A Numerical Investigation of Tidally Forced Internal Waves in the Ocean


Principal Investigator

Peter Holloway

School of Geography and Oceanography,

University of New South Wales

Australian Defence Force Academy

Internal waves in the ocean are generated through theaction of the tides moving density stratified water over sloping topography. This can occur over the continental margins as well as over steep topography in the deep ocean. Resulting internal waves are energetic producing strong currents and large vertical excursions of density interfaces. The motion contributes to mixing of properties in the ocean, can move sediment on the sea-floor and can be significant for the stability of offshore structures. The project aims to model the generation of internal waves by tidal flow over topography and the resulting propagation and evolution of the waves. Varying topographic situations are considered as well as the effects of varying stratification and forcing.  


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What are the results to date and the future of the work?

A fully three dimensional model of a region of the Australian North West Shelf has been implemented. The model is forced by observed semi-diurnal tidal elevations and predicts both the barotropic and internal tide signals. The model has been run for varying stratifications, representing summer and winter extremes, with particular emphasis placed on predicting the distribution of maxima in near-seabed currents. These results are significant for the study of sediment movement on the continental shelf and slope regions. Future work will extend the domain of this model and include additional tidal constituents in the model forcing.

Prompted by recent observations of energetic internal tides propagating away from the Hawaiian ridge, a study has been undertaken, and submitted for publication, on the generation of internal tides by seamounts, ridges and islands in the deep ocean. Using idealised topography, the generation of internal waves is found to be strongly dependant on the relationship between the slope of the topography and the slope of the group velocity vector of the internal waves. Strongest generation occurs when these are parallel. It is also found that the three dimensional nature of the topography and the way the tidal flow interacts with this topography is critical in determining the strength of the internal tide. Future work will look at real topography and conditions for sections of the Hawaiian ridge.

What computational techniques are used?

The modelling work uses a fully three-dimensional primitive equation model of oceanic flows. The model is nonlinear, hydrostatic, free surface and includes a turbulence sub-model for

Appendix B -


calculating sub-grid scale vertical mixing of momentum, heat and salt. The code is written in FORTRAN and uses a finite difference representation of the equations, a coupled set of partial differential equations, and solves the equations by stepping through time. Given three spatial dimensions and the time dependence, the solution involves a large number of nested DO loops. Also, large arrays are used requiring significant memory. Substantial output is written to disk.
Figure: Internal tide generation from tidal flow over a ridge in the ocean. The plot shows instantaneous velocity across the ridge which is three times longer than it is wede. Narrow beams of signal are generated over the top and sides of the ridge.
- Appendix B