Tensor geometry in the turbulent cascade
Stanford University
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. 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 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.
About the speaker
Dr. Nicholas Ouellette is a Professor of Civil and Environmental Engineering at Stanford University. He is broadly interested in the behavior of complex systems far from equilibrium, and in particular in the dynamical self-organization that is ubiquitous in such systems. Ouellette’s current research interests include turbulence; the transport of inertial, anisotropic, and active particles by fluid flows; the strength and failure of granular materials; and collective behavior in insect swarms, bird flocks, and other animal groups. Ouellette graduated from Swarthmore College in 2002 with majors in Physics and Computer Science, earned his Ph.D. in Physics from Cornell University in 2006, and did postdoctoral research at the Max Planck Institute for Dynamics and Self-Organization and in the Physics Department at Haverford College. Before coming to Stanford, he spent seven years on the faculty in Mechanical Engineering and Materials Science at Yale University. He is a Fellow of the American Physical Society, and has won teaching awards at both Stanford and Yale.
