Turbulent flows respond to bounding walls with a predominant spanwise heterogeneity – that is, a heterogeneity parallel to the prevailing transport direction – with the formation of Reynolds-averaged turbulent secondary flows. These 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 resultant 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 – can vary in time through the introduction of time-dependent parameters. Upon
substitution of the base flow into the streamwise momentum and streamwise vorticity transport equation, and via the use of a vortex forcing model, we can 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 are responsible for the large-scale reversals observed in the numerical and experimental datasets.
Dr. William Anderson
Eugene McDermott Professor and Associate Professor of Mechanical Engineering at the University of Texas at Dallas. He received his doctoral degree in Mechanical Engineering from Johns Hopkins University in 2011. His research interests are primarily numerical simulation of small-scale geophysical turbulence and fundamental processes in rough-wall turbulence. He is a 2014 recipient of the Air Force Office of Scientific Research Young Investigator Program award. His research has been supported by the Army Research Office, National Science Foundation, Air Force Office of Scientific Research, and Texas General Land Office.