2D magnetofluid models constructed by a priori imposition of conservation laws

TL;DR

This paper develops a geometric approach to construct 2D magnetofluid models by enforcing conservation laws, leading to new models that preserve key quantities and can serve as conservative regularizations of RMHD.

Contribution

It introduces a method to derive magnetofluid models from conservation laws, resulting in a family of models including regularizations that maintain key invariants.

Findings

Constructed a more general 2D magnetofluid model conserving the same quantities as RMHD.

Derived noncanonical Hamiltonian and Nambu descriptions for these models.

Identified models that can regularize RMHD by bounding enstrophy without viscosity.

Abstract

Motivated by a geometric method employed for the derivation of the Nambu bracket for ideal two-dimensional incompressible hydrodynamics, we reconstruct the reduced magnetohydrodynamic (RMHD) model by a priori imposition of its conservation laws. It turns out that there exists a more general model that conserves the same quantities with RMHD. The noncanonical Hamiltonian and Nambu description of this generic system are derived and in addition a canonical description is formed by Clebsch-parameterizing the vorticity and the magnetic flux function. The method for the construction of the dynamical equations is based on the imposition of the conservation laws as orthogonality conditions. Furthermore, this approach enabled us to construct three families of models that respect any combination of two out of the three conservation laws. Some of these models can serve as conservative regularizations of RMHD since under certain conditions they keep the enstrophy bounded without the need of introducing viscosity and may be candidates for incorporating small length scale physics into the RMHD framework.