of stratified shear flows
In this talk, we analyse how the stability of a shear flow is modified when placed in a stably stratified environment. It is first shown that stratification is stabilizing only if the directions of shear and stratification are aligned. When shear and stratification are not aligned, we demonstrate that an additional inviscid instability associated with the emission of internal gravity waves can take place. This radiative instability is analysed in details for models of boundary layer flows, plane jets and rotating flows. Both the mechanism of instability and explicit formulas for the characteristics of the instability are provided. Differences and similarities with the so-called strato-rotational instability are pointed out. Experimental results are also obtained for two types of rotating flows (a Gaussian vortex and the flow around a rotating cylinder when the rotation axis is aligned along with the direction of stratification). Finally, the results are discussed in the context of atmospheric flows and of astrophysical flows (accretion disks).

Ho Jin Lee & JH Park, M. Wimbush
Tidal effects on the intermediate waters of the East/Japan Sea
Although tides are believed to be the most important source for diapycnal mixing in the ocean, few studies have directly simulated open-ocean circulation including tides. Since the East/Japan/Sea (EJS) has been considered a �miniature ocean,� we here investigate tidal effects on the intermediate water of the EJS, using an eddy resolving Ocean General Circulation Model. The simulated temperature and salinity in the intermediate layer are significantly improved by including tides. The improvement results from the combined effect of M2 and K1 internal tides.

Paul F Linden
Gravity currents in a stratified ambient fluid
This talk discusses the role of internal waves in the propagation of a gravity current in a stably stratified fluid. We extend a model for the speed and height of a gravity current in an unstratified ambient fluid to the case where the ambient fluid is stratified with a constant vertical density gradient. Data from laboratory experiments and from two-dimensional direct numerical simulations are compared with the model and it is found that it provides an excellent prediction for the speeds of supercritical currents. On the other hand, subcritical currents, where waves are generated and travel ahead of the current, travel faster than predicted and it appears that the internal waves alter the upstream stratification.

Stefan G. Llewellyn Smith & Paul Martin, Tony Davis.
Boundary integral methods in internal wave generation and scattering
In laboratory experiments on internal waves, the waves are generated by the motion of an object in the fluid. In the internal tide problem, waves are generated by the interaction of a barotropic current and topography. Analytic or quasi-analytic solutions for internal-wave generation and scattering problems are known for only very simple geometries, such as cylinders and ellipses. A recent tool to investigate more complicated situations is the boundary int�gral technique. We review this approach and discuss its use and applicability to problems including visoscity, three-dimensional geometries and rotation.

Thomas Lund
Numerical Simulation of Gravity Wave Breaking in the Upper Atmosphere
A recently-developed computer code is used to perform high-resolution, three-dimensional numerical simulations of gravity wave breaking at altitudes as high as 160 km. The code solves the anelastic equations, which efficiently account for variations in background density while excluding acoustic waves. Detailed results are presented for a horizontal wavelength of 60 km and frequency N/3.7. Although the wave breaks initially at an altitude close to 160 km, the turbulent zone descends with time under the combined influences of momentum deposition and turbulent wrinkling of the potential temperature field. The flow dynamics are studied via animation of the vorticity field and some statistical measures are compared with the predictions of linear theory.

Leo Maas
Tide-topography interaction?
The classical linear two-dimensional internal tide generation problem can be solved exactly for a number of non trivially-shaped bottom topographies. In this talk, the derivation of the standard problem is sketched. Subsequently, the method to obtain exact solutions is discussed. It turns out that these solutions come with a �twist��

Jennifer MacKinnon
Energy cascades through the internal-wave field and implications for global mixing patterns
Energy input into the oceanic internal wave field is primarily in the form of large vertical scale (low-mode) waves, while the waves that ultimately break to produce turbulence are generally small-scale waves with comparatively high shear and strain. Thus one of the long-standing thrusts of internal wave research in the ocean has been an attempt to understand the linear and nonlinear dynamics that act to transfer energy from large to small-scale waves. Here I'll discuss the current state of research with an eye towards understanding the resultant global patterns of turbulent mixing and underway development of appropriate parameterizations of the process for use in global climate models, including a few detailed examples of recent numerical process studies.

