Astrophysics (index)

Navier-Stokes Equations

(NS Equations)
(equations that describe fluid dynamics)

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
  • v - flow velocity.
  • ρ - fluid density.
  • p - pressure.
  • T - deviatoric component of the stress tensor.
  • f - body of forces acting on the fluid.

No universally-applicable analytic solution is known so solutions are generally done through computation. For incompressible fluids, the constant density simplifies the equations somewhat.

They are central to Hydrodynamicses, and Magnetohydrodynamics uses a form that adds the forces of electromagnetism.

(fluid mechanics)

Referenced by:
Darcy Velocity Field
General Circulation Model (GCM)
Magnetohydrodynamics (MHD)
Reynolds Decomposition