Ocean dynamic equations with the real gravity

Abstract

Abstract Two different treatments in ocean dynamics are found between the gravity and pressure gradient force. Vertical component is 5–6 orders of magnitude larger than horizontal components for the pressure gradient force in large-scale motion, and for the gravity in any scale motion. The horizontal pressure gradient force is considered as a dominant force in oceanic motion from planetary to small scales. However, the horizontal gravity is omitted in oceanography completely. A non-dimensional C number (ratio between the horizontal gravity and the Coriolis force) is used to identify the importance of horizontal gravity in the ocean dynamics. Unexpectedly large C number with the global mean around 24 is obtained using the community datasets of the marine geoid height and ocean surface currents. New large-scale ocean dynamic equations with the real gravity are presented such as hydrostatic balance, geostrophic equilibrium, thermal wind, equipotential coordinate system, and vorticity equation.