Taylor-Green vortex sheet, reduced units
The Taylor-Green vortex sheet is a solution to the 2D Navier-Stokes equations for an incompressible Newtonian fluid: $latex \frac{d \mathbf{u}}{d t}= \nu \nabla^2 \mathbf{u} – \nabla p/\rho$ where $latex \mathbf{u}$ is the velocity field, $latex p$ is the pressure, $latex \nu=\mu/\rho$ is the kinematic viscosity, and $latex \rho$ is the fixed density of the fluid. The time derivative is a total derivative: $latex \frac{d \mathbf{u}}{d t} = \frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla) \mathbf{u}$.
error: $latex d \mathbf{u} = mathbf{u} $,
$latex \frac{d \mathbf{u}}{d t}$
It is common to choose parameters that simplify the equations, but that can obscure the role of the different parameters. In the following, I provide expressions with all relevant parameters included, with their physical dimensions. I later pass to dimensionless, or reduced, units, in terms of the Reynolds and Courant numbers.
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