Restricted Nonlinear Scales of Turbulent Secondary Flows over Spanwise Heterogeneous Roughness

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International Journal of Heat and Fluid Flow

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Recent studies, e.g., Wangsawijaya et al. (2020) have revealed the prevalence of streak meandering in turbulent flow over spanwise heterogeneous roughness. Here we exploit the scale decomposition inherent in the Restricted Nonlinear (RNL) modeling approach to further investigate this behavior. The RNL decomposition comprises a large-scale streamwise averaged mean with small-scale fluctuations about that mean defined through a dynamical restriction that leads to computational tractability. The simplified setting facilitates the study of secondary flow interacting with the large-scale streak via one-way coupling, thus enabling additional insight into relevant interaction mechanisms. In agreement with the experimental work, our results indicate that the energy of the large-scales is amplified over the low roughness region due to the secondary flow. The small-scales are shown to play a dominant role in the Reynolds stresses responsible for generation of the secondary flow. Conditional averaging of the RNL mean field reveals stronger momentum pathways and diminished energy over low roughness regions experiencing downwash in instances that differ from the time-averaged trends. Further analysis, via time-filtering, shows long time-scales pertinent to streak meandering are anti-correlated with instantaneous upwash/downwash motions that are the dominant contribution to the increased shear Reynolds stress observed over the low roughness strips.


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