Discrete Equation for the Available Potential Energy as an Exact Consequence of the Numerical Model Equations
Purpose. The work is aimed at obtaining a discrete equation for the rate of the available potential energy change in strict accordance with the finite-difference formulation that ensures adequate reproduction of discrete energy, and at analyzing its terms based on the results of a numerical experiment with realistic atmospheric forcing. Methods and Results. On the basis of the well-known methods of computational mathematics (method of indeterminate coefficients and imitation modeling), obtained was a finite-difference equation for the available potential energy which corresponded to its differential form. In the equation structure, an additional term which was conditioned by transition to a discrete problem and had a diffusion form appeared. Energy of the hydrological winter, 2011, in the Black Sea, having been analyzed, has shown that the available potential energy highest values in the upper layer took place in the central region of the sea. Below 100 m, the available potential energy increased towards the coast where intense mesoscale variability was observed. At the depths exceeding 200 meters, the available potential energy largest stock was concentrated in the Sevastopol and Batumi anticyclones. Action of the main forces, namely the forces of buoyancy, advection and horizontal diffusion, takes place in the coastal areas of the sea. Conclusions. The resulting difference equation for the rate of the available potential energy change exactly corresponds to the discrete formulation and, therefore, accurately reflects the energy of the discrete problem. Analysis of the equation permitted to show that in winter, the rate of the available potential energy change is influenced predominantly by eddy activity at the depth slope.