Self-organization and transitions in anisotropic turbulence: from geophysical to bacterial scales

点击翻译按钮获取中文摘要

Large-scale structures, such as vortices and jets are typically observed in geo- and astrophysical flows. Hurricanes and the Jet Stream are well known examples from Earth's atmosphere, but similar states are also observed on the gas giants and in stars, such as the Sun. Such flows are almost always highly turbulent, and display a wide range of dynamically active temporal and spatial scales. In addition, they are typically highly anisotropic, being subject to rapid planetary rotation, strong stratification, magnetic fields, or thin-layer geometries. On much smaller length scales, biological systems such as suspensions of bacteria, sperm cells, or other microswimmers, create similar flow patterns consisting of vortices, jets and strongly ordered states such as vortex lattices. These systems belong to the category of active matter, since individual swimmers consume energy to create fluid flow. Hence they are far from statistical equilibrium. Specifically, one speaks of active turbulence, although it is important to stress that these flows are not turbulent in the classical sense, being characterised by small to moderate Reynolds numbers. The similarity between the observed phenomena on very disparate length scales is formally reflected by the fact that the continuum descriptipn of both systems leads to similar equations. Geo- and astrophysical turbulence is typically born from instabilities, which explicitly depend on the evolving flow state. In active fluids, there are active stresses, in addition to viscious ones, which also depend explicitly (linearly) on the flow field. In this project, we study the self-organization of complex flows, at planetary, but also microscopic scales. First, we consider an idealized model of strongly anisotropic turbulence driven by instabilities. We consider two-dimensional flows, as well as thin three-dimensional fluid layers, where flow is created by a velocity-dependent body force. The goal is to extend existing results on the two-dimensional case, and to test their robustness with respect to three-dimensional perturbations. The second topic of this project is the Reynolds number dependence of this system. We vary the Reynolds number from small to large values, thus bridging the gap between the microscopic, active realization of the model, and the high-Reynolds number flow that applies to the geo- and astrophysical limit. Finally, we will also study specifically the application of these idealized results to rapidly rotating Rayleigh-Bénard convection, using novel numerically tools to study the emergence of large-scale structures, i.e. vortices and jets in this system. We also extend these investigations to the case of internal buoyancy sources due to moisture and phase changes, utilizing the recently introduced "Rainy-Bénard" model. This project will make a significant contribution to our fundamental understanding of self-organization across physical scales.