Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session M35: Turbulence: Theory and Semi-empirical Models |
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Chair: P.K. Yeung, Georgia Tech University Room: Oregon Ballroom 204 |
Tuesday, November 22, 2016 8:00AM - 8:13AM |
M35.00001: Scaling properties of the mean equation for passive scalar in turbulent channel flow Ang Zhou, Sergio Pirozzoli, Joseph Klewicki Data from numerical simulations of fully developed turbulent channel flows subjected to a uniform and constant heat generation are used to explore the scaling behaviors admitted by the mean equation for passive scalar transport. The analysis proceeds in a manner similar to previous studies of mean momentum transport. Based on the relative magnitude of terms, the leading order balances in the equation organize into a four layer structure. The wall-normal widths of the layers exhibit significant dependencies both on Reynolds and Prandtl number, and these dependencies are analytically surmised and empirically validated. The passive scalar equation also admits an invariant form on each of a hierarchy of scaling layers. As with the momentum case, this hierarchy is quantified by its inner-normalized widths. The present findings indicate that the layer width distribution is increasingly approximated by a linear function of wall normal position with increasing ratio of Reynolds number to Prandtl number on a domain of the hierarchy where the molecular diffusion effect loses leading order. The analysis indicates that across this domain the square of the slope of the width distribution function is equivalent to the scalar Karman constant as Reynolds number goes to infinity. The data provide convincing evidence in support of this finding. [Preview Abstract] |
Tuesday, November 22, 2016 8:13AM - 8:26AM |
M35.00002: Three-dimensional structure of alternative Reynolds stresses in turbulent channels Kosuke Osawa, Javier Jimenez As explained in another talk in this meeting, the ambiguity of the fluxes in the momentum conservation law allows alternative definitions for the Reynolds stresses. We study here the three-dimensional structures of the tangential stress that minimises the total r.m.s. flux fluctuations in turbulent channels at several $Re_{\tau}\ge 10^3$. As in the case of the classical shear stress, it is found that the structures can be classified into wall-detached and wall-attached families. The latter carry most of the overall stress and are geometrically self-similar, although less elongated than for the classical ones. Although they span the full range of scales from viscous to the channel height, larger structures are less common than in the classical case, apparently missing very large `global' modes. They are also less fractal $(D_F \approx 2.5)$ than the `sponges of flakes' of the classical quadrant structures $(D_F \approx 2.1)$, and more inclined with respect to the wall, $45^o$ versus $20^o$, suggesting that they may be related to the `hairpin legs' discussed by several authors. [Preview Abstract] |
Tuesday, November 22, 2016 8:26AM - 8:39AM |
M35.00003: Determination of the Reynolds stress in canonical flow geometries. T.-W. Lee We present a new theoretical result for solving for the Reynolds stress in turbulent flows, and show how it works for canonical flow geometries: flow over a flat plate, channel flow, and axi-symmetric jets. The theory is based on fundamental physics of turbulence transport. Comparison of the current theoretical result with experimental and DNS (direct numerical simulation) data show good agreement, and various considerations of the results indicate that this is not a fortuitous coincidence, and point to radically new solutions for Reynolds stress. The theory leads to a closed-form formula for the Reynolds stress in terms of the root variables, such as the mean velocity, velocity gradient, turbulence kinetic energy and a viscous term. The form of the solution also provides insight on how the Reynolds stress is generated and distributed. This is \textit{not} a modeling study, but a theoretical one based on physical principles although some of the nuances are still being examined. Details of the theory are submitted elsewhere, and also will be presented at the conference. The theoretical result for the Reynolds stress is compared with various experimental and DNS data. The agreement is nearly perfect at low Reynolds numbers, which gives some confidence that we have captured the true physics of turbulent transport, and that the results are not a fortuitous coincidence. [Preview Abstract] |
Tuesday, November 22, 2016 8:39AM - 8:52AM |
M35.00004: Corrections to the 4/5-law for decaying turbulence Jonas Boschung, Michael Gauding, Fabian Hennig, Dominik Denker, Heinz Pitsch We examine finite Reynolds number contributions to the inertial range solution of the third order structure functions stemming from the unsteady and viscous terms for decaying turbulence. Under the assumption that the second order correlations f and g are self-similar under a coordinate change, we are able to rewrite the exact second order equations as function of a normalised scale r only with the decay exponent as a parameter. We close the resulting system of equations using a power law and an eddy-viscosity ansatz. If we further assume K41 scaling, we find the same Reynolds number dependence as previously in the literature. [Preview Abstract] |
Tuesday, November 22, 2016 8:52AM - 9:05AM |
M35.00005: Wall-roughness induced ultimate Taylor-Couette turbulence Xiaojue Zhu, Roberto Verzicco, Detlef Lohse We use direct numerical simulations to examine the Taylor number ($Ta$) dependence of the torque required to drive rotating cylinders with smooth and/or rough walls in Taylor-Couette turbulence. With the introduction of both inner {\it{and}} outer wall roughness, the scaling of the dimensionless torque $Nu_\omega$ becomes $Nu_\omega \propto Ta^{0.5 \pm 0.01}$. We interpret this through an extension of the Grossmann-Lohse theroy [Phys. Fluids 23, 045108 (2011)], by accounting for the log-law of the wall in the presence of roughness. The logarithmic correction $L(Re)$ in the relation $Nu_\omega \propto Ta^{1/2} \times L(Re)$, which leads to the effective scaling $Nu_\omega \propto Ta^{0.38}$ in the ultimate regime for the smooth case, gets canceled out and Kraichnan's pure ultimate scaling $Nu_\omega \propto Ta^{1/2}$ [R. H. Kraichnan, Phys. Fluids 5, 1374 (1962)] is recovered. [Preview Abstract] |