Phil Marcus & Chung-Hsiang Jiang
Selection Rules for IGW and Inertial Wave Interactions and Reflections ? Applications to Oceans.
When two beams of IG waves or inertial waves interact, or when a single beam reflects from a surface, harmonic beams can be generated. We show that there are selection rules that prohibit most of the harmonic beams from forming. There are many examples where ocean data have been collected in anticipation of seeing harmonic beams, but there is no signature of the harmonic beams in the data. We show that the absence of the harmonic beams is consistent with the selection rules. We consider both two- and three-dimensional beams.

Kim I. Martini
Near-inertial internal wave observations in the Beaufort Sea
Preliminary results from a moored array deployed in the Beaufort Sea from August 2007 to August 2008 show near-inertial energy is generated at the sea surface, sometimes propagating nearly 300 m into the ocean interior. In the upper 100 m, average nearinertial kinetic energies are largest during the summer (21 J/m^2) but are generally smaller in winter (9 J/m^2). However, intermittently throughout the winter there are high-KE events (62 J/m^2) corresponding to decreased sea ice. This is contrary to previous wintertime observations where sea ice impeded surface internal wave generation. Reduced ice coverage and changing ice pack conditions may increase wintertime generation, possibly leading to internal wave induced mixing in the arctic interior. We discuss how the presence and properties of sea ice affect near-inertial internal wave generation in the Arctic.

Benjamin Maurer & Paul Linden
Intrusion-generated internal waves in a constantly stratified fluid
Intrusive Gravity Currents (IGCs) are the buoyancy driven horizontal intrusion of one fluid into a stratified ambient fluid at an intermediate depth. The stable ambient stratification necessary for IGCs also supports internal waves excited by the intruding fluid. We present an experimental and numerical study of the IGC-generated upstream internal wave field in a constantly stratified fluid channel. We note a strong influence of the level of IGC propagation on the forcing of particular supercritical wave modes, and we estimate the associated energy fluxes relative to the estimated available potential energy of the system.

James Munroe
Parametric Instability Growth Rates of Mode-1 Internal Waves
Internal waves are known to be inherently unstable and evolve in time by transferring energy to different length and time scales. While there has been substantial work investigating internal waves stability theoretically and numerically, there has been comparatively few laboratory studies examining these instabilities. Using a full-depth wave generator to force a vertical mode-1 wave in a narrow rectangular tank, we observe the evolution of the wave field. The fluid motion is quantitatively measured using synthetic schlieren. In particular, we investigate the growth rates of secondary waves due to parametric sub-harmonic instability and compare to theoretical predictions

David J. Muraki & Yuanxun Bao
Unravelling the Resonant Instabilities of a Stratified Gravity Wave
The resonant instability of a finite-amplitude, internal gravity wave is a thoroughly studied process, and has been investigated from a variety of distinct perspectives. The mathematical approach of Floquet/Fouriermethods leads to a linear algebraic computation of stability eigenvalues as a function of disturbance wavenumbers. In such a computation, the number of eigenvalues is determined by the numerical Fourier r�solution (# of modes) --- while the usual dispersion relation for gravity waves is only a double-valued function for (eigen)-frequencies for each wavevector. This apparent change of eigenvalue multiplicity is a known ambiguity of Floquet/Fourier methods. On the other hand, DNS simulations produce unambiguous Fourier spectral data. We present an untangling of this conundrum by showing that the complex analysis of Floquet spectral theory allows for an interpretation of the stability eigenvalues that exactly match the physical mechanisms of r�sonant interactions.

Jonas Nycander
Comparison of internal wave drag parameterizations for tidal models
By using linear wave theory, the internal wave drag can be expressed as a product of the barotropic tidal velocity and a friction tensor. The friction tensor in a point is obtained by computing a convolution integral around that point, using stratification and bottom topography as input data. The computed tensor field is then used in a tidal model to parameterize the wave drag. This parameterization has no adjustable parameters, and gives good agreement with inverse estimates of the tidal dissipation in the deep ocean. It is compared to two other, more heuristic parameterizations that have been used earlier, and which both contain one adjustable parameter. The total global energy flux to the internal wave field is similar with all three parameterizations, but the horizontal distribution of the energy flux differs significantly between them.

