Journal of Fluid Mechanics

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Reflecting tidal wave beams and local generation of solitary waves in the ocean thermocline

T. R. AKYLASa1, R. H. J. GRIMSHAWa2, S. R. CLARKEa3 and ALI TABAEIa1

a1 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

a2 Department of Mathematical Sciences, Loughborough University, Leics LE11 3TU, UK

a3 School of Mathematical Sciences, Monash University, Victoria 3800, Australia

Abstract

It is generally accepted that ocean internal solitary waves can arise from the interaction of the barotropic tide with the continental shelf, which generates an internal tide that in turn steepens and forms solitary waves as it propagates shorewards. Some field observations, however, reveal large-amplitude internal solitary waves in deep water, hundreds of kilometres away from the continental shelf, suggesting an alternative generation mechanism: tidal flow over steep topography forces a propagating beam of internal tidal wave energy which impacts the thermocline at a considerable distance from the forcing site and gives rise to internal solitary waves there. Motivated by this possibility, a simple nonlinear long-wave model is proposed for the interaction of a tidal wave beam with the thermocline and the ensuing local generation of solitary waves. The thermocline is modelled as a density jump across the interface of a shallow homogeneous fluid layer on top of a deep uniformly stratified fluid, and a finite-amplitude propagating internal wave beam of tidal frequency in the lower fluid is assumed to be incident and reflected at the interface. The induced weakly nonlinear long-wave disturbance on the interface is governed in the far field by an integral-differential equation which accounts for nonlinear and dispersive effects as well as energy loss owing to radiation into the lower fluid. Depending on the strength of the thermocline and the intensity of the incident beam, nonlinear wave steepening can overcome radiation damping so a series of solitary waves may arise in the thermocline. Sample numerical solutions of the governing evolution equation suggest that this mechanism is quite robust for typical oceanic conditions.

(Received December 01 2006)

(Revised August 23 2007)

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