VALIDATION OF A DOUBLE-LAYER BOUSSINESQ-TYPE MODEL FOR HIGHLY NONLINEAR AND DISPERSIVE WAVES

Abstract

A two-layer Boussinesq-type mathematical model has been recently introduced by the authors with the goal of modeling highly nonlinear and dispersive waves (Chazel et al. 2009). The analysis of this model has previously shown that it possesses excellent linear properties, up to kh = 10 at least, for dispersion, shoaling coefficient and vertical profile of orbital velocities. In the present work a numerical one-dimensional (1DH) version of model is developed based on a finite difference technique for meshing the spatial domain. It is then applied and verified against a set of three one-dimensional (1DH) test-cases for which either numerical or experimental reference results are available: i. nonlinear and dispersive regular waves of permanent form; ii. propagation of regular waves on a trapezoidal bar (laboratory experiments by Dingemans (1994)); iii. shoaling and propagation of irregular waves on a barred beach profile (laboratory experiments by Becq-Girard et al. (1999)). The test-cases considered in this study confirm the very good capabilities of the model to reproduce either exact solutions, high-precision numerical simulations and experimental measurements in a variety of non-breaking wave conditions and types of bottom profiles. Nonlinearity, dispersion and bathymetric effects are well accounted for by the model, which appears to possess a rather wide domain of validity while maintaining a reasonable level of complexity.