# Viscous diffusion of multiple vortex system

(Difference between revisions)
 Revision as of 05:54, 12 April 2007 (view source)DmzRly (Talk | contribs)m← Older edit Latest revision as of 07:40, 12 April 2007 (view source)Jola (Talk | contribs) m (Reverted edits by DmzRly (Talk); changed back to last version by Praveen) Line 13: Line 13: :$:[itex] - p(x,y,t) = -0.25( \cos 2x \cos 2y) e^{-4t/Re} + p(x,y,t) = -0.25( \cos 2x + \cos 2y) e^{-4t/Re}$ [/itex] where $u,v$ are the Cartesian velocity components, $p$ where $u,v$ are the Cartesian velocity components, $p$ is the pressure and $Re$ is the [[Reynolds number]]. is the pressure and $Re$ is the [[Reynolds number]].

## Latest revision as of 07:40, 12 April 2007

The following analytical solution satisfies the viscous, incompressible continuity and momentum equations in dimension-less form in the domain $0 \le x, y \le 2\pi$. The solution is periodic in both $x$ and $y$ coordinates.

$u(x,y,t) = -(\cos x \sin y) e^{-2t/Re}$
$v(x,y,t) = (\sin x \cos y) e^{-2t/Re}$
$p(x,y,t) = -0.25( \cos 2x + \cos 2y) e^{-4t/Re}$

where $u,v$ are the Cartesian velocity components, $p$ is the pressure and $Re$ is the Reynolds number.