# Vortex Flow

Time dependent decaying flow for standing vortices with the following analytical solution to the Navier-Stokes equations

\[
\begin{array}{l}
u = -cos(kx) sin(ky) e^{-2\nu k^2t} \\\

v = sin(kx) cos(ky) e^{-2\nu k^2 t} \\\

p = -\frac{1}{4}(cos(2kx)+cos(2ky)) e^{-4\nu k^2 t}
\end{array}
\]

The two-dimensional flow problem is solved for a unit square with *k = 2π* and
the exact solution as boundary and initial conditions.

This model is available as an automated tutorial by selecting **Model
Examples and Tutorials…** > **Fluid Dynamics** > **Vortex Flow**
from the **File** menu. Or alternatively, follow the linked
step-by-step instructions.