Mathematical Description of the Flows near the Bottom of the Ocean

Abstract—We construct an explicit solution for a boundary value problem for a system of partial differential equations which describes small linearized motions of three-dimensional stratified flows in the half-space. For large values of t, we obtain uniform asymptotical decompositions of the solutions on an arbitrary compact in the half-space. In the vicinity of the boundary plane, we establish the asymptotical properties of the boundary layer type: we can observe a worsening of the decay in the approximation to the bottom. The results can be used in the meteorological modelling of water flows near the bottom of the Ocean, as well as Atmosphere flows near the Earth surface.

Index Terms—Atmospheric modelling and numerical prediction, boundary layer, geophysics, partial differential equations, physical oceanography, stratified fluid.

A. Giniatoulline is with the Department of Mathematics, Los Andes University, Cra. 1 Este No 18A-10, Bogota D. C., Colombia, South America (e-mail: aginiato@uniandes.edu.co).

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Cite: A. Giniatoulline, "Mathematical Description of the Flows near the Bottom of the Ocean," International Journal of Environmental Science and Development vol. 10, no. 10, pp. 321-325, 2019.

Copyright © 2019 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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