Three-dimensional instability of elliptical flow

A theory is presented for Pierrehumbert's three-dimensional short-wave inviscid instability of the simple two-dimensional elliptical flow with velocity field u(x,y,z)=(-Ey,E-1x,0). The fundamental modes, which are also exact solutions of the nonlinear equations, are plane waves whose wave vector rotates elliptically around the z axis with period 2. The growth rates are the exponents of a matrix Floquet problem, and agree with those calculated by Pierrehumbert.