Mathematical aspects of internal wave-current interactions
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Date
2026-05-06
Authors
McCarney, Jordan
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Publisher
University College Cork
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Abstract
In this thesis we study various aspects of the mathematical theory of internal wave-current interactions in both the ocean and the atmosphere. In Chapter 2 we construct exact, nonlinear, three-dimensional solutions in Lagrangian coordinates describing internal ocean waves propagating on zonal currents in the presence of the Earth's rotation. In Chapter 3 we extend a recent exact nonlinear solution for vertically propagating mountain waves to incorporate the thermodynamics of a moist atmosphere and the the latent heat released during phase transitions of water vapour. Finally, in Chapter 4 we study coupled surface and internal small-amplitude water waves in a two-layer fluid with constant vorticity in the lower layer and an irrotational upper layer, and present results concerning particle trajectories.
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Keywords
Internal waves , Nonlinear waves , Geophysical water waves , Atmospheric mountain waves , Exact solution , Particle paths , Precipitation
Citation
McCarney, J. 2026. Mathematical aspects of internal wave-current interactions. PhD Thesis, University College Cork.