In this paper, a dynamic subgrid scale (SGS) stress model based on Speziale’s quadratic nonlinear constitutive relation [C. G. Speziale, J. Fluid Mech. 178, 459 (1987); T. B. Gatski and C. G. Speziale, J. Fluid Mech. 254, 59 (1993)] is proposed, which includes the conventional dynamic SGS model as its first-order approximation. The closure method utilizes both the symmetric and antisymmetric parts of the resolved velocity gradient, and allows for a nonlinear anisotropic representation of the SGS stress tensor. Unlike the conventional Smagorinsky type modeling approaches, the proposed model does not require an alignment between the SGS stress tensor and the resolved strain rate tensor. It exhibits significant flexibility in self-calibration of the model coefficients, and local stability without the need for plane averaging to avoid excessive backscatter of SGS turbulence kinetic energy and potential modeling singularity problems. It also allows for variable tensorial geometric relations between the SGS stress and its constituent terms, and reflects both forward and backward scatters of SGS turbulence kinetic energy between the filtered and subgrid scales of motions. Turbulent Couette flow for Reynolds numbers (based on channel height and one half the velocity difference between the two plates) of 2600 and 4762 was used in numerical simulations to validate the proposed approach.

An experimental study was undertaken to investigate the effects of roughness on the structure of turbulent boundary layers in open channels. The study was carried out using a laser Doppler anemometer in shallow flows for three different types of rough surface, as well as a hydraulically smooth surface. The flow Reynolds number based on the boundary layer momentum thickness ranged from 1400 to 4000. The boundary layer thickness was comparable with the depth of flow and the turbulence intensity in the channel flow varied from 2 to 4 percent. The defect profile was correlated using an approach which allowed both the skin friction and wake strength to vary. The wake parameter was observed to vary significantly with the type of surface roughness in contradiction to the “wall similarity” hypothesis. Wall roughness also led to higher turbulence levels in the outer region of the boundary layer. The profound effect of surface roughness on the outer region as well as the effect of channel turbulence on the main flow indicates a strong interaction, which must be accounted for in turbulence models. [S0098-2202(00)00803-8]

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In this paper, an experimental investigation of the turbulence characteristics of a plane wall jet over smooth and rough surfaces, using laser Doppler anemometry (LDA), is reported. The Reynolds number based on the slot height and exit velocity of the jet was approximately Re = 7500. A 36-grit sheet was used as the rough surface, creating a transitionally rough flow regime (44<ks+<70). Both inner and outer scales were used to analyze the effects of surface roughness on the Reynolds stress profiles. Comparisons between the present results and other LDA and hot-wire anemometry studies for a smooth surface indicate a similar behavior for the Reynolds stress profiles. However, the magnitudes of the peak values of the Reynolds stress were higher than in most previous studies due to the lower slot Reynolds number. The present results indicate that surface roughness does not appear to significantly modify the Reynolds stress profiles in the outer region of the jet except for a reduction in the level. In contrast, surface roughness modifies both the shape and magnitudes of the Reynolds stress profiles in the inner layer. Due to the much higher friction velocity for a rough surface, the magnitudes of both the streamwise and wall-normal Reynolds stress decrease in the inner region when normalized using inner scales compared to the smooth-wall values.

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