Simulations and observation of nonlinear internal waves on the continental shelf: Korteweg–de Vries and extended Korteweg–de Vries solutions

Abstract

Abstract. Numerical solutions of the Kortewegde Vries (KdV) and extended Korteweg-de Vries (eKdV) equations are used to model the transformation of a sinusoidal internal tide as it propagates across the continental shelf. The ocean is idealized as being a two-layer fluid, justified by the fact that most of the oceanic internal wave signal is contained in the gravest mode. The model accounts for nonlinear and dispersive effects but neglects friction, rotation and mean shear. The KdV model is run for a number of idealized stratifications and unique realistic topographies to study the role of the nonlinear and dispersive effects. In all model solutions the internal tide steepens forming a sharp front from which a packet of nonlinear solitary-like waves evolve. Comparisons between KdV and eKdV solutions are made. The model results for realistic topography and stratification are compared with observations made at moorings off Massachusetts in the Middle Atlantic Bight. Some features of the observations compare well with the model. The leading face of the internal tide steepens to form a shock-like front, while nonlinear high-frequency waves evolve shortly after the appearance of the jump. Although not rank ordered, the wave of maximum amplitude is always close to the jump. Some features of the observations are not found in the model. Nonlinear waves can be very widely spaced and persist over a tidal period.

Formation of Square-Shaped Waves in the Biscay Bay*

“…Consequently, we set the corresponding initial state and use an integral factor scheme for simulation. [28,29] The evolution results conform to the figures of the observation on squareshaped waves.…”