Some Characteristics of Exact Strained Solutions to the Two Dimensional Navier-Stokes Equations

Abstract

Exact strained solutions to the two dimensional Navier-Stokes equations are obtained which have two dimensional spatial periodic structures. The time developments of the circulation, the energy, the enstrophy and the palinstrophy are examined for several viscosities. In the inviscid limit, the enstrophy dissipation rate becomes independent of viscosity. The power spectrum of the energy behaves as k⁻³ in the inertial subrange for constant strain and different power laws are obtained depending on the time dependence of the strain.