4.2.3.2 Horizontal pressure gradient

The horizontal pressure gradient $-\nabla_{h}p$ acts to drive the fluid towards regions of low pressure. This gradient arises from spatial gradients in the pressure at the ocean surface (the barotropic pressure gradient) and pressure interior to the ocean (the baroclinic pressure gradient). Baroclinic pressure gradients arise from density gradients as determined through the hydrostatic relation. The steady state balance of the Coriolis force and the total pressure gradient force forms the geostrophic balance. This balance is relevant for large scale ocean circulation. All of the other terms in the velocity equation act to make the flow deviate from geostrophy.