= Viscous attenuation of an internal gravity wave
{title2=$|\widehat\sigma(z)|\propto e^{-\nu K^2z/(2c_{gz})}$}
With weak <kinematic viscosity> $\nu$, zero buoyancy diffusion and locally unchanged <plane internal gravity wave> polarization, the <displacement pseudomomentum of an internal gravity wave> obeys $P_t+\partial_z(c_{gz}P)=-\nu K^2P$. For constant <wavenumbers> and a stationary wave envelope, $P\propto|\widehat\sigma|^2$ proves the displayed amplitude decay. Decay is along the <group velocity>, so $c_{gz}<0$ describes a source above the receiving level. In a slowly varying <shear flow>, use <wave action> and the changing <intrinsic frequency> rather than treating $P/|\widehat\sigma|^2$ as constant.
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