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Enhanced inverse-cascade of energy in the averaged Euler equations

Balu T. Nadiga·Steve Shkoller
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Abstract

For a particular choice of the smoothing kernel, it is shown that the system of partial differential equations governing the vortex-blob method corresponds to the averaged Euler equations. These latter equations have recently been derived by averaging the Euler equations over Lagrangian fluctuations of length scale $\a$, and the same system is also encountered in the description of inviscid and incompressible flow of second-grade polymeric (non-Newtonian) fluids. While previous studies of this system have noted the suppression of nonlinear interaction between modes smaller than $\a$, we show that the modification of the nonlinear advection term also acts to enhance the inverse-cascade of energy in two-dimensional turbulence and thereby affects scales of motion larger than $\a$ as well. This latter effect is reminiscent of the drag-reduction that occurs in a turbulent flow when a dilute polymer is added.

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Balu T. Nadiga, Steve Shkoller. 2000-05-03. Enhanced inverse-cascade of energy in the averaged Euler equations. https://arxiv.org/abs/math/0005035

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