Exact relation between spatial mean enstrophy and dissipation in confined incompressible flows

TL;DR: In this article, an exact relation between spatial mean enstrophy and dissipation in closed incompressible flows is derived analytically, which also applies to unbounded fluid domains when the velocity decays to zero sufficiently rapidly at infinity.

Abstract: An exact non‐trivial relation between spatial mean enstrophy and dissipation in closed incompressible flows is derived analytically, which also applies to unbounded fluid domains when the velocity decays to zero sufficiently rapidly at infinity. The quantity 〈ω2−σ2〉 is shown to depend only on the boundary conditions, and it is pointed out that in many confined flows, the equality 〈ω2〉=〈σ2〉 is not satisfied.