I am familiar with the Courant-Friedrich-Lewy Condition in as far as it applies to the stability of explicit finite difference schemes for standard parabolic and hyperbolic PDEs.  However, when solving the Navier-Stokes Equations, the non-linearity of the PDEs make it difficult to derive a CFL condition analytically.  I see that the Courant number is often  estimated by the CFL condition of the 1st order wave equation or the residence time.  Is it common practice to do so for all Reynolds numbers?  Are there some Reynolds numbers under which an alternative formula is used to estimate the Courant number?
Estimating the Courant number for the Navier-Stokes Equations under differing Reynolds number regimes
fluid dynamics;stability
Strictly speaking, it doesn't make sense to speak of a Courant number for the Navier-Stokes equations at finite Reynolds number.  The Courant number is defined in terms of a characteristic velocity, and solutions of parabolic equations (like Navier-Stokes) aren't described by characteristics.  The CFL condition implies that no explicit solver with finite stencil width can be convergent (for parabolic problems like Navier-Stokes) when the ratio $\Delta t/\Delta x$ is fixed.Nonlinearity doesn't cause any problem in defining the Courant number for hyperbolic PDEs, since you can still find the maximum characteristic velocity.