Vortex Structure, Inverse Cascades, and Turbulent Bursts in Rotating, Stratified Flows

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Three-dimensional simulations of fluid turbulence in rotating and stratified flows will be carried out using spectral methods using new efficient basis functions. The calculations will increase our understanding and ability to model and calculate turbulence in anisotropy and inhomogeneous settings that are commonly found in geophysical and astrophysical flows and is many engineering applications. Rotation and stratification tend to make the fluid act nearly 2-dimensional (2D) at some locations, at some length scales, and/or for some intervals of time. It is commonly thought that when and where the flows behave as if they were fully 3D, energy is transferred ("forward cascades") from large to small scales, and small-scale turbulence acts primarily as a passive "sponge" dissipating energy. When and where the flows behave as if it were 2D, energy inverse cascades from small to large scales. In these cases the small-scale turbulence is much more complex and difficult to model, and its effects on the large-scales are more profound. A mathematical model of the inverse cascade will be developed and scaling laws for the strengths and widths of planetary jet streams will be developed and compared against simulations, experiments and observations. Asymptotics, and mathematical models for the turbulence will permit construction of new sub-grid-scale turbulence models to be used in large-eddy numerical simulations. The simulations will be compared to laboratory experiments and observations and observations of geophysical and astrophysical flows.The specific features of this investigation place it outside of the norm for most studies of turbulent/vortical motions. It is expected that the distinct results to be obtained will not only serve to illuminate the "2-D" turbulence problem but also the more general turbulent flow processes by noting the similarities/differences between the two.