Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session HA: Turbulence Theory II |
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Chair: Robert Rubinstein, NASA Langley Room: Long Beach Convention Center 101A |
Monday, November 22, 2010 10:30AM - 10:43AM |
HA.00001: Effect of polymer additives on bulk turbulence Heng-Dong Xi, Haitao Xu, Eberhard Bodenschatz In recent years, there is a rising interest on the effect of polymer additives on homogeneous and isotropic turbulence. We investigate experimentally the effect of minute high-molecular-weight polymers on the bulk turbulence. The experiments are carried out in a fully developed turbulent von Karman flow between two counter-rotating baffled disks. Using the three-dimensional Lagrangian Particle Tracking technique, we follow simultaneously many tracer particles seeded in the flow, from which we extract both Eulerian and Lagrangian statistics of the turbulence. We report the results from independently varying the control parameters: the Reynolds number, the Weissenberg number, and the polymer concentration in our experiments, with the focus on the last two. [Preview Abstract] |
Monday, November 22, 2010 10:43AM - 10:56AM |
HA.00002: de Gennes's theory of polymer drag reduction revisited Dong-Hyun Lee, Rayhaneh Akhavan The original theory of polymer drag reduction proposed by de Gennes $[1]$ and its re-interpretation for wall-bounded flows proposed by Sreenivasan \& White $[2]$ give predictions which are orders of magnitude off from both DNS results and available experimental data. A revised version of this theory is developed, in which the effect of the mean shear on polymer stretching is included, and the polymer is assumed to affect the dynamics of a turbulent scale when a small fraction, on the order of $\sim 3\%$, of the turbulence kinetic energy at that scale is redirected into the elastic energy of polymer. The revised theory gives predictions in quantitative agreement with DNS and experimental results for a number of polymer drag reduction features, including the criteria for onset of drag reduction, saturation of drag reduction, MDR, and the range of turbulent scales affected by the polymer. A complete theory of polymer drag reduction is proposed to show how this minimal exchange of energy between the polymer and turbulence can lead to the dramatic drag reductions observed with polymers.\\[4pt] [1] de Gennes, Physica {\bf 140A}, p.9 (1986).\\[0pt] [2] Sreenivasan \& White, J.~Fluid Mech. {\bf 409}, p.149 (2000) [Preview Abstract] |
Monday, November 22, 2010 10:56AM - 11:09AM |
HA.00003: Statistics of the Energy Dissipation Rate and Local Enstrophy in Turbulent Channel Flow Joerg Schumacher, Peter E. Hamlington, Dmitry Krasnov, Thomas Boeck Using high-resolution direct numerical simulations, the height and Reynolds number dependence of the higher-order statistics of the energy dissipation rate and local enstrophy are examined in incompressible, fully-developed turbulent channel flow. The statistics are studied at a range of wall distances, spanning the viscous sublayer to the channel flow centerline, for friction Reynolds numbers $Re_\tau=180$ and $Re_\tau=381$. The high resolution of the simulations allows dissipation and enstrophy moments up to fourth order to be calculated. These moments show a dependence on the distance from the wall, and Reynolds number effects are observed at the edge of the logarithmic layer for the enstrophy. Conditional analysis based on locations of intense vorticity is also carried out in order to determine the contribution of vortical structures to the moments of the dissipation and enstrophy. Our analysis shows that, for the simulation at the larger Reynolds number, the small-scale fluctuations of both dissipation and enstr ophy become independent of distance from the wall for $z^+ > 100$. [Preview Abstract] |
