Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session G6: Turbulence Theory II |
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Chair: Robert Rubinstein, NASA Langley Research Center Room: 309 |
Monday, November 21, 2011 8:00AM - 8:13AM |
G6.00001: Dependence of decaying homogeneous turbulence on initial/boundary conditions Pedro Valente, Christos Vassilicos The von K\'arm\'an-Howarth equation implies an infinity of invariants corresponding to an infinity of different asymptotic behaviours of the double and triple velocity correlation functions at infinite separations. Given an asymptotic behaviour at infinity for which the Birkhoff-Saffman invariant is not infinite, there are either none, or only one or only two finite invariants. If there are two, one of them is the Loitsyansky invariant and the decay of large eddies cannot be self-similar. We examine the consequences of this infinity of invariants on turbulence decay. We then analyse recent wind tunnel data by Krogstad which show that the far-downstream decay of approximately homogeneous isotropic turbulent flows are, invariably, clearly different from Saffman turbulence; and that very clearly marked differences exist between the far downstream turbulence behaviours generated by conventional grids and multiscale cross grids. (See Phys. Lett. A375, 1010-1013 (2011) and http://arxiv.org/pdf/1106.0603) [Preview Abstract] |
Monday, November 21, 2011 8:13AM - 8:26AM |
G6.00002: Direct Numerical Simulations of Homogeneous Turbulent Shear Flow with Initial Mean Helicity Frank Jacobitz, Kai Schneider, Wouter Bos, Marie Farge Direct numerical simulations of homogeneous turbulent shear flows are performed in order to investigate the impact of mean helicity imposed on the isotropic initial conditions. As the flows are advanced in time, exponential growth of the turbulent kinetic energy is found after flow anisotropy has developed. The mean helicity, however, is observed to decay due to the symmetry properties of the flow. Distributions of helicity are observed to be skewed according to its initial value. A wavelet-based scale-dependent analysis shows that this skewness is largest for large scales of the turbulent motion and decreases for smaller scales. In addition, a trend to two-dimensionalization for large scales of motion and a preference for helical motion at small scales is found. Joint probability distribution functions show a strong correlation of the signs of helicity and super-helicity for all cases, including Gaussian random fields. This correlation supports the conjecture that super-helicity dissipates helicity. [Preview Abstract] |
Monday, November 21, 2011 8:26AM - 8:39AM |
G6.00003: Determination of the Turbulent Decay Exponent J. Blair Perot, Chris Zusi All theories concerning the decay of isotropic turbulence agree that the turbulent kinetic energy has a power law dependence on time. However, there is significant disagreement about what the value of the exponent should be for this power law. The primary theories, proposed by researchers such as Batchelor, Townsend, and Kolmogorov, have the decay exponent at values of 1, 6/5, 10/7, 3/2, 2, and 5/2. The debate over the decay exponent has remained unresolved for many decades because the decay exponent is an extremely sensitive quantity. Experiments have decay times which are too short to be able to accurately differentiate between the various theoretical possibilities, and all prior numerical simulations of decaying turbulence impose the decay rate \textit{a priori} via the choice of initial conditions. In this work, direct numerical simulation is used to achieve very long decay times, and the initial turbulence is generated by the Navier-Stokes equations and is not imposed. The initial turbulence is created by the stirring action of the flow past 768 small randomly placed cubes. Stirring occurs at 1/30$^{th}$ of the simulation domain size so that the low wavenumber and large scale behavior of the turbulent spectrum which dictates the decay rate is generated by the fluid and is not imposed. It is shown that in all 16 simulations the decay exponent closely matches the theoretical predictions of Saffman at both high and low Reynolds numbers. Perot, AIP Advances~\textbf{1}, 022104 (2011). [Preview Abstract] |
Monday, November 21, 2011 8:39AM - 8:52AM |
