TransTurb

European Union H2020 Project - Marie Sklodowska-Curie Actions

LARGE DEVIATIONS AND RARE TRANSITIONS IN TURBULENT FLOWS

Turbulent flows, like planetary atmospheres, oceans, or flow around an airfoil or a wind turbine, undergo strong fluctuations. Sometimes, the system may even undergo abrupt transitions between entirely different flow configurations. Such transitions seem to occur at random times, in an unpredictable manner.

These extreme events are crucial for weather, climate, and many engineering applications. One may think for instance about the occurrence of heat waves or cold spells in the mid-latitudes, related to fluctuations of the strong turbulent jet going around the planet, the Jet Stream, which have a large impact on society and global economy. Similarly the most important factor for designing devices like wind turbines is not the average mechanical forces they will be subjected to, but rather the strongest ones. Finally, the existence of tipping points within the climate system, leading to abrupt climate change, is a major question for climate projections in the 21st century. Because turbulent flows have in general several metastable attractors, it can be expected that such abrupt transitions exist in the ocean and atmosphere, due solely to their turbulent nature.

There are two overarching difficulties in studying these problems: one is essentially technical, the other more fundamental.

The first deadlock is that we are interested in rare events, for which, by definition, we have few observations. Direct numerical simulations of the system do not really alleviate the problem, because models for turbulent flows or the climate system are computationally expensive. To solve this sampling problem, numerical algorithms have been developed over the past few years to simulate rare events efficiently. The first main goal of the project is to show that these algorithms can be adapted to address relevant questions for rare events in turbulent flows.

The second major aspect of the problem is to understand which properties of such rare events are predictable, and which properties are not. For noise-induced transitions, for instance, transition times are unpredictable, but the dynamics of the transition is in general predictable: the system always follows the same path to produce the rare event. The second main goal of the project is to test whether such ideas, inspired from statistical physics, and more specifically, large deviation theory, hold for complex systems such as turbulent flows and climate models. To start with, we intend to establish on a solid basis if noise-induced transitions between bistable states exist at all in the atmosphere.

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