Adjustment of vorticity fields with specified values of Casimir invariants as initial condition for simulated annealing of an incompressible, ideal neutral fluid and its MHD in two dimensions

A method is developed to adjust a vorticity field to satisfy specified values for a finite number of Casimir invariants. The developed method is tested numerically for a neutral fluid in two dimensions. The adjusted vorticity field is adopted as an initial condition for simulated annealing (SA) of an incompressible, ideal neutral fluid and its magnetohydrodynamics (MHD), where SA enables us to obtain a stationary state of the fluid. Since the Casimir invariants are kept unchanged during the annealing process, the obtained stationary state has the required values of the Casimir invariants specified by our method.