G6.00004: On the local nature of the pressure Hessian in fluid turbulence Laurent Chevillard, Emmanuel Leveque, Francesco Taddia, Charles Meneveau, Huidan Yu, Carlos Rosales The Lagrangian dynamics of the velocity gradient tensor A in isotropic and homogeneous turbulence depend on the joint action of the self-streching term and the pressure Hessian. Existing closures for pressure effects in terms of A are unable to reproduce one important statistical role played by the anisotropic part of the pressure Hessian, namely the redistribution of the probabilities towards enstrophy production dominated regions. As a step towards elucidating the required properties of closures, we study several synthetic velocity fields and how well they reproduce anisotropic pressure effects. It is found that synthetic (i) Gaussian, (ii) Multifractal and (iii) Minimal Turnover Lagrangian Map (MTLM) incompressible velocity fields reproduce many features of real pressure fields that are obtained from numerical simulations of the Navier Stokes equations, including the redistribution towards enstrophy-production regions. The synthetic fields include both spatially local, and nonlocal, anisotropic pressure effects. However, we show that the local effects appear to be the most important ones: by assuming that the pressure Hessian is local in space, an expression in terms of the Hessian of the second invariant Q of the velocity gradient tensor can be obtained. This term is found to be well correlated with the true pressure Hessian both in terms of eigenvalue magnitudes and eigenvector alignments. [Preview Abstract] |
Monday, November 21, 2011 8:52AM - 9:05AM |
G6.00005: The intriguing mechanism of drag reduction by dilute polymer solutions Rayhaneh Akhavan, Dong-Hyun Lee The mechanism of drag reduction by dilute polymer solutions is investigated using results from DNS in turbulent channel flow. Drag reductions of up to 56\%, corresponding to Virk's MDR, are achieved through a most intriguing, energetically insignificant, yet dynamically significant, mechanism. The cornerstone of this mechanism is a redirection of a small fraction, of no more than 5\% on a volume-averaged basis, of the turbulence kinetic energy (TKE) into the elastic energy of the polymer at select turbulent scales. This redirection of energy leads to a decrease in the fluctuating strain-rate at the affected scales, which, in turn, results in a drop in the pressure-strain correlation at these and neighboring scales. The drop in the pressure-strain correlation inhibits the transfer of TKE from the streamwise to cross-stream directions, resulting in a highly anisotropic state at the affected scales. This anisotropy inhibits the normal cascade of TKE to smaller scales. Thus the minute extraction of energy by the polymer initiates a ``self-amplifying'' sequence of events in which turbulence loses its three-dimensionality and the turbulence energy cascade is inhibited. The magnitude of drag reduction is determined by the range of affected scales, which is a function of $We_\tau$ and polymer concentration. For maximum drag reduction, all large scales throughout the channel need to experience the minimal initial extraction of TKE by the polymer. [Preview Abstract] |
Monday, November 21, 2011 9:05AM - 9:18AM |
G6.00006: Skin-Friction Drag Reduction in Turbulent Channel Flow by a Scale-Dependent Molecular Viscosity Dong-Hyun Lee, Rayhaneh Akhavan In prior work, we have proposed that the primary mechanism of drag reduction by dilute polymer solutions is the polymer's extraction of a minute amount of turbulence kinetic energy from the large turbulent scales. Here, we mimic this mechanism by performing DNS with a scale-dependent molecular viscosity in turbulent channel flow. Simulations were performed in channels of size $10h \times 5h \times 2h$ and $40h \times 10h \times 2h$ at a base Reynolds number of $Re_{\tau} \sim 230$. Drag reductions of $50\%$ and higher were observed when the molecular viscosity was artificially raised from $\nu_s$ to $(3-4)\nu_s$ in a band of large-scale wavenumbers corresponding to $0.01 < \sqrt{k_x^2 +k_y^2}/k_d < 0.1$. Many characteristics of drag reduction by dilute polymer solutions were reproduced by the scale-dependent molecular viscosity, including strong anisotropy in the turbulence structure, interruption of the turbulent energy cascade, a pileup of turbulence kinetic energy at the large scales in the streamwise component of the fluctuating velocity, and a shift of the peak of turbulence production away from the wall. These results open up new possibilities for devising novel turbulent skin-friction drag reduction strategies in wall flows. [Preview Abstract] |
Monday, November 21, 2011 9:18AM - 9:31AM |
