Establishment of the ocean dynamic system with four sub-systems and the derivation of their governing equation sets

Based on their differences in physical characteristics and time-space scales, the ocean motions have been divided into four types in the present paper: turbulence, wave-like motion, eddy-like motion and circulation. Applying the three-fold Reynolds averages to the governing equations with Boussinesq approximation, with the averages defined on the former three sub-systems, we derive the governing equation sets of the four sub-systems and refer to their sum as “the ocean dynamic system”. In these equation sets, the interactions among different motions appear in two forms: the first one includes advection transport and shear instability generation of larger scale motions, and the second one is the mixing induced by smaller scale motions in the form of transport flux residue. The governing equation sets are the basis of analytical/numerical descriptions of various ocean processes.