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Effects of rotation on self-resonant internal gravity waves in the ocean
Responsible organisation
2010 (English)In: Ocean Modelling, ISSN 1463-5003, E-ISSN 1463-5011, Vol. 31, no 3-4Article in journal (Refereed) Published
Abstract [en]

The Resonant Triad Model (RTM) developed in (Ibragimov, 2007), is used to study the Thorpe’s problem (Thorpe, 1997) on the existence of self-resonant internal waves, i.e., the waves for which a resonant interaction occurs at second order between the incident and reflected internal waves off slopes. The RTM represents the extension of the McComas and Bretherton’s three wave hydrostatic model (McComas and Bretherton, 1977) which ignores the effects of the earth’s rotation to the case of the non-hydrostatic analytical model involving arbitrarily large number of rotating internal waves with frequencies spanning the range of possible frequencies, i.e., between the maximum of the buoyancy frequency (vertical motion) and a minimum of the inertial frequency (horizontal motion). The present analysis is based on classification of resonant interactions into the sum, middle and difference interaction classes. It is shown in this paper that there exists a certain value of latitude, which is classified as the singular latitude, at which the coalescence of the middle and difference interaction classes occurs. Such coalescence, which apparently had passed unnoticed before, can be used to study the Thorpe’s problem on the existence of selfresonant waves. In particular, it is shown that the value of the bottom slope at which the second-order frequency and wave number components of the incident and reflected waves satisfy the internal wave dispersion relation can be approximated by two latitude-dependent parameters in the limiting case when latitude approaches its singular value. Since the existence of a such singular latitude is generic for resonant triad interactions, a question on application of the RTM to the modeling of enhanced mixing in the vicinity of ridges in the ocean arises.

Place, publisher, year, edition, pages
Elsevier , 2010. Vol. 31, no 3-4
Keyword [en]
Self-resonant interval waves, Boussinesq approximation, Effects of rotation
National Category
Mathematics Mathematical Analysis
Identifiers
URN: urn:nbn:se:bth-7532DOI: 10.1016/j.ocemod.2009.10.003Local ID: oai:bth.se:forskinfo4DF7E33586739890C12578B70034D24EOAI: oai:DiVA.org:bth-7532DiVA: diva2:835156
Note
www.elsevier.com/locate/ocemodAvailable from: 2012-09-18 Created: 2011-06-22 Last updated: 2015-06-30Bibliographically approved

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CiteExportLink to record
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