= Two-dimensional viscous shearing wave
{title2=$\dot Z=-\nu k^2Z$}
For $k_z=v_z=0$ and $k_y\ne0$, define $Z=i(k_xv_y-k_yv_x)$. Uniform rotation does not enter its evolution: $\dot Z=-\nu k^2Z$, $v_x=ik_yZ/k^2$ and $v_y=-ik_xZ/k^2$. With $T=k_x/k_y$ and $\mathrm{Re}=A/(\nu k_y^2)$, the perturbation <energy> ratio is $E(T)/E(T_0)=[(1+T_0^2)/(1+T^2)]\exp[-(T+T^3/3-T_0-T_0^3/3)/\mathrm{Re}]$. Leading waves can gain <energy> as shear reduces their <wavevector> magnitude, before <viscosity> and subsequent winding damp them.
// Target: hydrodynamic-stability.bigb
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