New Internal-Wave Model in a Two-Layer Fluid

Abstract

To model internal waves, high-level Green-Naghdi (GN) equations that are strongly nonlinear were developed for a two-layer fluid with a rigid lid over the upper layer. The GN models were applied to two internal-solitary-wave cases: weakly dispersive and strongly dispersive. In the weakly dispersive case, the ratio between the upper and lower layers was 1:4.13. In the strongly dispersive case, the two depth ratios between the upper and lower layers were 1:24 and 10.13:1. For both the weakly and strongly dispersive test cases, the converged GN results for wave speed, wave profile, and velocity distribution agreed well with the experimental data and the solution of Euler equations, even for large-amplitude solitary waves. For the strongly nonlinear and strongly dispersive cases, the converged GN results showed better accuracy than some other strongly nonlinear models.