Geometry and Ordering in the Turbulent Cascade
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September 7, 2017 - 1:00pm to 2:00pm
Nicholas Ouellette, Stanford University
Turbulent flows are inherently multi-scale. The mechanism that drives motion on many scales arises from the nonlinearity in the Navier-Stokes equations, which expresses the interaction of wavenumber triads that couple dynamics on different length scales. In turbulence, these triads self-organize to produce a net transfer of energy from the scales at which it is injected into the flow to the scales at which it is dissipated. Typically, we think about this transfer of energy in a Fourier description; but in doing so, we obscure its mechanistic origins and lose any connection to the spatial structure of the flow field.I will discuss an alternative way to study the spatiotemporally localized exchange of energy between scales that is based on a filtering technique. Using this methodology, I will describe our recent work in both two-dimensional and three-dimensional aimed at characterizing the characteristic geometric structure of the turbulent cascade, which is manifest in the relative alignment of the turbulent strain rate and a turbulent stress that is the manifestation of the nonlinearity in the Navier-Stokes equations. I will also discuss how this alignment varies in time and space, which gives us clues as to why turbulence behaves the way it does.