Monday, November 22, 2010 11:09AM - 11:22AM |
HA.00004: On a self-sustaining process at large scale in the turbulent channel flow Yongyun Hwang, Carlo Cossu The near-wall region of wall-bounded turbulent flows has been understood as the place where an independent self-sustaining cycle exists, and the associated coherent motions in this region have been rigorously described with traveling waves and/or unstable periodic orbits in the phase space. On the other hand, in the outer region, turbulent motions have often been thought to be produced from the active near-wall cycles via so called the `bottom-up' process. However, recent investigations revealed that outer layer motions can experience significant non-normal amplifications. These findings suggest that self-sustaining processes could also exist at large scale. In this study, we consider a fully-developed turbulent channel at $Re_\tau \approx 550$. We show that large-scale and very-large-scale motions in the outer region can sustain even when smaller-scale structures in the near-wall and the logarithmic regions are artificially quenched. The self-sustaining process is active only at the lengths scales larger than $L_x \times L_z \approx 3h \times 1.5h$, in good accordance with the most energetic length scales observed in the outer region. [Preview Abstract] |
Monday, November 22, 2010 11:22AM - 11:35AM |
HA.00005: An analytical formulation for the 1D energy spectra in equilibrium wall-bounded turbulence Yifeng Tang, Rayhaneh Akhavan While a number of analytical formulations exist for the inertial
and dissipation range 3D energy spectra in homogeneous, isotropic
turbulence, none of these formulations can be directly applied to
the near-wall region of equilibrium wall-bounded flows due to
the strong anisotropy of the turbulence structure in the
near-wall region. In homogeneous, isotropic turbulence, the 1D
spectrum is related to the 3D spectrum through
$E^{1D}(k/k_d)/(\varepsilon\nu^5)^{\frac{1}{4}} =
2\int_{k/k_d}^{\infty}{E^{3D}(\tilde{k})/(\varepsilon\nu^5)^{\frac{1}{4}}}{\frac{d\tilde{k}}{\tilde{k}}}
=
2\int_{k/k_d}^{\infty}{A_K\tilde{k}^{-\frac{5}{3}}F(\tilde{k})}{\frac{d\tilde{k}}{\tilde{k}}}$,
where $A_K$ is the Kolmogorov constant, $F(\tilde{k})$ is the
dissipation range correction to the Kolmogorov spectrum,
$\varepsilon$ is the volume-averaged rate of dissipation, and
$k_d = (\varepsilon/\nu^3)^{\frac{1}{4}}$ is the Kolmogorov
wavenumber. It is shown that an analytical formulation for the
inertial and dissipation range 1D energy spectra in equilibrium
wall-bounded turbulence can be obtained from
$E^{1D}(k_\alpha/k_{d,\alpha})/(\varepsilon_\alpha\nu^5)^{\frac{1}{4}}
=
2\int_{k_\alpha/k_{d,\alpha}}^{\infty}{A_K\tilde{k}^{-\frac{5}{3}}F(\tilde{k})}{\frac{d\tilde{k}}{\tilde{k}}}$,
where $\varepsilon_\alpha(z) = \langle{
3\nu[{\frac{\partial{u_i}}{\partial{x_\alpha}}\frac{\partial{u_i}}{\partial{x_\alpha}}}
+
{\frac{\partial}{\partial{x_\alpha}}(u_i\frac{\partial{u_\alpha}}{\partial{x_i}})}]
}\rangle$ denotes the contribution of the gradients in the
$\alpha$-direction to the total dissipation at wall-normal
location $z$, $\langle{~.~}\rangle$ denotes an ensemble average,
and $k_{d,\alpha} = (\varepsilon_\alpha/\nu^3)^{\frac{1}{4}}$.
