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 α, 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 α, 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 α as well. This latter effect is reminiscent of the drag-reduction that occurs in a turbulent flow when a dilute polymer is added. 1 The two-dimensional incompressible, Euler equations are ∂tω + ∇ · (uω) = 0, ∇ · u = 0, ω(t = 0) = ω0, (1