Numerical Experiments on the Breaking of Solitary Internal Wavesover a Slope–Shelf Topography

Abstract

A theoretical study of the transformation of large amplitude internal solitary waves (ISW) of permanent form over a slope–shelf topography is considered using as basis the Reynolds equations. The vertical fluid stratification, amplitudes of the propagating ISWs, and the bottom parameters were taken close to those observed in the Andaman and Sulu Seas. The problem was solved numerically. It was found that, when an intense ISW of depression propagates from a deep part of a basin onto the shelf with water depth Hs, a breaking event will arise whenever the wave amplitude am is larger than 0.4(Hs − Hm), where Hm is the undisturbed depth of the isopycnal of maximum depression. The cumulative effect of nonlinearity in a propagating ISW leads to a steepening and overturning of a rear wave face over the inclined bottom. Immediately before breaking the horizontal orbital velocity at the site of instability exceeds the phase speed of the ISW. So, the strong breaking is caused by a kinematic instability of the propagating wave. At the latest stages of the evolution the overturned hydraulic jump transforms into a horizontal density intrusion (turbulent pulsating wall jet) propagating onto the shelf. The breaking criterion of the ISW over the slope was found. Over the range of examined parameters (0.52° < γ < 21.8°, where γ is the slope angle) the breaking event arises at the position with depth Hb, when the nondimensional wave amplitude a = am/(Hb − Hm) satisfies the condition a ≅ 0.8°/γ + 0.4. If the water depth Hs on a shelf is less than Hb, a solitary wave breaks down before it penetrates into a shallow water zone; otherwise (at Hs > Hb) it passes as a dispersive wave tail onto the shelf without breaking.