G6.00007: Energy Dissipation Rate in Stably Stratified Turbulence Saba Almalkie, Stephen de Bruyn Kops One of the key issues in modeling complex flows is the characteristics of small scale turbulence under the influence of large scale anisotropies. We study turbulence dynamics under stabilizing effect of stratification using direct numerical solutions of horizontally homogeneous, vertically stratified turbulence. The simulations use up to $4096\times4096\times2048$ grid points to resolve the dissipation scales. The Froude number ranges from 0.125 to 1 and the buoyancy Reynolds number from 9 to 219. The small scale turbulence is characterized in terms of one and two-point statistics of the local and locally averaged energy dissipation rate. Intermittency of the energy dissipation rate and its scale dependency gives us insight into the scaling characteristics of the stratified flows and deviation of the scaling laws from those of the isotropic turbulence as a function of Froude number. The effects of stratification on the intermittency of energy dissipation rate and the scales of turbulent bursts are discussed. [Preview Abstract] |
Monday, November 21, 2011 9:31AM - 9:44AM |
G6.00008: Strong Thin Shear Layers in High Reynolds Number Turbulence Takashi Ishihara, Julian C.R. Hunt, Yukio Kaneda Data analysis of high resolution DNS of isotropic turbulence with the Taylor scale Reynolds number $R_\lambda=1131$ shows that there are strong thin shear layers of thickness of the order of Taylor microscale, consisting of a cluster of strong vortex tubes. There are big velocity jumps of the order of the rms of the fluctuation velocity not only across the layers, but also over a small distance of order $10\eta$ ($\eta=$the Kolmogorov length scale), due to the strong vortex tubes within the layers. On average there is a balance between the energy dissipation and the energy transfer within the layers where the most intense vortices and dissipation occur. The large fluctuation of the energy transfer implies that not only downscale energy transfer but also upscale energy transfer is very active at the regions adjacent the layer. The DNS data show that the layer as well as the surrounding is moving and there is a net contraction flow on opposite sides of the layer; the interface of the layer is sharper at the side where stronger contraction occurs. The DNS data are consistent with a picture that the downscale and the upscale energy transfers correspond respectively to small eddies being distorted inhomogeneously by larger eddies, as they impinge onto and separate from the thin shear layers. [Preview Abstract] |
Monday, November 21, 2011 9:44AM - 9:57AM |
G6.00009: Lagrangian statistics in compressible isotropic homogeneous turbulence Yantao Yang, Jianchun Wang, Yipeng Shi, Shiyi Chen In this work we conducted the Direct Numerical Simulation (DNS) of a forced compressible isotropic homogeneous turbulence and investigated the flow statistics from the Lagrangian point of view, namely the statistics is computed following the passive tracers trajectories. The numerical method combined the Eulerian field solver which was developed by Wang et al. (2010, \emph{J. Comp. Phys.}, \textbf{229}, 5257-5279), and a Lagrangian module for tracking the tracers and recording the data. The Lagrangian probability density functions (p.d.f.'s) have then been calculated for both kinetic and thermodynamic quantities. In order to isolate the shearing part from the compressing part of the flow, we employed the Helmholtz decomposition to decompose the flow field (mainly the velocity field) into the solenoidal and compressive parts. The solenoidal part was compared with the incompressible case, while the compressibility effect showed up in the compressive part. The Lagrangian structure functions and cross-correlation between various quantities will also be discussed. [Preview Abstract] |
Monday, November 21, 2011 9:57AM - 10:10AM |
G6.00010: Scaling and statistics in three-dimensional compressible turbulence Jianchun Wang, Xiantu He, Yipeng Shi, Lian-ping Wang, Zuoli Xiao, Shiyi Chen The scaling and statistical properties of three-dimensional (3D) compressible turbulence are studied using high resolution numerical simulation. The two-point statistics of solenoidal component of velocity field are found to be no significant difference from those in the incompressible turbulence, while scaling exponents for compressive component of velocity structure functions are saturated at high orders, similar to one-dimensional (1D) Burgers turbulence. Both numerical results and theoretical analysis based on the probability density function (PDF) equation reveal that the power law exponent in the PDF of 3D velocity divergence is different from that in the Burgers turbulence. The effect of various terms in the dynamic equation on PDF will also be presented. [Preview Abstract] |
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