To examine the influences of a hydrostatic approximation on the numerical accuracy of coastal current simulations, we have performed the computation for a vertical 2-D density front under a wide range of grid resolutions. For this purpose, we use the numerical models with and without the hydrostatic approximation. The computational results indicate that the differences of density-front structures appear appreciably in the hydrostatic and non-hydrostatic models and furthermore are strongly dependent on the horizontal grid resolutions. It is also found that the evaluation of a hydrodynamic pressure is a crucial importance on the numerical accuracy in the non-hydrostatic model.
Although coastal current simulations have frequently been performed in various flow fields, numerical models for coastal ocean current are usually based on several simplifications and approximations for turbulence models, coordinate systems, vertical fluid motion and etc (e. g., Haidvogel and Beckmann, 1998). It is therefore required to examine the influence of these simplifications on coastal current simulations. In most numerical models, the hydrostatic approximation, one of these simplifications in numerical models, is used for a vertical fluid motion (e. g., Blumberg and Mellor, 1983), because a horizontal length scale of fluid motion is much larger than a vertical length scale. Although previous studies have been conducted for this purpose (e.g., Causulli & Stelling, 1999; Kinoshita, 2001), the numerical accuracy of the hydrostatic approximation under a variety of computational conditions has been poorly investigated. In the present study, we have attempted to study the influences of the hydrostatic approximation on computational results of coastal current simulations. For this purpose, we have done the computations for a vertical 2-dimensional gravity front, so called ‘lock exchange problem’ (Turner, 1973) under a wide range of grid resolutions by using numerical models for coastal current with and without the hydrostatic approximation.
