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Monday, August 29, 2022 – 12:00PM to 1:00PM
Professor William Anderson, Mechanical Engineering, University of Texas at Dallas
Turbulent flows respond to bounding walls with a predominant heterogeneity in the streamwise or spanwise direction with formation of an internal boundary layer or counter-rotating secondary rolls, respectively; the former has been the topic of a sustained research effort, while the latter has only very recently captured the attention of the wall turbulence community. For the case of spanwise heterogeneity, the resultant secondary rolls are known to be a manifestation of Prandtl's secondary flow of the second kind: driven and sustained by the existence of spatial heterogeneities in the Reynolds (turbulent) stresses, all of which vanish in the absence of spanwise heterogeneity. Results from large-eddy simulations and complementary experimental measurements of flow over spanwise-heterogeneous surfaces are shown: the secondary cell location is clearly correlated with the surface characteristics, which ultimately dictates the Reynolds-averaged flow patterns. However, results also show the potential for instantaneous sign reversals in the rotational sense of the secondary cells. This is accomplished with probability density functions and conditional sampling. In order to address this further, a base flow representing the streamwise rolls is introduced. The base flow intensity - based on a leading-order Galerkin projection - is allowed to vary in time through the introduction of time-dependent parameters. Upon substitution of the base flow into the streamwise momentum and streamwise vorticity transport equations, and via use of a vortex forcing model, we are able to assess the phase-space evolution (orbit) of the resulting system of ordinary differential equations. The system resembles the Lorenz system, but the forcing conditions differ intrinsically. Nevertheless, the system reveals that chaotic, non-periodic trajectories are possible for sufficient inertial conditions. Poincaré projection is used to assess the conditions needed for chaos, and to estimate the fractal dimension of the attractor. Its simplicity notwithstanding, the propensity for chaotic, non-periodic trajectories in the base flow model suggests similar dynamics is responsible for the large-scale reversals observed in the numerical and experimental datasets. New results on flow response to large-scale heterogeneity at oblique angles are also shown.