Mathematical modeling of Eulerian currents induced by wind and waves at the sea surface

This paper deals with the study of mathematical modeling of Eulerian currents in ocean circulations. The wave-wave interaction of four progressive waves traveling with four wave numbers and four frequencies are elegantly described by Komen et al. (J. Phys. Oceanogra., 14 (1984), 1271–1285).Therefore, detailed investigations are avoided in this present paper. We shall rather devote our study to the description of the analytic solutions of the Eulerian currents present in the ocean circulation. This study contains the mathematical descriptions of nonlinear wave interactions, wind and wave induced surface currents, unsteady Eulerian currents in one-dimension,and steady two-dimensional Eulerian currents in ocean circulations. A variety of solutions that satisfy the governing equations with their initial and boundary conditions are obtained. A Laplace transform method in conjunction with the convolution concept is used as a solution technique and the accuracy of the solution is confirmed by using the powerfulseparation of variables method.Some ofthe solutionsare graphicallyillustratedin non-dimensionalforms and the physical meaning is described.