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An immersed boundary technique is used to model a riblet covered surface on one wall of a channel bounding fully developed turbulent flow. The conjecture that the beneficial drag reduction effect of riblets is a result of the damping of cross-flow velocity fluctuations is then examined. This possibility has been discussed by others but is unverified. The damping effect is explicitly modelled by applying a cross-flow damping force field in elongated streamwise zones with a height and spacing corresponding to the riblet crests. The same trends are observed in the turbulence profiles above both riblet and damped surfaces, thus supporting cross-flow damping as a beneficial mechanism. It is found in the examples presented that the effect of the riblets on the mean flow field quantities (mean velocity profile, velocity fluctuations, Reynolds shear stress, and low–speed sreak spacing) is small. The riblests cause a relatively small drag reduction of about 4%, a figure that is in rough agreement with experiments and other computations. The simulations also suggest a mechanism for the observed displacement of the turbulence quantities away from the wall. The immersed boundary technique used to model the riblets consists of creating an externally imposed spatially localized body force which opposes the flow velocity and creates a riblet-like surface. For unstead viscous flow the calculation of the force is done with a feedback scheme in which the velocity is used to iteratively determine the desired value. In particular, the surface body force is determined by the relation f ( x s , t ) = α ∫ t 0 U ( x s , t ′)d t ′ + β U ( x s , t ) for surface points x s , velocity U time t and negative constants α and β. All simulations are done with a spectral code in a single computational domain without any mapping of the mesh. The combination of the immersed boundary and spectral techniques can potentially be used to solve other problems having complex geometry and flow physics.
Goldstein et al. (Fri,) studied this question.