The flow about an obstacle in horizontal motion relative to a stratified Boussinesq fluid in a deep, rapidly rotating container is studied. Numerical and asymptotic analyses of the linearized boundary-value problems for a shallow topography are made to delineate the influence of stratification and ground topography on wave and flow structure, and to ascertain the presence of a solitary anticyclonic, or cyclonic, disturbance in the far field at high as well as low stratification. Although the analyses are restricted to the rapidly rotating case corresponding to a vanishingly small Rossby number, it is pointed out that the cyclonic feature remains a valid inviscid description in the far field except for an infinite Rossby number corresponding to no rotation.

A study is made of the wave disturbance generated by a localized steady pressure distribution travelling at a speed close to the long-water-wave phase speed on water of finite depth. The linearized equations of motion are first used to obtain the large-time asymptotic behaviour of the disturbance in the far field; the linear response consists of long waves with temporally growing amplitude, so that the linear approximation eventually breaks down owing to finite-amplitude effects. A nonlinear theory is developed which shows that the generated waves are actually of bounded amplitude, and are governed by a forced Korteweg-de Vries equation subject to appropriate asymptotic initial conditions. A numerical study of the forced Korteweg-de Vries equation reveals that a series of solitons are generated in front of the pressure distribution.