The Navier-Stokes Equations (NS Equations) describe the motion of fluids, relating viscosity, Newtons laws and pressure. The general form:
ρ(∂v/∂t+v·∇v) = -∇p + ∇·T + f
No universally-applicable analytic solution is known so solutions are generally done through computation. For incompressible fluids, the constant density simplifies the equations somewhat.
Darcy Velocity Field
General Circulation Model (GCM)