An experimental and numerical study of nonlinear internal waves

Abstract

Nonlinear internal waves were measured on the large rotating platform at the Institut de Mécanique de Grenoble (I.M.G.). The experimental data complement the results presented in Renouard et al. [J. Fluid Mech. 177, 381 (1987)] and support the assumption that the solitary Kelvin wave is accompanied by Poincaré waves. Based on the assumption of weak nonlinear, dispersive, and rotational effects, governing equations of the Boussinesq type are derived to model the evolution of an initial disturbance in a two-layer rotating fluid. The numerical study is based on these equations which are analogous to the Boussinesq equations of shallow-water theory and are not constrained to almost unidirectional propagation. Comparison of numerical solutions of the equations and experimental results are very good for moderately nonlinear conditions. These results provide supporting evidence for the resonant interaction of nonlinear Kelvin waves and linear Poincaré waves, as described by Melville et al. [J. Fluid Mech. 206, 1 (1989)].