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If we employ Prandtl's logarithmic velocity profile (du/dy = [u.sub.*]/ky) in formula (11), then the Rouse formula (3) can be achieved.
A logarithmic velocity profile as presented in Figure 3 is created using user-defined functions (UDF) in Fluent based on the following formulation [22]:
This displacement can be expressed formally by introducing an equivalent viscosity [[mu]] into the well-known logarithmic velocity profile, giving: