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Numerical studies of wind forced internal waves with a nonhydrostatic model

Abstract

The nonhydrostatic pressure effects on the generation and propagation of wind-forced internal waves are studied with a two-dimensional numerical ocean model. A one-way directed wind pulse over a stratified ocean initiates surface and internal waves in a closed basin. The studies are performed with horizontal grid sizes in the range from 1 km to 62.5 m. The experiments are performed with both a hydrostatic and a nonhydrostatic model, facilitating systematic studies of the sensitivity of the numerical model results to the grid size and to the nonhydrostatic pressure adjustments. The results show that the nonhydrostatic pressure effects are highly dependent on the grid size and grow with increased resolution. In the internal depression wave, the horizontal nonhydrostatic pressure gradients reach the same order of magnitude as the hydrostatic gradients in the high-resolution nonhydrostatic studies. In these studies, the nonhydrostatic pressure gradients approximately balance the corresponding hydrostatic pressure gradients in the internal depression wave, and the wave degenerates into a train of soliton waves. The time for the soliton form to develop agrees with the steepening timescale calculated from Korteweg-de Vries theory. In the high-resolution hydrostatic model, the internal depression wave takes the form of a single wave front. When the internal waves are generated in the boundary layers, the nonhydrostatic pressure gradients are much smaller than the hydrostatic gradients and the generation processes are not effected by the nonhydrostatic pressure with the present range of grid sizes.

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Acknowledgements

We thank Philip Hall and Alan M. Davies for providing Fig. 2a. We thank two anonymous reviewers for constructive feedback whose comments led to substantial improvement of the paper. This work was supported by the Research Council of Norway through the MARE programme grant 164501/S40.

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Correspondence to Jon Bergh.

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Responsible editor: Phil Dyke

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Bergh, J., Berntsen, J. Numerical studies of wind forced internal waves with a nonhydrostatic model. Ocean Dynamics 59, 1025–1041 (2009). https://doi.org/10.1007/s10236-009-0226-1

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Keywords

  • Wind forcing
  • Nonlinear internal waves
  • Nonhydrostatic pressure
  • Numerical ocean model