Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session E23: Turbulence: Theory III - Wall-Bounded Flows |
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Chair: Dennice Gayme, Johns Hopkins University Room: 318 |
Sunday, November 24, 2013 4:45PM - 4:58PM |
E23.00001: Phase relationships and amplitude modulation in wall turbulence Beverley McKeon, Daniel Chung We present a framework for predicting the interactions between the large-scale motion and the underlying stress fluctuations in wall turbulence, or the apparent amplitude modulation effect described by, e.g., Mathis et al (Phys. Fluids, 2011). The dynamical equations for stress fluctuations are obtained from a scale decomposition of the governing equations which can be shown to be consistent with the resolvent analysis of McKeon \& Sharma (2010). The spatial phase shift between the large-scale motion and stress fluctuations is revealed as being related to critical layer behavior identified therein. Consistent with experiments, the analysis predicts that the zero-crossing height of the amplitude modulation statistic, and corresponding $\pi/2$ lead of the small scales with respect to the large scale identified via cross-correlation techniques, coincides with the wall-normal location of the peak large-scale energetic activity. Simple approximations in the logarithmic region of the mean velocity link the behavior of the amplitude modulation statistic to the wall-normal profiles of the background (mean) turbulent stresses. [Preview Abstract] |
Sunday, November 24, 2013 4:58PM - 5:11PM |
E23.00002: An Integral Method to Evaluate Wall Heat Flux Suitable For Experimental Data Alireza Ebadi, Faraz Mehdi, Christopher White An integral method to evaluate wall heat flux in turbulent boundary layers is presented. The method is mathematically exact and has the advantage of having no explicit streamwise gradient terms, thus making it amenable to experimental data. Using existing data sets, the method is shown to work in both zero- and adverse-pressure gradient boundary layers. The method is particularly useful for the latter case where Reynolds analogy does not hold and the wall heat flux must be measured directly. [Preview Abstract] |
Sunday, November 24, 2013 5:11PM - 5:24PM |
E23.00003: Universal Karman constant in canonical wall turbulence Zhen-Su She, Xi Chen, Fazle Hussain A universal Karman constant $\kappa \approx 0.45$ is obtained for all three canonical wall-bounded turbulent flows (channel, pipe and turbulent boundary layer - TBL) for Reynolds numbers (\textit{Re}) larger than 5,000. A New method for measuring $\kappa $ from mean velocity profile (MVP) data, reported previously, is applied to 54 sets of recent experimental data (24 for smooth pipe, 8 for rough pipe, 6 for smooth channel and 16 for smooth TBL) and 3 sets of DNS data (2 for smooth channel, 1 for smooth pipe), which uniformly supports the idea that Karman constant is universal, contrary to the recent suggestions that kappa is a function of Re and geometry; its value is almost 10{\%} larger than the classical value of 0.41, with even higher values reported at moderate \textit{Re}. The validity of the log-law seems to be thus firmly established. [Preview Abstract] |
Sunday, November 24, 2013 5:24PM - 5:37PM |
E23.00004: Variation approach to describe bulk flow of wall turbulence Xi Chen, Fazle Hussain, Zhen-Su She A mean field theory for the mean velocity profile in the bulk of canonical wall bounded turbulence (channel, pipe and turbulent boundary layer) is developed, in good agreement with empirical data over a wide range of the Reynolds number (Re). In analogy to the Landau's mean field theory (1937) using order parameter to explain phase transition in critical phenomena, the current theory builds a variational description for a characteristic length scale, which minimizes the effective free energy for turbulent momentum flux. It leads to a defect power law for the characteristic length scale, not only offering a novel derivation for the logarithmic mean velocity profile, but also quantifying the geometry effect in turbulent channel and pipe flows. Finally, the Karman constant is proved to be a universal constant under such the variational description, and its physical interpretation is also presented. [Preview Abstract] |
Sunday, November 24, 2013 5:37PM - 5:50PM |
E23.00005: Nonlinearity and the energy cascade in the resolvent analysis of wall turbulence Ati Sharma, Beverley McKeon The resolvent analysis of wall turbulence can be used to characterise velocity response modes derived from a gain analysis of the linear resolvent operator obtained from the Navier-Stokes equations projected into wavenumber-frequency space ($k,n,\omega$), e.g. McKeon \& Sharma (JFM, 2010). Simple combinations of response modes that are triadically consistent in ($k,n,\omega$) have been shown to give rise to complex coherent structure, Sharma \& McKeon (JFM, 2013), however the selection of these combinations was phenomenologically-driven. In the full analysis, the nonlinear interaction between response modes necessarily gives rise to self-sustaining turbulence. In this paper, we report how the nonlinearity acts to reinforce certain combinations of modes over others, cascades energy between wavenumbers and modes, and determines the relative phase and amplitude of the resolvent response modes. [Preview Abstract] |
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