The validity of the proposed formulation is demonstrated using 1D
spectra obtained from DNS databases of turbulent channel flow
with $180 |
Monday, November 22, 2010 11:35AM - 11:48AM |
HA.00006: The log layer in incompressible and compressible turbulence Robert Rubinstein The ``log law'' for incompressible wall-bounded turbulence describes a self-similar flow the properties of which follow from the hypothesis that a constant stress region exists. The compressible extension is not straightforward because the density dependence requires an additional assumption. The ``compressible law of the wall'' of van Driest follows by requiring that the length scale be independent of density. We consider the consistency of this and alternative hypotheses with the variable density Navier-Stokes equations and derive the locality conditions imposed by the relation between the log layer and the viscous sub-layer and wake region. [Preview Abstract] |
Monday, November 22, 2010 11:48AM - 12:01PM |
HA.00007: Quantifying the Effects of Large Scale Intermittency in Turbulence Daniel Blum, Greg Voth We report on the effect of fluctuating energy at the largest scales on various turbulence statistics. Measurements were made in a flow between oscillating grids which contains nearly homogeneous turbulence in an 1,100 l tank which produces R{\_}lambda= 285. By modulating the oscillating grid frequency we can introduce temporal variations in the injected energy which allows us to control the level of large scale intermittency. We measure the effects of this large scale intermittency by conditioning Eulerian structure functions on the large scale velocity. With constant oscillating grid frequency, the conditional functions show a clear dependence on the large scale velocity, but increasing the large scale intermittency (by increasing the frequency modulation) substantially increases this dependence. Such control allows us to quantify the effects of large scale intermittency on the various length scales of the structure functions, down to the small scales. [Preview Abstract] |
Monday, November 22, 2010 12:01PM - 12:14PM |
HA.00008: Small-scale intermittency in anisotropic stably stratified turbulence Saba Almalkie, Stephen de Bruyn Kops The statistical characteristics of small scale turbulence in the presence of large-scale anisotropies are examined using high-resolution direct numerical simulation of stably stratified turbulence. The effects of stratification and residual anisotropy at smaller scales on turbulence intermittency is of primary interest. The scale dependency of intermittency in stratified turbulence is quantified using statistics of the locally averaged energy dissipation rate and the scaling exponents of its moments over a range of Froude numbers. The results are compared to the corresponding statistics from simulations of isotropic homogeneous turbulence with comparable numerical resolution and Reynolds numbers. The reliability of conventional surrogates of energy dissipation rate in estimating intermittency of flows dominated by large scale anisotropy is also discussed. [Preview Abstract] |
Monday, November 22, 2010 12:14PM - 12:27PM |
HA.00009: Measuring anisotropy of conditional structure functions in turbulence using real-time image compression Susantha Wijesinghe, Daniel Blum, Greg Voth We use SO(3) decomposition to study the anisotropy of conditional structure functions in a turbulent flow between oscillating grids. The flow between two grids in a 1m x 1m x 1.5m tank achieves R$_{\lambda}$=285 while having a central region that is nearly homogeneous with low anisotropy and a region near the grid with much greater inhomogeneity and anisotropy. A 3D particle tracking system with 4 high speed digital cameras records particle trajectories. We condition Eulerian velocity structure functions on the large scale velocity which reveals the effects of large scales on small scale statistics. Real-time image compression using an FPGA (Field Programmable Gate Array) makes it possible to continuously record the huge data sets necessary to decompose conditional structure functions to extract the anisotropic contributions. [Preview Abstract] |
Monday, November 22, 2010 12:27PM - 12:40PM |
HA.00010: On Multiscale Geometrical Statistics of Anisotropic Homogeneous Turbulence Frank Jacobitz, Kai Schneider, Wouter Bos, Marie Farge Statistical geometrical properties of a variety of prototypical turbulent flows, including forced isotropic turbulence, sheared turbulence, rotating sheared turbulence, and rotating turbulence, are investigated in this study using results obtained from direct numerical simulations. Distributions of velocity helicity show a preference for two-dimensionalization for flows with growing turbulence and a trend to helical motion for decaying turbulence. A scale-dependent analysis shows a trend to two-dimensionalization for large scales of motion and a preference for helical motion at small scales. These results are consistent for all flows considered in this study. Joint probability distribution functions show a strong correlation of the signs of velocity helicity and vorticity helicity for all cases. This correlation supports the conjecture of Sanada (PRL 1993) that the vorticity helicity diminishes velocity helicity. [Preview Abstract] |
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