Theresa Paluszkiewicz
An Overview of Internal Wave Research Programs at ONR
The U.S. Office of Naval Research funds studies of ocean internal waves using an integrated, interdisciplinary approach with the long-term goal of incorporating internal waves into regional ocean forecasts. Teams of research scientists with complementary skills in field observations, laboratory and numerical modeling and remote sensing are tasked with solving long standing questions about the generation, fate, and transformation of internal tides and internal waves in order to better represent the basic physics in forecast models. An overview of the science topics, approaches, and recent results is presented and features material from three example programs. The talk is intended to concentrate on how the integrated approach facilitated scientific progress; several of the conference participants will delve into specific results from these experiments. The Non-Linear Waves Initiative (NLIWI) program fielded experiments in the South China Sea and on the shelf of New Jersey and addressed the processes governing the transformation from internal tide to non-linear wave. The Initiation of Waves in Straits Experiment (IWISE) program just completed a pilot program to look at the generation of waves in straits and takes many of its motivating hypothesis from NLIWI and from the Philippine Sea Experiment (PhilEx). The PhilEx program captured the interaction of internal tides, topography, and basin scale circulation for an example archipelago straits role in internal wave modification.

Emilian Parau
Gravity-capillary and gravity interfacial waves with a free surface
Computations of steady two-dimensional gravity-capillary waves and gravity interfacial waves are presented. The upper layer is bounded above by a free surface, whilethe lower layer is of finite depth. The Euler equations in each layer will be used and the full nonlinear boundary conditions at the interface and on the free surface will be imposed. The solutions are computed either by using a boundary integral equation based on Green functions, or based on Cauchy integral equation. Free and forced waves will be considered.

Robert Pinkel
Vertical Wavenumber Spectra of Strain and Shear in the Thermocline
Existing fine-scale parameterizations for the eddy diffusivity of mass are based on measured vertical wavenumber spectra of shear and strain. The parameterizations are justified in terms of cascade models of energy flow that relate spectral levels at 10-50 m vertical scales to steady-state levels of turbulent dissipation. Such cascades might be quite different depending on whether the principal contributors to the spectra are internal wave or vortical processes. Here I examine wavenumber-frequency spectra of strain and shear from the HOME Farfield experiment at 18 N, 157 W with the objective of isolating internal wave and sub-inertial contributors to the shear and strain fields. South of Hawaii the shear is principally near inertial, with distinct traveling (σ ⁄ � = 1.01) and local (σ ⁄ � = 1.001) constituents. The strain field is dominated by a vortical contribution that is band limited in vertical wavenumber over scales 10 - 50 m. The internal wave constituent is substantially near-inertial and red in vertical wavenumber. With increasing encounter-frequency, the spectrum is reduced in amplitude. The reduction is more pronounced at lower wavenumbers than high; eventually leading to a blue wavenumber dependence at high frequency. Estimates of the wavenumber spectrum of strain for the upward and downward waves and for the sub-inertial peak will be presented.

Michel Rieutord
Inertial waves in a spherical shell
We shall present our latest results on the asymptotic properties of inertial waves propagating in a fluid confined in spherical shell. In particular we shall show that the width of shear layers stemming from the singularities of the Poincar� equation is scaling with the one thirdpower of the Ekman number, unlike the two-dimensional models. An extension of these results to the case of gravito-inertial waves, propagating in a rotating stably stratified medium will be presented through preliminary results.

Tamara Rogers
Internal Gravity waves in Stellar Interiors
Internal Gravity Waves (IGW), such as those observed in our own atmosphere surely exist in the solar radiative interior. Such waves have received a great deal of attention recently, both because of their ability to transport angular momentum and because of their observational potential. While these waves have been studied extensively in our own atmosphere, in the Sun they are generated at the interface between the convective and radiative regions, in precisely the region thought to house a strong magnetic field. In this talk I will discuss the propagation, dissipation and angular momentum transport by IGW in the presence of magnetic fields. I will show that, in the presence of magnetic fields, wave properties and the angular momentum transport by such waves will be altered.

