Statistical Stability in Fluid Shear Flows

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Understanding which flow solutions a fluid adopts in particular conditions (e.g. boundary conditions and imposed forcing) is a fundamental challenge in fluid mechanics.While stability theory based on the Navier-Stokes equations has got us so far, it has not helped with understanding the properties of more temporally-complicated states. For example, turbulence can be made to relaminarise under certain conditions and coherent flow motions can emerge from the apparent incoherence of turbulence. This project will explore the new concept of statistical stability which is based upon equations which evolve the statistical properties of the flow instead. The hope is this should provide a new way to understand the dynamics of turbulence.