This article can be considered as an extension of the paper of Fukagata et al. [Phys. Fluids 14, L73 (2002)] which derived an analytical expression for the constituent contributions to skin friction in a turbulent channel, pipe, and plane boundary layer flows. In this paper, we extend the theoretical analysis of Fukagata et al. (formerly limited to canonical cases with two-dimensional mean flow) to a fully three-dimensional situation allowing complex wall shapes. We start our analysis by considering arbitrarily shaped surfaces and then formulate a restriction on a surface shape for which the current analysis is valid. A theoretical formula for skin friction coefficient is thus given for streamwise and spanwise homogeneous surfaces of any shape, as well as some more complex configurations, including spanwise-periodic wavy patterns. The theoretical analysis is validated using the results of large eddy simulations of a turbulent flow over straight and wavy riblets with triangular and knife-blade cross-sections. Decomposition of skin friction into different constituent contributions allows us to analyze the influence of different dynamical effects on a skin friction modification by riblet-covered surfaces.
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Peet et al. (2009) studied this question.