F. Senf & Ulrich Achatz
On the impact of middle-atmosphere thermal tides on the propagation and dissipation of gravity waves
The interaction between gravity waves and thermal tides is an important aspect of wave dynamics in the middle atmosphere. Solar thermal tides cause large variations in the background conditions, especially wind, through which gravity waves propagate. This induces a modulation of gravity-wave pseudo-momentum fluxes and thus a force back on the tidal structures. In past studies, the gravity-wave forcing on thermal tides was derived from gravity wave parameterizations with many underlying assumptions. Gravity-wave parameterizations work in vertical columns in which time-dependence and horizontal inhomogeneities of the background conditions have been neglected. The main aim of the present study is to evaluate these assumptions, especially concerning the propagation in thermal tides. We use a global ray-tracing algorithm combined with tidal data from a general circulation model. For a consistent comparison and for an evaluation of the conventional parameterization approach, we apply three different ray-tracing experiments in which successively assumptions on horizontal and temporal dependence of the background conditions have been omitted. This allows to mimic the effect of a conventional gravity wave parameterization within the ray-tracing setup. We show that, on one hand, time-dependence of the background conditions leads to a modulation of gravity-wave observed frequencies. The frequency modulation causes a modulation of the gravity-wave phase velocity so that it follows the shape of the background wind. Transient critical layers disappear. The force due to gravity waves is smeared out over larger vertical distances. The amplitude of the diurnal forcing is reduced by the effect of frequency modulation. On the other hand, horizontal inhomogeneities in the background conditions induce a refraction of the gravity waves into the jet-stream cores, thus minimizing their vertical travel time. Horizontal propagation can lead to large meridional displacements and an interhemispheric exchange of gravity wave energy. Local gravity-wave forces due to horizontal refraction can be attributed to three different mechanisms: horizontal divergence of the pseudo-momentum flux-tensor, turning of the horizontal wave vector and horizontal stretching or shrinking of the gravity-wave field, respectively. The first two contributions are mainly of the order of 10 to 30% whereas the last may reach up to 60% of the dominant forcing in the lower mesosphere. We introduce generalized equivalent Rayleigh friction coefficients which map the gravity-wave force on tidal winds and accelerations. Using these, it is shown that a clear, mostly uniform tidal damping, which originates from the Lindzen-type saturation hypothesis, disappears when horizontal and time dependence of the tidal background conditions are taken into account.

Emily Shroyer
Observations of Large-amplitude, Mode-2 waves over the New Jersey Shelf
Observations of a mode-2 nonlinear wave packet were obtained off the New Jersey coast in a ship-tracking experiment conducted in August 2006. The leading mode-2 wave evolved rapidly and formed a tail of short, small-amplitude mode-1 waves. The wavelength of the mode-1 oscillations was consistent with that for a co-propagating tail, based on comparison of the mode-2 wave speed to the linear mode-1 wave speed. Turbulent mixing and radiation of mode-1 waves contributed to energy loss in the leading wave, and the estimated decay time scale was consistent with the short time period over which the packet could be reliably tracked. An idealized modeling study is being conducted in an effort to better understand what processes controlled the evolution of this wave packet.

Harper Simmons
Modeling Near-Inertial Wave Generation and Radiation at the Global Scale -- Implications for the Geography of Mixing
A long-term goal of the oceanographic community has been to develop a global internal wave prediction system analogous to those already in place for surface waves. Toward this end the community has begun to make progress connecting internal wave energy sources, the large-scale distribution of internal waves, and energy sinks in the form of internal wave breaking and dissipation. We report further progress on the wind-generation contribution to the internal wave "climate" using a high-resolution eddy resolving numerical model of the ocean general circulation.
This allows us to diagnose the wind input into near inertial motions and the energy redistribution via wave radiation. This provides a direct analogue to previous results for global scale predictions of internal tide generation, and allows the analogous maps of wave-driven mixing to be postulated. Inputs are compared to observations from drifters and simpler one-dimensional models, and radiation is quantified and compared to previous inferences from historical mooring records.