Tuesday, November 22, 2016 9:05AM - 9:18AM |
M35.00006: Turbulent boundary-layer flow over a long plate with a uniformly rough surface D.I. Pullin, N. Hutchins, D. Chung We develop a semi-empirical model for a zero-pressure-gradient turbulent boundary layer flowing over a flat plate of length $L$ and covered with homogeneous, uniform roughness of equivalent sand-grain roughness $k_s$. Use is made of the log-wake model for the stream-wise mean velocity that includes a transitional-asymptotic roughness correction together with the K\'arm\'an integral relation. For $Re_L=U_\infty\,L/\nu$ very large, the velocity ratio $S=U_\infty/u_\tau$ at $x=L$, the plate drag coefficient $C_D$ and other mean-flow properties can be obtained for given $Re_L$ and $k_s/L$. Three distinct cases are discussed; the smooth-wall, fully-rough and long-plate limits. Of these, the most important is the fully-rough case where $k_s/L$ is fixed with $Re_L\to \infty$, giving that $C_D=f_1(k_s/L)$, $\delta_L/L=f_2(k_s/L)$ independent of $Re_L$. This agrees qualitatively with Granville (1958) although somewhat different $C_D(k_s/L)$ is obtained owing to the present use of a wake function. Thus for a given $k_s$ and $x = L$ location on a fully rough vehicle, the boundary layer thickness and the drag coefficient is invariant with unit Reynolds number $U_\infty/\nu$. [Preview Abstract] |
Tuesday, November 22, 2016 9:18AM - 9:31AM |
M35.00007: Sonic eddy model of the turbulent boundary layer Robert Breidenthal, Paul Dintilhac, Owen Williams A model of the compressible turbulent boundary layer is proposed. It is based on the notion that turbulent transport by an eddy requires that information of nonsteady events propagates across the diameter of that eddy during one rotation period. The finite acoustic signaling speed then controls the turbulent fluxes. As a consequence, the fluxes are limited by the largest eddies that satisfies this requirement. Therefore "sonic eddies" with a rotational Mach number of about unity would determine the skin friction, which is predicted to vary inversely with Mach number. This sonic eddy model contrasts with conventional models that are based on the energy equation and variations in the density. The effect of density variations is known to be weak in free shear flows, and the sonic eddy model assumes the same for the boundary layer. In general, Mach number plays two simultaneous roles in compressible flow, one related to signaling and the other related to the energy equation. The predictions of the model are compared with experimental data and DNS results from the literature. [Preview Abstract] |
Tuesday, November 22, 2016 9:31AM - 9:44AM |
M35.00008: Decay of passive scalar fluctuations in axisymmetric turbulence Katsunori Yoshimatsu, Peter A. Davidson, Yukio Kaneda Passive scalar fluctuations in axisymmetric Saffman turbulence are examined theoretically and numerically. Theoretical predictions are verified by direct numerical simulation (DNS). According to the DNS, self-similar decay of the turbulence and the persistency of the large-scale anisotropy are found for its fully developed turbulence. The DNS confirms the time-independence of the Corrsin integral. [Preview Abstract] |
Tuesday, November 22, 2016 9:44AM - 9:57AM |
M35.00009: Characteristics of space-time energy spectra in turbulent Shear flows Ting Wu, Chenghui Geng, Shizhao Wang, Guowei He An energy spectrum over wavenumbers is preliminarily characterized by its mean and standard deviation. The mean is corresponding to the characteristic wavenumber at the center of mass of energy spectrum and the standard deviation corresponding to the bandwidth of energy spectrum. In the present study, we derive the exact expressions for the characteristic wavenumbers and the bandwidths of space-time energy spectra at fixed frequencies. The characteristic wavenumbers are used to calculate the phase velocities that bridge from temporal spectra to space-time spectra. The bandwidths are used to measure the well-known spectral broadening. It is shown that phase velocities alone are insufficient to determine the bandwidths of energy spectra. As a result, Taylor's frozen-flow model and Kraichnan and Tannekes' random-sweeping model predict the narrower bandwidths of energy spectra. Therefore, in addition to phase velocities, bandwidths are introduced to rescale the space-time energy spectra that are obtained from phase velocities, leading to the correct bandwidths of energy spectra. Existing data from direct numerical simulation of turbulent channel flows is used to validate this rescaling technique. [Preview Abstract] |
Tuesday, November 22, 2016 9:57AM - 10:10AM |
M35.00010: Irreversibility-inversions in 2D turbulence Andrew Bragg, Filippo De Lillo, Guido Boffetta We consider a recent theoretical prediction that for inertial particles in 2D turbulence, the nature of the irreversibility of their pair dispersion inverts when the particle inertia exceeds a certain value (Bragg et al., Phys. Fluids 28, 013305, 2016). In particular, when the particle Stokes number, $St$, is below a certain value, the forward-in-time (FIT) dispersion should be faster than the backward-in-time (BIT) dispersion, but for $St$ above this value, this should invert so that BIT becomes faster than FIT dispersion. This non-trivial behavior arises because of the competition between two physically distinct irreversibility mechanisms that operate in different regimes of $St$. In 3D turbulence, both mechanisms act to produce faster BIT than FIT dispersion, but in 2D, the two mechanisms have opposite effects because of the inverse energy cascade in the turbulent velocity field. We supplement the qualitative argument given by Bragg et al. (Phys. Fluids 28, 013305, 2016) by deriving quantitative predictions of this effect in the short-time dispersion limit. These predictions are then confirmed by results of inertial particle dispersion in a direct numerical simulation of 2D turbulence. [Preview Abstract] |
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