The predictability/unpredictability of nonlinear internal gravity waves in the ocean: generation, shoaling and dissipation

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Internal gravity waves exist in density-stratified fluids when gravitational restoring forces act on vertically displaced fluid. They occur in the interior of the fluid, e.g., below the ocean surface, where the density varies. They are ubiquitous in our oceans, lakes and atmosphere where they propagate both horizontally and vertically. Internal waves affect ocean circulation and biogeochemical processes by mixing heat and nutrients, they re-suspend and transport sediments and nutrients, and their currents can impact offshore structures. They have been hypothesized to play a role in shaping the continental shelf and fish have been observed to migrate vertically in response to the passing of large internal waves to optimize their feeding strategy. Internal waves can propagate thousands of kilometers from their generation site so wave generation in one location can have an impact at great distances.Internal waves are primarily generated by tidal currents flowing over topographic features such as ridges and the continental shelf slope, or by winds acting on the ocean surface. Tide-topography interaction forces fluid up and down the sloping bottom while variations in wind stress at the ocean surface drive horizontal currents which push fluid together or spread it apart resulting in downward and upward motion. These vertical motions drive internal waves. Internal waves are nonlinear-dispersive waves. The nonlinearity transfers energy among different waves while dispersion results in energy in different waves propagating with different velocities. Nonlinearity transfers energy from the large scales at which it is injected to small scales at which it is dissipated and mixing occurs. Many internal waves in the ocean are strongly nonlinear with internal solitary waves being the most striking example. Here nonlinearity and dispersion act in concert to create a large coherent wave that can propagate large distances. Extreme examples of these waves have amplitudes approaching 200 m (four times the height of Niagara Falls) though amplitudes of tens of meters are the norm. Currents associated with internal solitary waves modify the surface wave field making their presence detectible from space and can impact off-shore structures making these waves of interest to the off-shore oil industry. The proposed research will address aspects of the predictability and unpredictability of internal waves via numerical simulations and mathematical modelling. It will address the generation of internal waves by tide-topography interactions focussing on energy transfer to internal solitary waves and their role in vertical mixing. A case study will focus on wave generation on the Peruvian shelf where observations suggest that internal waves are responsible for the vertical mixing of heat and for the seasonal variability in biological productivity. The shoaling of internal solitary waves with an emphasis on the occurrence of breaking will be studied and shear instabilities in internal solitary waves, which result in the vertical mixing of heat and nutrients, will be investigated. Other aspects of the predictability of these waves will be investigated including the interaction of internal waves of tidal frequency with eddies and vortices in the ocean, which affects the long-distance propagation of internal waves, and the occurrence of different forms of internal waves, e.g., breathers which are special nonlinear, pulsating wave packets. This research will improve our capability to predict the internal wave field in the ocean and will enable better predictions of processes such as large scale ocean circulation, cross-shelf exchange, biological productivity and the shaping of our continental shelf and help in the design and operation of off-shore structures.