The structure of turbulence in the presence of a mean-flow is a fundamental question that remains poorly understood. Even in the most basic setting of a pressure driven pipe flow, a first-principles description is lacking. The main problem is that at high Reynolds numbers, the interactions between the mean-flow and turbulence are strong, and closed equations describing each component separately cannot be obtained. Over the past few years, it has been understood that significant progress could be achieved by studying 2D flows, which behave quite differently from 3D flows: in 2D, turbulence can spontaneously generate a mean-flow, rather than feeding on it.
With Anna Frishman (Princeton University), we have just published a preprint which presents a step in this direction, for a 2D vortex condensate where the mean-flow is born out of turbulence. Combining a first-principles theoretical framework and state-of-the-art numerical simulations, we provide an explicit formula for the turbulent kinetic energy and direct evidence for the structure of the momentum flux. We explain that two fundamentally different mechanisms determine these two objects: the momentum flux is fixed by a balance between forcing and mean-flow advection, while the turbulent energy is determined only by mean-flow advection.
Turbulence statistics in a 2D vortex condensate
Anna Frishman, Corentin Herbert