From UW-Math Wiki
Jump to navigation Jump to search

ACMS Abstracts: Fall 2020

Nick Ouellette (Stanford)

Title: Tensor Geometry in the Turbulent Cascade

Abstract: Perhaps the defining characteristic of turbulent flows is the directed flux of energy from the scales at which it is injected into the flow to the scales at which it is dissipated. Often, we think about this transfer of energy in a Fourier sense; but in doing so, we obscure its mechanistic origins and lose any connection to the spatial structure of the flow field. Alternatively, quite a bit of work has been done to try to tie the cascade process to flow structures; but such approaches lead to results that seem to be at odds with observations. Here, I will discuss what we can learn from a different way of thinking about the cascade, this time as a purely mechanical process where some scales do work on others and thereby transfer energy. This interpretation highlights the fundamental importance of the geometric alignment between the turbulent stress tensor and the scale-local rate of strain tensor, since if they are misaligned with each other, no work can be done and no energy will be transferred. We find that (perhaps surprisingly) these two tensors are in general quite poorly aligned, making the cascade a highly inefficient process. Our analysis indicates that although some aspects of this tensor alignment are dynamical, the quadratic nature of Navier-Stokes nonlinearity and the embedding dimension provide significant constraints, with potential implications for turbulence modeling.

Harry Lee (UW Madison)

Title: Recent extension of V.I. Arnold's and J.L. Synge's mathematical theory of shear flows