Problemas de circulacao oceanica equatorial: determinacao da estrutura horizontal dos modos baroclinicos por equacoes integrais de contorno / Problems of equatorial oceanic circulation: determination of horizontal

AUTOR(ES)
DATA DE PUBLICAÇÃO

1991

RESUMO

This work contains a detailed presentation of a new methodology for the numerical simulation of tropical ocean circulation. Specifically, one considers the linearized shallow water equations on the equatorial Ò-plane, which may be used to describe the horizontal dependence of each baroclinic mode in a vertical normal mode expansion. A general boundary value problem for these equations, with slip boundary conditions applied at a boundary of arbitrary geometry, is reformulated as a boundary integral equation for the unknown boundary pressure distribution. In this way, one obtains integral equations describing both the wind-forced circulation and the scattering of free equatorial waves by islands and continental margins of arbitrary geometry. The kernels of the integral operators appearing in the boundary integral equations are analytically represented as expansions in free equatorial waves involving the Hermite functions Öm(y), where y is the non-dimensional latitude. In certain cases of interest, it is inconvenient to compute the kernels through these expansions, because of their slow convergence. Physically, this arises from the superposition of equatorial waves with complex wave numbers (zonally damped modes). A general theory is developed for the asymptotic evaluation of the remainder of a Hermite expansion, when the series is truncated after a sufficiently large number of terms. This theory, which is applicable to a variety of oceanographically relevant expansions, allows the efficient numerical computation of the kernels of the integral operators. Procedures for the numerical solution of the boundary integral equations by the boundary element method are developed and implemented in a set of routines in FORTRAN 77. Advantages of the present formulation include the possibility of evaluating the solution in selected areas of the ocean, the ease .in the representation of complex coastal geometries, and the unified treatment of all frequencies of oceanographic interest without using approximations such as those of long waves or low frequencies. The new methodology is illustrated by a study of the scattering of equatorial Rossby waves with periods between 50 and 90 days by the western Atlantic boundary. Some of the resulting interference patterns exhibit a region of large amplitudes of oscillation, whose center is located between 3-9¢X N, 35-47¢X W. Evidence is found that this effect arises from the constructive interference of zonally damped modes which are excited south of the Equator at the ocean boundary.

ASSUNTO(S)

interacao oceano atmosfera ciencias meteorologicas simulacao numerica circulacao oceanica

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