Numerical simulation and analysis of the sensitivity of large-scale ocean dynamics

This work deals with the numerical modelling of ocean dynamics and an analysis of the the sensitivity of the obtained solutions. We give the numerical procedure of solving primitive equations which is based on the decomposition of the space operator in the problem (the weak approximation method). The original equations written in a-coordinates are reduced to the system of evolutionary equations which satisfies an integral relation for total energy. We consider the representation (decomposition) of the operator in the given differential problem as a sum of suboperators. The corresponding energy relation must necessarily hold for each suboperator. The decomposition of the problem operator may be of different depth, down to the splitting by separate coordinates. Each isolated suboperator can be then approximated in space by a specific method, its characteristic features taken into account. The above approach is exemplified by the solution of the numerical problem of thermohaline dynamics in the Greenland-Iceland-Norwegian sea and the study of its features when decreasing the coefficients of turbulent viscosity. A decrease of the coefficients of turbulent viscosity entails the necessity of tripling the grid resolution in the solution of locally one-dimensional equations of convection-diffusion of temperature and salinity in horizontal variables. We interpret the variability of current dynamics under changes of the model parameters by a sensitivity function. As this function we choose the functional of the adjoint equation of convection-diffusion of a passive tracer.