Abstract
A numerical study of the internal gravity waves excited by an obstacle in the flow of a linearly stratified Boussinesq fluid is described. Solutions of the Navier–Stokes equations agree quantitatively well with the solutions of Grimshaw and Yi’s equation [J. Fluid Mech. 229, 603 (1991)] near resonance. The equation of Grimshaw and Yi can describe well the upstream waves even when the Froude number F is fairly small (F=0.5). Therefore it is a good model of the nonlinear internal waves excited in a linearly stratified Boussinesq fluid. When the wave amplitude is large, the first disappearance of the horizontal velocity is also well predicted by the solution of the equation of Grimshaw and Yi, although the equation cannot predict the subsequent time development.