Principles of nonlocal ocean hydrodynamics

This article is devoted to developing the foundations of a nonlocal hydrodynamic approach to describing hydrophysical processes and fields in the ocean, based on rigorous results of nonequilibrium statistical mechanics and adaptive systems control theory. Experimental studies and theoretical work in the second half of the twentieth century established that the ocean, influenced by solar energy, celestial bodies, and the Earth’s rotation, and interacting with the atmosphere, complex bottom topography, and coastal boundaries, is an open nonequilibrium system. The multi-scale processes occurring in the ocean under the influence of these factors are highly nonequilibrium and together lead to the self-organization of the ocean.

Classical continuum mechanics methods and their modifications are currently used to describe ocean dynamics. This allows us to solve a number of practically important problems. However, the differential models developed are valid for describing systems whose state is close to the local thermodynamic equilibrium. Therefore, they are not suitable for describing the formation of turbulent eddy-wave structures, and attempts to apply classical hydrodynamic models to describe highly nonequilibrium processes lead to solutions that are inadequate to nature.

The development of a nonlocal hydrodynamic approach allowed us to formulate a closed-loop formulation of the problem of self-organization of a dynamic structure in an open system. This formulation consists of integro-differential transport equations with model integral kernels. The model parameters, which determine the sizes and lifetimes of the medium’s dynamic structure, satisfy nonlinear differential evolution equations according to the speed gradient algorithm. Internal control is formed in the system through feedback between the structural dynamics and the hydrodynamic behavior of the medium. The formulation is supplemented by the initial parameters of the medium’s structure and the initial rate of its deformation.

Based on the developed nonlocal hydrodynamic approach to the description of highly nonequilibrium systems, principles for the application of nonlocal models to describe a complex of processes and phenomena in the ocean are formulated.

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