Karim Slaoui & J. Lambrechts, V. Legat, J.-F. Remacle
High-order efficient discontinuous Galerkin stereographic method
An e_cient approach is proposed to solve vectorial conservation laws on the sphere, using the stereographic projection and the Discontinuous Galerkin Method. This new approach combines all the advantages of previous techniques described in the litterature. We describe a robust and accurate way to discretize partial di_erential equations on the sphere by means of the _nite element method. The key idea is a dialog between the global coordinates of the vertices of an element and its local coordinates. This allows for the integration to take place on the stereographic plane instead of a curved space. The technique is validated on the sphere, using the shallow water equation for computing standard atmospheric benchmark. In particular, the Williamson test case is used to analyze the impact of the change of variable on the convergence rate for discretization error.

Jonathan Snively
Ducted gravity waves in the mesosphere and lower thermosphere
Ducted internal gravity waves near the Brunt-Vaisala frequency are ubiquitous in the mesosphere and lower thermosphere, and observed by their perturbations to airglow photochemistry. Typical waves exhibit periods ~4-8 minutes, horizontal wavelengths ~10-30 km, and temperature perturbations of a few to tens of Kelvin. Via airglow measurements, nonlinear effects associated with strong wave propagation are observed simultaneously to those associated with strong perturbations to the chemical system. Here, we numerically model the propagation of ducted waves at realistic amplitude under typical mesospheric conditions, and their perturbations of layered minor species participating in airglow photochemistry, to investigate sources of apparent nonlinearity in observed data.

Joel Sommeria
Overview of internal gravity wave studies at the Coriolis platform, dynamical similarity with the ocean.
While dynamical similarity with natural media cannot be fully achieved, partial similarity can be obtained for specific processes. Generation, propagation and wave instability processes can be reproduced in distinct experiments with different scaling choices. Examples of internal gravity waves on the Coriolis platform will be discussed. Beyond its use for physical modeling, the analysis of similarity properties can deepen our physical understanding. In the limit of small aspect ratios, the hydrostatic approximation applies, leading to a property of invariance by a change of aspect ratio. The limit of validity of this property will be examined in relation with the limitations of the hydrostatic approximation. Application to the production of solitary waves will be discussed.

Louis St. Laurent
Internal waves at Mid-Ocean Ridges
Mid-Ocean ridges comprise the most extensive topographic features of the global ocean. They span across the basin scales, and are most pronounced in the Atlantic and Indian Oceans where the tectonic plates are spreading slowly. These regions are characterized by deep fracture zones consisting of quasi-regular ridge and valley networks, in addition to a central axis defining the apex of the ridge system. Combined with the stratified deep waters of the ocean, the tides, geostrophy, and density driven flows; mid-ocean ridges are enhanced sites of internal wave generation.
Mid-ocean ridges are unique in their ability to generate high-mode waves, in contrast to abrupt topography such as island arcs and trenches, where low modes dominate. The high-mode wave field is favorable to dissipation, as enhanced shear and wave-wave interactions are efficient at decaying the wave. Given the remote nature of most mid-ocean ridge sites, the tides often provide the most significant forcing, leading to the generation of internal tides. Higher frequency internal waves may be generated in fracture zones and passages, where strong flows often occur in the presence of hydraulic phenomena.
Recent studies have examined several mid-ocean ridge sites with an emphasis on understanding their role in internal wave generation and the subsequent decay of waves into turbulence. Here, we will review measurements of internal waves from sites along the Mid-Atlantic, East Pacific, and Southern Ocean ridge systems. These sites represent different forcing regimes of internal waves, with internal tides dominating the Mid-Atlantic sites, and inertial and lee waves dominating the Phoenix Ridge in the Drake Passage. Relevant theory, and findings from field studies, will be discussed for each case.

