| Effects of
latitude on self-resonant waves in the vicinity of ridges in the ocean Ranis Ibragimov (New Mexico Tech) ABSTRACT: The Resonant Triad Model (RTM) is used to study the Thorpe's problem onthe 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 & Bretherton's three wave hydrostatic model 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 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 self-resonant waves. In particular, it is shown that the value of the bottom slope at which the second-order frequency and wavenumber 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. |