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This article can be considered as an extension of the paper of Fukagata et al. ͓Phys. Fluids 14, L73 ͑2002͔͒ 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 flow͒ 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.

An overlapping mesh methodology that is spectrally accurate in space and up to third-order accurate in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The ability to decompose a global domain into separate, but overlapping, subdomains eases mesh generation procedures and increases flexibility of modeling flows with complex geometries. The methodology employs implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrallyaccurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. The overlapping mesh methodology is thoroughly validated using two-dimensional and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal convergence is documented and is in agreement with the nominal order of accuracy of the solver. The influence of long integration times, as well as inflow-outflow global boundary conditions on the performance of the overlapping grid solver is assessed. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics with the overlapping grids is validated against published available experimental and other computation data. Scaling tests are presented that show near linear strong scaling, even for moderately large processor counts.

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Actuator line aerodynamics (AL) model is becoming increasingly popular for characterization of the flow field and the turbulent wake created by the rotating turbines. AL model does not require boundary layer resolution of the flow around turbine blades and is thus significantly more efficient than the fully-resolved computations. The current paper aims at performing spectral element simulations of AL model wind turbine response to a realistic neutral atmospheric boundary layer (ABL) flow field. In the present paper, we incorporate the benchmark results of neutral ABL simulations using a rough wall LES model at very high Reynolds number and results of wind turbine response to ABL flows using AL model.

We investigate the stability of a temporal discretization of interface terms in grid overlapping methods. A matrix stability analysis is performed on a model problem of the one-dimensional diffusion equation on overlapping grids. The scheme stability is first analyzed theoretically, and a proof of the unconditional stability of the first-order interface extrapolation scheme with the firstand second-order time integration for any overlap size is presented. For the higher-order schemes, we obtain explicit estimates of the spectral radius of the corresponding discrete matrix operator and document the values of the stability threshold depending on the number of grid points and the size of overlap. The influence of iterations on stability properties is also investigated. Numerical experiments are then presented relating the obtained stability bounds to the observed numerical values. Semidiscrete analysis confirms the derived scaling for the stability bounds.

It is known that longitudinal ribs manufactured in a flat surface act to reduce turbulent skin-friction drag, providing a moderate drag reduction of 4 to 8%. It is shown in this paper that this value can be increased by at least 50% if sinusoidal-like rods are used instead of conventional straight riblets. Large Eddy Simulation of a turbulent flow over a riblet-covered surface is performed for three cases: straight riblets and sinusoidal riblets with two different values of wavelength. All riblets have triangular cross-section. It is found that drag reduction with sinusoidal riblets depend strongly on the wavelength, showing a benefit over straight riblets for a larger value of the wavelength, and an opposite trendfor a smaller value. Different nature of the flow over straight and sinusoidal riblet surfaces is revealed by looking at crossflow motion in transverse planes, mean and instantaneous streamwise vorticity, and organized coherent structures. Turbulent statistics is compared between all three cases, crossflow turbulence intensity is reduced for sinusoidal riblets as opposed to straight riblets.