The World Ocean

Abstract

In the ocean, as in the atmosphere, synoptic and global processes require individual description. They can also be characterized with the aid of the simplified equations of hydrodynamics (9.1)−(9.4), (9.3′), (9.4′), if g = ϱw is taken to be the density of seawater. The boundary conditions for the velocity field at the ocean floor, the relief of which z = − hw (θ, λ) is assumed to be specified, remain the same as those for the velocity of air currents at the land surface (here, by analogy with the atmospheric boundary layer, we can introduce a “parametrized” near-bottom boundary layer). However, the boundary conditions at the ocean surface z = ξ (θ, λ, t) now have to be specified more precisely than was the case for the atmosphere (since the quantity ξ (θ, λ, t) plays a significant role in the ocean dynamics, and it is an unknown function which must be determined from these boundary conditions): here it can no longer be assumed that ξ = 0 everywhere, but for large-scale processes ξ will be small (of the order of decimeters, as a rule). The kinematic boundary condition at the ocean surface can then be written as