## Reynolds-averaged Navier–Stokes equations

The Reynolds-averaged **Navier–Stokes Stokes** equations (or RANS equations) are time-averaged [ 1 ] equations of motion for fluid flow . The idea behind the equations is Reynolds decomposition , whereby an instantaneous quantity is decomposed into its time-averaged and fluctuating quantities

**wikipedia.org**| 2011/4/13 15:15:55

## Stokes operator

The **Stokes** operator , named after George Gabriel **Stokes** , is an unbounded linear operator used in the theory of partial differential equations , specifically in the fields of fluid dynamics and electromagnetics . [ edit ] Definition If we define P σ as the Leray-Helmholtz projector

**wikipedia.org**| 2010/9/25 15:22:43

## Derivation of the Navier–Stokes equations

The intent of this article is to highlight the important points of the derivation of the **Navier–Stokes Stokes** equations as well as the application and formulation for different families of fluids. Contents 1 Basic assumptions 2 The Material derivative 3 Conservation laws

**wikipedia.org**| 2010/9/26 10:43:01

## Navier–Stokes existence and smoothness

The **Navier–Stokes Stokes** equations are one of the pillars of fluid mechanics . These equations describe the motion of a fluid (that is, a liquid or a gas) in space. Solutions to the **Navier–Stokes Stokes** equations are used in many practical applications. However, theoretical understanding

**wikipedia.org**| 2011/4/6 2:10:50

## Hagen–Poiseuille flow from the Navier–Stokes equations

In fluid dynamics , the derivation of the Hagen–Poiseuille flow from the **Navier–Stokes Stokes** equations shows how this flow is an exact solution to the **Navier–Stokes Stokes** equations . [ 1 ] [ 2 ] [ edit ] Derivation The flow of fluid through a pipe of uniform (circular) cross

**wikipedia.org**| 2011/5/5 5:34:11

## Stokes boundary layer

In fluid dynamics , the **Stokes** boundary layer , or oscillatory boundary layer , refers to the boundary layer close to a solid wall in oscillatory flow of a viscous fluid . Or, it refers to the similar case of an oscillating plate in a viscous fluid at rest, with the oscillation direction

**wikipedia.org**| 2011/5/1 8:41:06

## Stokes flow

For this type of flow, the inertial forces are assumed to be negligible and the **Navier–Stokes Stokes** equations simplify to give the **Stokes** equations: where is the stress tensor , and an applied body force. There is also an equation for conservation of mass . In the common case of

**wikipedia.org**| 2011/7/19 14:29:16