Rotation and curvature effects on Reynolds stresses in boundary-layers

Rotation effects on Reynolds stresses in boundary layers are studied by using Reynolds stress equations modelled in a rotating reference system. The resulting equations are applied to particular cases in which the rotation vector is either parallel or perpendicular to the plane of mean shear. Using a few simplifying hypotheses, Reynolds stresses are expressed by means of algebraic formulas from which rotation effects can be demonstrated. It is found that the rotation and curvature effects contribute significantly even for small values of rotation parameters. Thus, the classic hypothesis which consists of keeping terms in du/dy in Reynolds stress equations is a too restrictive hypothesis; any extra rate of strain needs to be kept in Reynolds stress equations even if it is small compared with du/dy. An analogy is also demonstrated between the effects of longitudinal wall curvature in the case of a stationary body and the effects of rotation of a two-dimensional boundary layer.