Enhancement of the inverse-cascade of energy in the two-dimensional Lagrangian-averaged navier-stokes equations

Journal article

The recently derived Lagrangian-averaged Navier-Stokes equations model the large-scale flow of the Navier-Stokes fluid at spatial scales larger than some a priori fixed α>0, while coarse-graining the behavior of the small scales. In this communication, we numerically study the behavior of the two-dimensional (2D) isotropic version of this model, also known as the α model. The inviscid dynamics of this model exactly coincide with the vortex blob algorithm for a certain choice of smoothing kernel, as well as the equations of an inviscid second-grade non-Newtonian fluid. While previous studies of this system in 3D 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 2D turbulence and thereby affects scales of motion larger than α as 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 polymer is added, and (c) can be qualitatively understood in terms of known dimensional arguments. © 2001 American Institute of Physics.

Authors: Nadiga, B; Shkoller, S

• Journal: Physics of Fluids
• Volume: 13
• Issue: 5
• Pages: 1528-1531
• Publication date: 2001-05-01
• DOI: 10.1063/1.1359764
• ISSN: 1070-6631
• Language: English