The effect of viscosity and heat conduction on internal gravity waves at a critical level

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Abstract
The differential equation for the vertical velocity of a gravity wave in an inviscid shear flow is singular at a level where the mean fluid velocity is equal to the horizontal phase velocity of the waves. It has been shown that a wave travelling through such a layer has its amplitude attenuated by a constant factor dependent on the local Richardson number. In this paper the results obtained by solving numerically the full sixth order differential equation, which is derived by including viscosity and heat conduction in the problem, (and is not singular) are discussed, and the same attenuation factor is found. Some experiments which confirm certain aspects of the theory are described in an appendix.

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