Enhancement of the inverse-cascade of energy in the two-dimensional Lagrangian-averaged Navier-Stokes equations

The recently derived Lagrangian-averaged Navier-Stokes equations model the large-scale flow of the Navier-Stokes fluid at spatial scales larger than s ome a priori fixed alpha >0, while coarse-graining the behavior of the smal l scales. In this communication, we numerically study the behavior of the t wo-dimensional (2D) isotropic version of this model, also known as the alph a model. The inviscid dynamics of this model exactly coincide with the vort ex blob algorithm for a certain choice of smoothing kernel, as well as the equations of an inviscid second-grade non-Newtonian fluid. While previous s tudies of this system in 3D have noted the suppression of nonlinear interac tion between modes smaller than alpha, we show that the modification of the nonlinear advection term also acts to enhance the inverse-cascade of energ y in 2D turbulence and thereby affects scales of motion larger than alpha a s well. This, we note, (a) may preclude a straightforward use of the model as a subgrid model in coarsely resolved 2D computations, (b) is reminiscent of the drag-reduction that occurs in a turbulent flow when a dilute polyme r is added, and (c) can be qualitatively understood in terms of known dimen sional arguments. (C) 2001 American Institute of Physics.