Ocean Dynamics - Primitive Equations

Primitive Equations

Ocean dynamics are governed by Newton's equations of motion expressed as the Navier-Stokes equations for a fluid element located at (x,y,z) on the surface of our rotating planet and moving at velocity (u,v,w) relative to that surface:

• the zonal momentum equation:

• the meridional momentum equation:

• the vertical momentum equation (assumes the ocean is in hydrostatic balance):

• the continuity equation (assumes the ocean is incompressible):

• the temperature equation:

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• the salinity equation:

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Here "u" is zonal velocity, "v" is meridional velocity, "w" is vertical velocity, "p" is pressure, "ρ" is density, "T" is temperature, "S" is salinity, "g" is acceleration due to gravity, "τ" is wind stress, and "f" is the Coriolis parameter. "Q" is the heat input to the ocean, while "P-E" is the freshwater input to the ocean.