Two-Dimensional Turbulent Mixing Layer
The velocity profile of a low Mach number two-dimensional turbulent mixing layer between two fluid layers of velocities u1 and u2 is shown in Figure 15.4. In nondimensional form, the mean velocity profile may be represented analytically (see the book by White) by an error function.
where 8ш is the maximum vorticity thickness defined by
u1 — u2
The velocity profile of a mixing layer tends to a constant as |y| ^ to. For this reason, the profile has no Fourier transform in the usual sense. However, the velocity gradient du/dy is a well-behaved function. It is a well-known fact that the integral of a function is smoother and better behaved than its derivative. Therefore, if the mesh size is chosen to be able to resolve du/dy, then the mesh should be able to provide adequate resolution for computing u(y). Thus, the function to be considered is
Figure 15.5. Spatial resolution curve for two-dimensional mixing layers.