The principal balance in the equations of motion comes from a balance of momentum acceleration, vertical momentum diffusion and the Coriolis force due to the Earth's rotation:
where U and V are the E--W and N--S components of the
velocity, f is the Coriolis parameter and 
is the coefficient of
turbulent momentum diffusion. The transport equation for heat
balances vertical diffusion of heat and incident solar radiation
in 1-D models, and also advection of heat in 3-D models (1-D
meaning that the spatial gradients in only one direction, in this
case z, are retained. In other words, fluid flow is regarded as
horizontally homogeneous). Thus,
where T is the temperature. There is similarly a transport equation for salt,
where 
and 
are turbulent diffusion coefficients for heat and salt,
respectively, and S is salinity.
