Super-inertial internal waves trapped in a vortex

Kaoru Ito, United States and Tomohiro Nakamura, Hokkaido Univ, Sapporo, Japan
The breaking and dissipation of internal waves is a major energy source of vertical mixing, which affects thermohaline circulaton, material circulation, eco-system, and more.Interaction between vortices and internal waves is an important process for internal-wave dissipation. In particular, the wave-capture theory has suggested that relatively short internal waves are quickly refracted by meso-scale eddies, leading to mixing. However, in the oceans, there is a parameter range that is not examined by previous theories. For example, wavelength can be much longer than diameter of vortices for the interaction of low-mode internal tides and widely distributed sub-mesoscale vortices. In this study, we have examined the collision of vortices and internal waves with numerical experiments and a theoretical analysis.
We found super-inertial trapped waves with a sliced orange shape, which are generated by the collision(interaction) in a parameter range outside of previous theories, from numerical experiments. To give a theoretical support for this kind of waves, we derived a theoretical solution without using a WKB approach. This type of waves have the following properties in both numerical and theoretical results. The horizontal structure of the trapped waves is characterized by isophase lines extending radially from the vortex center with amplitude maximum located near the location of vortex flow maximum. The phase velocity is directed against the vortex flow. The frequency is the same as the incident wave frequency. The existense of the trapped waves is associated with the gradient of the background vorticity due to a vortex. The sliced orange shape trapped waves would dissipate eventually in a vortex and result in mixing. This is therefore a new way of internal wave dissipation casued by the interaction of waves and vortices.