Stability Results for Idealised Shear Flows on a Rectangular Periodic Domain

Holger Dullin, Joachim Worthington

We present a new linearly stable solution of the Euler fluid flow on a torus. On a two-dimensional rectangular periodic domain $[0,2\pi )\times [0,2\pi /\kappa )$ for $\kappa \in {\mathbb{R}}^{+}$, the E…