On the Solution of Long's Equation with Shear

Long’s equation describes two dimensional stratified flow over terrain. Its numerical solutions under various approximations were investigated by many authors under the assumption that the base flow field is without shear. Special attention was paid to the properties of the gravity waves that are predicted to be generated as a result. In this paper we address, analytically, the nature and properties of these solutions when shear is present and derive some constraints on the possible generation of gravity waves under these circumstances.

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