Nonlinear entropy production operators for magnetohydrodynamic plasmas

Publisher Website
Google Scholar
Abstract
A method for constructing closure relations based on the invariants of the tensors representing nonequilibrium thermodynamic forcing within the plasma is presented. This approach leads to closure relations that describe all higher‐order forcing effects contained within the continuum description. Nonlinear convective‐momentum transport and nonlinear momentum‐exchange operators are constructed as applications of the method. Closure is achieved by relating the pressure tensor to invariants of the rate of strain tensor, and the momentum‐exchange operator to invariants of the gradient of magnetic fieldtensor. These operators lead to positive definite viscous and Joule entropy production and enhance high wave number dissipative couplings over all other dissipative couplings. The nonlinear dissipative action is localized in physical space, where velocity and magnetic gradients are large, while allowing nearly ideal behavior elsewhere. The operators are computationally tested against the standard magnetohydrodynamic(MHD) operators using three‐dimensional configurations that lead to vortex street formation and magnetic reconnection. The nonlinear operators allow greater spatial structure and have flatter modal energy spectra than the standard MHD dissipation operators. Closures that describe the plasma response to nonequilibrium thermodynamic forcing of all orders can be constructed using this approach.