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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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Nonlin. Processes Geophys., 25, 217-231, 2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
20 Mar 2018
Multi-scale phenomena of rotation-modified mode-2 internal waves
David Deepwell, Marek Stastna, and Aaron Coutino Department of Applied Mathematics, University of Waterloo, Waterloo, Canada
Abstract. We present high-resolution, three-dimensional simulations of rotation-modified mode-2 internal solitary waves at various rotation rates and Schmidt numbers. Rotation is seen to change the internal solitary-like waves observed in the absence of rotation into a leading Kelvin wave followed by Poincaré waves. Mass and energy is found to be advected towards the right-most side wall (for a Northern Hemisphere rotation), leading to increased amplitude of the leading Kelvin wave and the formation of Kelvin–Helmholtz (K–H) instabilities on the upper and lower edges of the deformed pycnocline. These fundamentally three-dimensional instabilities are localized within a region near the side wall and intensify in vigour with increasing rotation rate. Secondary Kelvin waves form further behind the wave from either resonance with radiating Poincaré waves or the remnants of the K–H instability. The first of these mechanisms is in accord with published work on mode-1 Kelvin waves; the second is, to the best of our knowledge, novel to the present study. Both types of secondary Kelvin waves form on the same side of the channel as the leading Kelvin wave. Comparisons of equivalent cases with different Schmidt numbers indicate that while adopting a numerically advantageous low Schmidt number results in the correct general characteristics of the Kelvin waves, excessive diffusion of the pycnocline and various density features precludes accurate representation of both the trailing Poincaré wave field and the intensity and duration of the Kelvin–Helmholtz instabilities.
Citation: Deepwell, D., Stastna, M., and Coutino, A.: Multi-scale phenomena of rotation-modified mode-2 internal waves, Nonlin. Processes Geophys., 25, 217-231,, 2018.
Publications Copernicus
Short summary
We have used numerical simulations to investigate the impact that rotation has on large waves existing internally in the ocean. In coastal regions these waves become trapped along the coast because of rotation. We have found that this trapping results in an adjustment of the form of the waves. The adjustment leads to heightened mixing along the coast, which has implications for nutrient and chemical distribution.
We have used numerical simulations to investigate the impact that rotation has on large waves...