Skip to main content
×
Home
    • Aa
    • Aa

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

  • T. R. AKYLAS (a1), R. H. J. GRIMSHAW (a2), S. R. CLARKE (a3) and ALI TABAEI (a1)
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.

Copyright
References
Hide All
Azevedo A., da Silva, J. C. B. & New A. L. 2006 On the generation and propagation of internal solitary waves in the southern Bay of Biscay. Deep-Sea Res. 53, 927941.
Bell T. H. 1975 Lee waves in stratified flows with simple harmonic time dependence. J. Fluid Mech. 67, 705722.
Delisi D. P. & Orlanski I. 1975 On the role of density jumps in the reflexion and breaking of internal gravity waves. J. Fluid Mech. 69, 445464.
Gerkema T. 2001 Internal and interfacial tides: beam scattering and local generation of solitary waves. J. Mar. Res. 59, 227255.
Grimshaw R. 2001 Internal solitary waves. In Environmental Stratified Flows (ed. Grimshaw R.). Kluwer.
Grimshaw R. H. J., Ostrovsky L. A., Shrira V. I. & Stepanyants Yu. A. 1998 Long nonlinear surface and internal gravity waves in a rotating ocean. Nonlinear Processes Geophys. 19, 289338.
Helfrich K. R. & Melville W. K. 2006 Long nonlinear internal waves. Annu. Rev. Fluid Mech. 38, 395425.
Khatiwala S. 2003 Generation of internal tides in an ocean of finite depth: analytical and numerical calculations. Deep-Sea Res. 50, 321.
Lamb K. G. 2004 Nonlinear interaction among internal wave beams generated by tidal flow over supercritical topography. Geophys. Res. Lett. 31, doi: 10.1029/2003GL019393.
Maslowe S. A. & Redekopp L. G. 1980 Long nonlinear waves in stratified shear flows. J. Fluid Mech. 101, 321348.
New A. L. & Pingree R. D. 1990 Large-amplitude internal soliton packets in the central Bay of Biscay. Deep-Sea Res. 37, 513524.
New A. L. & Pingree R. D. 1992 Local generation of internal soliton packets in the central Bay of Biscay. Deep-Sea Res. 39, 15211534.
New A. L. & da Silva, J. C. B. 2002 Remote-sensing evidence for the local generation of internal soliton packets in the central Bay of Biscay. Deep-Sea Res. 49, 915934.
Pingree R. D. & New A. L. 1989 Downward propagation of internal tidal energy into the Bay of Biscay. Deep-Sea Res. 36, 735758.
Pingree R. D. & New A. L. 1991 Abyssal penetration and bottom reflection of internal tidal energy in the Bay of Biscay. J. Phys. Oceanogr. 21, 2839.
Romanova N. N. 1981 Generalization of the Benjamin–Ono equation for a weakly stratified atmosphere. Izv. Atmos. Oceanic Phys. 17, 98101.
Thorpe S. A. 1998 Nonlinear reflection of internal waves at a density discontinuity at the base of the mixed layer. J. Phys. Oceanogr. 28, 18531860.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 47 *
Loading metrics...

Abstract views

Total abstract views: 123 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th October 2017. This data will be updated every 24 hours.