Enhanced inverse-cascade of energy in the averaged Euler equations
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 , 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 , 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 as well. This latter effect is reminiscent of the drag-reduction that occurs in a turbulent flow when a dilute polymer is added.
Keywords
Cite
@article{arxiv.math/0005035,
title = {Enhanced inverse-cascade of energy in the averaged Euler equations},
author = {Balu T. Nadiga and Steve Shkoller},
journal= {arXiv preprint arXiv:math/0005035},
year = {2025}
}