Effects of rotation on self-resonant internal gravity waves in the ocean

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Ranis Ibragimov, Nail H. Ibragimov
Title: Effects of rotation on self-resonant internal gravity waves in the ocean
Journal: Ocean Modelling
Year: 2010
Volume: 31
Issue: 3-4
Pagination: 80–87
ISSN: 1463-5003
Publisher: Elsevier
URI/DOI: 10.1016/j.ocemod.2009.10.003
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. of Mathematics & Natural Sciences (Sektionen för ingenjörsvetenskap - Avd.för matematik och naturvetenskap)
School of Engineering S-371 79 Karlskrona
+46 455 38 50 00
Authors e-mail: nib@bth.se
Language: English
Abstract: 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.
Subject: Mathematics\Analysis
Keywords: Self-resonant interval waves, Boussinesq approximation, Effects of rotation
Note: www.elsevier.com/locate/ocemod