A 2D numerical study on Kuroshio currents with free slip coastal boundary

Abstract

The paper presents a comprehensive analysis of generating a Kuroshio current-like phenomenon using a novel mathematical model and advanced numerical methods. It helps to understand the streamline behavior on the western boundary over the time scales due to the presence of free slip conditions at the north and at the south coastal boundaries.

The ocean is modeled as a square domain occupied by homogeneous, incompressible fluid of constant density and a variable surface height. Dynamics of the flow are examined in a shallow water system. The salient parameters investigated here are the wind stress coefficient, the stochastic wind force coefficient, and time scales.

It is proved that streamlines are crowded on the western boundary through numerical study, and also these are bifurcated when the wind stress coefficient is 3.12. The bifurcation of the flow indicates the stability. It is also reported that the Milstein method and a standard numerical method are in good agreement while the Fokker–Planck equation-based method and the Milstein method are partially agreed. The solution by the Milstein method diverged while the solution by the Fokker–Planck method converged when $\omega \ge 0.2$.