By using the box method and the method of indefinite coefficients, we perform the analysis of finite-difference schemes with two invariants for the equations of motion in the barotropic approximation. We establish a functional dependence, which makes it possible to construct difference schemes with the properties of antisymmetry of the solution and conservation of energy and/or enstrophy. Two approximations of nonlinear terms in the equations of motion are analyzed. The first of these approximations guarantees the conservation of two quadratic invariants for the barotropic divergent motion. In the second approximation, the same is true for the barotropic nondivergent motion. The results of prognostic experiments (20 yr of model time) demonstrate that the first scheme gives a more accurate quantitative description of the well-known physical features of large-scale circulation in the Black Sea.
Physical Oceanography – Springer Journals
Published: Feb 10, 2006
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