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Viscous diffusion of multiple vortex system

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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.

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