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 (MHD) uses a form that adds the forces of electromagnetism.

(fluid mechanics)

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