A Numerical Study of the Wind-Driven Transient Circulation in a Homogeneous Ocean

摘要

The primitive hydrostatic equations for a homogeneous incompressible ocean are formulated in terms of the vertically integrated flow and a variable free water surface. A rectangular ocean 4000 km by 5920 km with a uniform undisturbed depth of 400 m is considered on a beta-plane, with a lateral boundary condition of zero slip. From an initial state of rest, the development of the circulation and deformation of the free surface is followed for 60 days with a space-staggered finite-difference grid of 80 km mesh size. For an assumed wind stress varying only as the cosine of the north-south coordinate with maxima at the northern and southern boundaries, a generally clockwise ocean circulation is established in the first few days, and persists throughout the calculation. A piling of water of the order of 1 m occurs near the western ocean shore, and is in approximate geostrophic equilibrium with an intense northward boundary current (whose speed is of the order of 1 m sec-1) and a weaker offshore southward countercurrent. Frictional dissipation is assumed in the form of lateral eddy diffusion, with a constant coefficient of 10 to the 8th sq cm sec-1.