= Excess dissipation of a Burgers vortex
{title2=$\mathcal D=\alpha\Gamma^2/(8\pi)$}
The swirl <viscous dissipation> of a steady <Burgers vortex>, integrated per unit <length> and per unit density, is $\nu\int\omega_z^2\,dA=\alpha\Gamma^2/(8\pi)$. It remains finite as <kinematic viscosity> tends to zero at fixed <strain> and <circulation>. This is excess over the background <strain>: the uniform <strain> itself has infinite total <viscous dissipation> over an infinite cross-section.
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