Long Axisymmetrical Waves In A Viscous Ocean Around A Circular Island
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The problem of long waves due to any applied normal surface stress in a viscous liquid ocean surrounding a circular island is solved. The expression of the surface displacement ζ correct to O(ν) terms, ν being the coefficient of viscosity, is obtained. Assuming the stress to be time-periodic the surface displacement ζ , is shown to attain a steady-state and the resulting wave forms at any distance from the island are determined. Numerical studies of the results along with illustrations are provided to bring out the effect of viscosity and the presence of an island on the ocean waves otherwise devoid of them. Keywords: coefficient of viscosity, long wave motion, asymptotic analysis, turbulence. 1 Introduction The three-dimensional problem of short waves due to arbitrary initial timedependent surface pressure together with an elevation of the surface in a viscous fluid of finite depth h without any other boundaries has been investigated by Nikitin and Potetyunko  and Bandyopadhyay [3, 4]. Assuming the same fluid regime, Oborotov studies the problem of free long waves in the axisymmetric case in which however the condition of zero tangential stress on the surface was not fully utilized. In the oceanographic context it is, however, natural to investigate problems in the presence of a boundary, enclosed or otherwise, in the ocean. Recently, Das and Ghosh analyzed the initial value problem of generation of storm surges by a symmetrically distributed and time-periodic surface wind near a circular island with variable topography [11,12]. For this purpose, Das used a depth-averaged Reynolds’ equation together with the usual assumption of shallow water wave theory and the f-plane approximation. It seems that hitherto
coefficient of viscosity, long wave motion, asymptotic analysis, turbulence.