Chantal Staquet & Nicolas Grisouard
Local generation of internal solitary waves in a pycnocline
Oceanic observations have provided evidence of the generation of internal solitary waves due to an internal tidal beam impinging on a seasonal pycnocline from below. The purpose of this talk is to present direct numerical simulations of such a generation process with a fully nonlinear nonhydrostatic model. An academic two-dimensional configuration in a vertical plane is considered. We shall show that, depending on the parameters, different modes of internal solitary waves can be excited in the pycnocline and we shall provide examples of internal solitary waves as first, second and third modes, trapped in the pycnocline. A criterion for the selection of a particular mode will be put forward, in terms of phase speeds. Application to the Bay of Biscay will then be considered.

Eivind Stoylen
Internal Kelvin waves in a jet-type Arctic fjord
We consider the propagation of internal waves of tidal periodicity in a jet-type stratified Arctic fjord. The existence of such waves have been debated in literature, due to the hydraulic conditions at the fjord mouth (Stigebrandt and Aure, 1989), however recent research confirm their presence (Inall et.al, 2004, 2005; Stashchuk et.al, 2007). In our study we look at a wide Arctic fjord, the Van Mijenfjord in Svalbard. We measure thirteen-hour CTD time series at various near-coast locations, in addition to simulating the conditions numerically. Our observations show a large amplitude variation in the isopycnals of periodicity about twelve hours, appearing only on the right hand side of the fjord. Preliminary model results are able to reproduce this behavior, indicating the presence of internal Kelvin waves in this jet-type fjord during summer conditions.

Bruce Sutherland
Drag Parameterization for Large-Amplitude Atmospheric Waves
The diagnoses of internal wave propagation, anelastic growth and breaking in the middle atmosphere are assessed in general circulation models through heuristics based upon observations and the predictions of linear theory. Before wave breaking occurs, however, internal waves grow to moderately large amplitude and so the predictions of linear theory are drawn into question. Weakly nonlinear theory shows that the dominant weakly nonlinear dynamics are determined by interactions between internal waves and the mean flow that they induce (their ``Stokes drift''). Fully nonlinear simulations show, as a consequence, that the nonlinearly modulated waves break at lower levels in the atmosphere than predicted by linear theory. These ideas have been introduced into an efficient parameterization of gravity wave drag in general circulation models thus giving better physical justification for the low tuning of breaking parameters currently being used in climate simulations.

Vijayantee Teeluck
Internal tide generation by Kelvin waves at the continental shelf
Analytical models of internal tide generation by large, steep topography are typically two-dimensional. However, coastal tides often take the form of Kelvin waves travelling alongshore, which have an inherently three-dimensional structure. We model the generation of internal tides by such waves, using a two-layer stratification, a simple step topography to represent the continental shelf break, and linear wave equations. We first calculate barotropic Kelvin wave solutions which, due to the presence of the step, have strong cross-shore flows at the shelf break. These barotropic waves are then used to force three-dimensional internal tides.

Sylvaine Turck-Chi�ze
Seismology of Sun and stars    
Acoustic and gravity modes are induced by surface convection or kappa mechanism (opacity fluctuations) and propagate in the stellar interior in a stationary way. They are now detected in Sun and centuries of stars. The stellar insight reveals dynamical processes that are not yet properly described in stellar evolution. After a rapid description of the theoretical context, I shall present the 30 years results obtained for the solar case, then I shall show the potentiality of asteroseismology, the open questions and the waiting answers.

Val�rie Van Grootel
Sounding the cores of stars by gravity-mode asteroseismology
Asteroseismology is a recent branch of astrophysics that studies the interiors of stars by the interpretation of their pulsation spectra. A wide variety of stars exhibit pulsations, including gravity-modes (driven by buoyancy) that usually penetrate deep inside the stars. By probing these deep layers unreachable from classical observations, the g-mode oscillations bring invaluable information for stellar evolution and astrophysics in general. I will illustrate in my talk the power of g-mode asteroseismology by the example of Extreme Horizontal Branch stars, that are on an intermediate stage of evolution, and show how g-modes allow us to determine the properties of the cores in these stars, including their convective characteristics, size and composition.

