Nonhydrostatic Model of Marine Circulation

Abstract

Our study is devoted to the construction of such a hierarchic nonhydrostatic model of marine dynamics. The principal requirement is that the model should be able to resolve the physical problems of different levels of complexity. The hierarchic structure of the model is based on the method of splitting with respect to physical processes [4, 14, 15]. The model is an improvement of the model based on the equations of the general circulation in the ocean (primitive equations) written in the spherical σ -coordinate system [15]. The model was improved in two directions. First, account for the nonhydrostatic effect, and, second, “ k – � ” parametrization of the processes of turbulent exchange were applied. Since the input model is based on the splitting method, its program realization is modular. Individual splitting stages are represented by individual program units. The principal improvement of the model—the allowance for the nonhydrostatic effect—was achieved by adding a complementary splitting stage to the input model. The program package was provided with a new unit for the calculation of the nonhydrostatic dynamics, with the base of the model kept unchangeable. We managed to achieve this owing to the equivalent transformation of the initial equations of motion. The transformation needs a new function to be introduced, a function describing pressure variations. This technique is similar to the representation of pressure as a sum of the hydrostatic and nonhydrostatic components, which was used in [12]. In this paper, we present the formulation of the nonhydrostatic σ -model and the method of its numerical solution. The model is used for the calculations of the thermohaline marine dynamics within an ideal rectangular area, conventionally called an “academic basin,” which simulates the conditions in the central Baltic Sea. The main goal of the numerical experiments was to approbate the nonhydrostatic model and to assess the nonhydrostatic effect under such ideal conditions. In addition, to illustrate the adequacy of the model, we present the results of the calculations of the dynamics of the Gulf of Finland.