Numerical studies of the long-term dynamics of the 2D Navier-Stokes equations applied to ocean circulation

Rodolfo Bermejo ^[1] ; Pedro Galán del Sastre ^[1]
1. [1] Universidad Complutense de Madrid
  
  Universidad Complutense de Madrid
  
  Madrid, España
Localización: XVII Congreso de Ecuaciones Diferenciales y Aplicaciones ; VII Congreso de Matemática Aplicada: Salamanca, 14-28 septiembre 2001 / coord. por Luis Ferragut Canals , Anastasio Pedro Santos Yanguas , 2001, ISBN 8469961446, págs. 15-34
Idioma: inglés
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Resumen
- We present in this paper a numerical study of long-term calculations of an idealized mid-latitude ocean circulation model. The objective of this paper is twofold. First, we present an efficient semi-Lagrangia scheme for eddy resolving ocean circulation models, and second, we use the so called proper orthogonal decomposition technique to characterize the finite dimensional manifold that contains the attractor of the solution. Using a Galerkin projection on this man- ifold we reduce the high dimensional system obtained by the application of the finite element method, to a low-dimensional one and , thus, we can calculate the bifurcation diagram with the horizontal eddy viscosity coefficient as a control parameter.