The Integral Invariants of Two-Dimensional Inviscid Flow and Their Role in the Theory of Two-Dimensional Turbulence

Abstract

It is shown that the invariance of the vorticity, kinetic energy and enstrophy integrals determines the form of the partial differential equation that governs the detailed evolution of two-dimensional nondivergent flows of homogeneous inviscid fluids, to within an arbitrary time scale. As a result, the invariance of integrals of other functions of vorticity is not independent of the invariance of the three basic integrals. An even more important consequence is that the nonlinear interactions between different scales of motion in two-dimensional isotropic turbulence are completely characterized by the invariance of the kinetic energy and enstrophy integrals in inviscid flow.