Unsteady Buoyant Jet Simulations Using Dynamic Connection Scheme of Hydrostatic and Non-Hydrostatic Zone

Most of ocean models employ hydrostatic approximation because the horizontal scale is usually much larger than the vertical scale in oceanic phenomena. In hydrostatic approximation, dynamic pressure is neglected and the momentum equation in vertical direction needs not to be solved. But for the phenomena of buoyant jet from the sea bottom such as submarine groundwater discharge, hydrothermal plume and so on, hydrodynamic pressure cannot be neglected and the momentum equation of vertical direction must to be taken into account. Non-hydrostatic analysis requires so much computation time that it is usually difficult to calculate the current field in the wide ocean area by this approach. On the other hand, analysis assuming the hydrostatic approximation needs less computational time and usually gives reasonable results for large scale ocean phenomena such as tidal current. In the present study, the authors developed a new type of ocean model for multi-scale analysis, which conducts hydrostatic analysis for phenomena in wide area and non-hydrostatic analysis for the detail flow around the buoyant jet simultaneously. The application limit of hydrostatic approximation for ocean model was investigated, and a dynamic connection method of hydrostatic zone with non-hydrostatic zone was developed. By theoretical consideration employing parameter δ and ε which represent the ratio of grid size Δz to Δx and the ratio of vertical velocity to horizontal velocity, it was found that hydrostatic approximation can be applied if δε and ε² are minute. To examine the developed method, simulations for lock-exchange problem and vertical jet under oscillating current were conducted. The result by the present model was similar to that of non-hydrostatic model in the case that hydrostatic approximation was applied on the area of δε<0.005 and ε²<0.005.