A comparison of hydrostatic and nonhydrostatic pressure components in seiche oscillations

Abstract

The hydrostatic pressure assumption has been widely used in studying water movements in shallow waters where the water depth ( D) is much smaller than the horizontal length scale ( L). It is assumed that the pressure field in a shallow water flow is hydrostatic because the nonhydrostatic pressure component ( pn) is much smaller than the hydrostatic pressure component ( ph) and thus be safely neglected in model simulations. With this assumption, a three-dimensional, hydrodynamic model can be significantly simplified because the momentum equation in the vertical direction is reduced to an expression of hydrostatic pressure. While such a simplification is valid in many shallow water applications, there exist no rigorous guidelines as to what extent can the hydrostatic assumption be safely used without any problems. In an effort to get a better understanding of the effect of nonhydrostatic pressure on free-surface flow, this paper presents a comparison of hydrostatic and nonhydrostatic pressure components and their horizontal gradients in two seiches. The first seiche represents a deepwater wave oscillation, while the second one is a shallow water wave oscillation. A nonhydrostatic model was used to simulate the two oscillations, and simulated hydrostatic and nonhydrostatic pressure components were compared. A scale analysis was also carried out for the two pressure components in seiching. It is found that although the nonhydrostatic component was about 2 to 3 orders of magnitude smaller than the hydrostatic component for the two oscillations, the horizontal gradient of the nonhydrostatic component is not necessarily smaller than that of hydrostatic pressure by 2 to 3 orders of magnitude. On the other hand, while the horizontal gradient of nonhydrostatic pressure may be in the same order of magnitude as that of hydrostatic pressure, it does not necessarily require nonhydrostatic pressure itself to be in the same order of magnitude as hydrostatic pressure. Model simulations also show that the nonhydrostatic portion of the horizontal pressure gradient affects the velocity field during the course of the oscillation and its effects are not negligible even when the aspect ratio is less than 0.05.