Finite‐amplitude wave propagation is considered in flows of boundary‐layer type when the wavelength is long compared to the boundary layer thickness. In this limit, the evolution of the amplitude is governed by the Benjamin‐Ono equation and we have computed the coefficients of its nonlinear and dispersive terms for the specific case of Tietjens's model. The propagation of wave packets is also considered, and it is found that for packets centered about anO(1) wavenumber questions again arise relative to long waves, except that now the packet‐induced mean flow is the “long wave.” By introducing an appropriate scaling for the far field and employing multiple scales in the direction transverse to the flow, it is shown how the mean‐flow distortion can be made to vanis
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