= Equality of top-hat jet parity growth rates
{title2=$\gamma=\tfrac12|kV|\sqrt{1-e^{-4|k|L}}$}
For a <top-hat planar jet> in stationary fluid of the same <mass density>, odd and even <velocity potentials> have the same <temporal growth rate>. Put $s=\tanh(|k|L)$. Their <dispersion relations> use $s$ and $1/s$, but $\sqrt{s}/(1+s)=\sqrt{1/s}/(1+1/s)$. Their real <phase velocities> are respectively $Vs/(1+s)$ and $V/(1+s)$. The common <growth rate> is strictly below $|kV|/2$ for finite $|k|L>0$, approaching the isolated <vortex sheet> value when the sheets decouple.
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