Theoretical analysis of vertical mode internal waves affected by a vortex.

Interaction between vortices and internal waves plays important roles in mixing and the formation of local internal wave spectra. This interaction has attracted attention, and remarkable theories have been achieved in the parameter range of weak meso-scale eddies with relatively short internal waves, which allows WKB like approach.

However, processes outside of the above parameter range are not well known; for example, universally located sub-mesoscale vortices and tide-induced internal gravity waves of various wavelengths. In such a parameter range incident wavelength is sometimes comparable to spatial scale of a vortex. This requires a non-WKB like method.

Here, we investigated the interaction between a single vortex and incident internal waves by a perturbation method. We obtained scattered wave solutions for azimuthal modes, whose sum gives the total scattered wave field. In the analysis, a useful non-dimensional parameter arose. This parameter represents a product of ratios of length and nonlinearity scales, and is available for classifing the interaction dynamics.