Two-Dimensional Turbulent Mixing Layer

Подпись: 1 2 Подпись: 1 + erf

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

Подпись: du

Подпись: ш
Подпись: dy Подпись: maximum
Подпись: 8

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.