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.