The governing equations for a real fluid are the Navier-Stokes equations (conservation of linear momentum and mass) along with conservation of salt, conservation of heat (the first law of thermodynamics), and an equation of state

However, these equations support fast acoustic modes and involve nonlinearities in many terms that make solving them both difficult and expensive and particularly ill suited for long time scale calculations. Instead, a series of approximations are made to simplify the Navier-Stokes equations to yield the “primitive equations,” which are the basis of most general circulation models