Evolution equations for long nonlinear internal waves in a compressible fluid are derived, with the aim of comparing these equations with their counterparts in an incompressible fluid. Both the Korteweg-de Vries equation, and the deep fluid equation are discussed, for both dry and moist atmospheres. It is shown that the effects of compressibility, or non-Boussinesq terms, are generally small, but measurable, and are manifested mainly in the nonlinear term of the evolution equation. For the case of a moist atmosphere the effect of a gain in energy by latent heat release is compared with the energy lost by radiation damping.
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Grimshaw, R. Solitary waves in a compressible fluid. PAGEOPH 119, 780–797 (1980). https://doi.org/10.1007/BF01131255
- Internal waves in compressible fluid/incompressible fluid
- Internal solitary waves