= Unstable band of a three-layer stratified shear flow
{title2=$2\alpha/(1+e^{-2\alpha})<1+J<2\alpha/(1-e^{-2\alpha})$}
For the <three-layer stratified piecewise-linear shear flow>, set $\alpha=kh/2$. The <dispersion relation> is quadratic in squared nondimensional <phase velocity>. Its constant term is $[2\alpha-(1+J)(1+e^{-2\alpha})][2\alpha-(1+J)(1-e^{-2\alpha})]/(4\alpha^2)$. Throughout the displayed band this is negative, so one squared speed is negative and gives an exponentially growing <normal mode>.
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