A parametrization of two-dimensional turbulence based on a maximum entropy production principle with a local conservation of energy

摘要

In the context of two-dimensional (2D) turbulence, we apply the maximumentropy production principle (MEPP) by enforcing a local conservation ofenergy. This leads to an equation for the vorticity distribution that conservesall the Casimirs, the energy, and that increases monotonically the mixingentropy ($H$-theorem). Furthermore, the equation for the coarse-grainedvorticity dissipates monotonically all the generalized enstrophies. Theseequations may provide a parametrization of 2D turbulence. They do not generallyrelax towards the maximum entropy state. The vorticity current vanishes for anysteady state of the 2D Euler equation. Interestingly, the equation for thecoarse-grained vorticity obtained from the MEPP turns out to coincide, aftersome algebraic manipulations, with the one obtained with the anticipatedvorticity method. This shows a connection between these two approaches when theconservation of energy is treated locally. Furthermore, the newly derivedequation, which incorporates a diffusion term and a drift term, has a nicephysical interpretation in terms of a selective decay principle. This gives anew light to both the MEPP and the anticipated vorticity method.