Evolution Equations for Long, Nonlinear Internal Waves in Stratified Shear Flows

Evolution equations for long, nonlinear internal waves are derived when the basic stratified shear flow has a slow temporal and spatial variation as well as the usual dependence on the vertical coordinate. When the horizontal waveguide has a limited vertical extent the evolution equation is a variable coefficient Korteweg‐deVries equation, while in the deep fluid case the evolution equation is a variable coefficient Benjamin‐Davis‐Ono equation. Explicit expressions are obtained for the coefficients of these equations.