ABSTRACT
The hydrostatic primitive equation initial boundary value problem is often used in physical oceanography to describe ocean waters and their movements. However, this problem is ill-posed in the open ocean, unless it is solved in a domain that moves with the flow [Bennett and Chua, 1999]. In this work, we use Lagrangian coordinates to solve in a domain that moves with the flow. Solutions in Lagrangian coordinates are trajectories of particles, which may become chaotic. However, accurate solutions of the spherical shallow water equations in Lagrangian coordinates with pseudo-spectral and Runge-Kutta methods are found for realistic time scales in the ocean.