Pseudo-advective relaxation to stable states of inviscid two-dimensional fluids

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Abstract
The continuous transformation of one flow into another of higher or lower energy while preserving the potential vorticity of all particles can be accomplished by advection with an artificial velocity field. Since isolated extremal energy states are stable states, this method can be used to find stable stationary flows on a prescribed isovortical sheet. A series of numerical simulations of this method for two-dimensional fluids that demonstrates its feasibility and utility is presented. Additionally, a corollary to Arnol'd's nonlinear stability theorems is discussed, which shows that there can be at most two Arnol'd stable states per isovortical sheet.