The role of sea water viscidity in modeling the vertical movement of internal tides

A numerical closure scheme has been developed to introduce dissipation processes in particular for the vertical movement of internal tides. This scheme is based on the assumption that a vertically oscillating water mass disturbs the pressure field and feels the viscosity from its neighborhood at the same time. The horizontal viscosity term, referred in this paper as the internal-tide viscosity (ITV) term, is retained in the vertical movement equation, which introduces a quasi-hydrostatic assumption. Therefore, a new expression of the total perturbation pressure has been derived. By applying this expression in a 5′ × 5′ z-coordinate regional ocean model, the results show great improvements. With consideration of the ITV-term, the numerically enhanced vertical movement locally near a ridge has been damped in a z-coordinate system, and the propagation of internal tides away from the ridge has been converted into a more reasonable dissipative mode. With the tunable parameter Cw equals to 0.2, the values of the simulated vertical velocity have been reduced to approximately 50%. And the simulated thermocline structure has been preserved, as well.