Julie Vanderhoff
Internal wave evolution through the atmosphere
Internal waves are generated continuously throughout the atmosphere. Estimating their evolution through steady and unsteady shear, changing buoyancy frequency, and other common atmospheric phenomenon is necessary to characterize their resultant affect on larger scale atmospheric flows. An effective way to track the propagation and refraction of internal waves is by applying the ray, or WKBJ, approximation and performing numerical ray-tracing. In regions of strong refraction, amplitudes may be captured using Airy function techniques, or a phase-space formulation. A review of these methods and how they apply to wave propagation through varying atmospheric profiles will be discussed.

Bruno Voisin
Green's function, added mass, and the conversion rate of barotropic energy into internal tides
The Green's function approach of internal tidal generation replaces forcing at the seafloor topography by a distribution of singularities, and the boundary condition at the topography by an integral equation for the distribution. Introducing the concept of added mass, we show how the conversion rate of barotropic energy into internal tides can be expressed solely in terms of the dipole strength of the distribution, without requiring the calculation of the internal tide itself. We consider afterwards the effect of viscosity on the conversion rate, and show that it is unlikely to be significant.

Geoff Wake
The Role of Internal Waves in Offshore Engineering Design.
Nonlinear internal waves are a ubiquitous feature of the global ocean, and as such, have the propensity to affect offshore oil and gas design, installation and operation. This talk focuses on the oil and gas industry off the Australian North West Shelf to illustrate the types of offshore operations that are routinely carried out and then discusses the potentially severe implications of nonlinear internal wave activity on offshore design, operation and installation.

Patrick Weidman
Near-Resonant Solitary Waves Travelling on Separate Pycnoclines
The problem of near-resonant solitary waves studied experimentally by Weidman\& Johnson (1981) is revisited using a modern numerical code to follow the long-time inviscid evolution of isolated mode-two disturbances on neighboring, but separate, pycnoclines. The dependence of solutions on the three fluid densities and the two interface thicknesses, for fixed initial conditions are studied in detail. For most parameter values, the initial disturbances separate immediately and evolve into solitary waves, each with a distinct speed. In a narrow region of parameter space, however, the waves pair up and oscillate for some time in leapfrog fashion with a nearly equal average speed. The motion is clearly not periodic, as each wave sheds energy to its respective dispersive tail, which causes the oscillation magnitude and period to increase until the waves eventually separate. We report the separation time, oscillation magnitude and period, and the final amplitudes and celerities of the separated waves as a function of the input parameters, and give evidence that no perfect periodic solutions occur. A simple asymptotic model is developed to aid in interpretation of the numerical results.

Paul Williams
Internal Waves Emitted from Balanced Flow: Observations, Properties, and Consequences
This presentation describes laboratory observations of internal inertia�gravity waves emitted from balanced fluid flow. In a rotating two-layer annulus experiment, the wavelength of the inertia�gravity waves is very close to the deformation radius. Their amplitude varies linearly with Rossby number in the range 0.05�0.14, at constant Burger number (or rotational Froude number). This linear scaling challenges the notion, suggested by several dynamical theories, that inertia�gravity waves generated by balanced motion will be exponentially small. It is estimated that the balanced flow leaks roughly 1% of its energy each rotation period into the inertia�gravity waves at the peak of their generation. The findings of this study imply an inevitable emission of inertia�gravity waves at Rossby numbers similar to those of the large-scale atmospheric and oceanic flow. Extrapolation of the results suggests that inertia�gravity waves might make a significant contribution to the energy budgets of the atmosphere and ocean. In particular, emission of inertia�gravity waves from mesoscale eddies may be an important source of energy for deep interior mixing in the ocean.

Vladimir Zeitlin
Wave resonances and instabilities of buoyancy-driven currents.
Instabilities of buoyancy-driven coastal currents are understood and quantified in terms of resonances of Frontal, Kelvin, Rossby and Poincare waves in the simplest 2-layer model of the outcropping front. Thus identified unstable modes are used to initialize high-resolution DNS with a new-generation well-balanced finite-volume numerical scheme, which allows to treat outcropping and loss of hyperbolicity associated to shear, Kelvin-Helmholtz type, instabilities. We show how nonlinear saturation of the instabilities leads to reorganization of the mean flow. The mean-flow then undergoes secondary large-scale instabilities leading to coherent vortex formation and cut-off.