3 DIMENSIONAL NUMERICAL SEA MODEL USING THE GALERKIN METHOD WITH A POLYNOMIAL BASIS SET

The linear hydrodynamic equations which describe the motion of the sea under the influence of an externally applied surface stress are solved using a finite difference grid in the horizontal and the Galerkin method through the vertical. The horizontal components of current are expanded in terms of depth-varying functions (the basis functions) and coefficients that vary with horizontal position and time. Comparisons of computed current profiles show that accurate profiles can be computed using a basis set of six Chebyshev or Legendre polynomials, and that expansions of these polynomials have faster convergence at all depths than expansions of cosine functions or B-splines. The surface stresses computed with a finite number of polynomial basis functions, converge rapidly, as the number of basis functions increases, to the value of the externally applied stress. This convergence can be used as a guide in determining the number of basis functions required to accurately compute the current profile. © 1979 IPC Business Press Ltd.