  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 Euler equations admit a family of
stationary solutions given by the vorticity profiles $\Omega^*(\mathbf{x})=
\Gamma \cos(p_1x_1+ \kappa p_2x_2)$. We show linear stability for such flows
when $p_2=0$ and $\kappa \geq |p_1|$ (equivalently $p_1=0$ and
$\kappa{|p_2|}\leq{1}$). The classical result due to Arnold is that for $p_1 =
1, p_2 = 0$ and $\kappa \ge 1$ the stationary flow is {nonlinearly} stable via
the energy-Casimir method. We show that for $\kappa \ge |p_1| \ge 2, p_2 = 0$
the flow is linearly stable, but one cannot expect a similar nonlinear
stability result. Finally we prove nonlinear instability for all equilibria
satisfying $p_1^2+\kappa^2{p_2^2}>\frac{{3(\kappa^2+1)}}{4(7-4\sqrt{3})}$. The
modification and application of a structure-preserving Hamiltonian truncation
is discussed for the $\kappa\neq 1$ case. This leads to an explicit Lie-Poisson
integrator for the truncated system.
