Numerical Study of Turbulent Channel Flows Perturbed by Spanwise Topographic Heterogeneity: Inner-Outer Interactions within Low- and High-Momentum Pathways

This work presents a study on secondary flows, driven and sustained due to topographical variations in the domain. The effects of these secondary flows on inner-outer interactions are then analyzed. This type of interaction between the large-scale structures residing in the logarithmic region and the small-scale structures in the near-wall region have been under extensive study recently. And efforts are being made to develop a predictive model for the dynamics of near-wall structures based on the measurements at a certain certain distance from the wall. Such a model has immense practical implication for large-eddy simulations. Existing work on amplitude modulation has been focused on smooth-wall flow, however recently roughness-induced changes on amplitude and frequency modulation are being studied which provides a better understanding of the interaction in real conditions. Here a similar study is presented using wavelet analysis to examine how spanwise heterogeneity affects the spectral density and correlation profiles, which provides a basis for the understanding of amplitude and frequency modulation. The topography under consideration are two Gaussian mounds placed 2H apart, where H is the flow depth, which induce a domain-scale secondary motion in the flow. The counter-rotating vortices are flanked on either side of the topography such that prominent upwelling and downwelling occurs above the low and high roughness respectively. Two cases with the maximum height of the topography as h/H = 0.05 and 0.1 are considered, and the results are compared with a homogeneous roughness case (h/H = 0). A change in the inclination angle of coherent structures is observed within downwelling region of the flow, however, it does not diminish inner-outer interactions. The extent to which secondary flows disrupts the distribution of spectral density across constituent wavelengths throughout the depth of the domain are also quantified. It is observed that the outer peak associated with the large-scale motions is preserved within the upwelling zone, but vanishes in the downwelling zone. Single- and two- point correlation profiles for low-, intermediate- and high-resolution are compared which validates the resolution independence. An important observation indicates that the selection of reference location while computing the two-point correlation profiles is quintessential. It is also revealed that the strength of modulation is not determined by the wavelength at which the spectral energy resides, but by a mere presence of energy above the separation scale.