Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session G20: Turbulence: Theory I |
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Chair: Bruce Turkington, University of Massachusetts Amherst Room: 208 |
Monday, November 23, 2015 8:00AM - 8:13AM |
G20.00001: Deriving statistical closure from dynamical optimization Bruce Turkington Turbulence theorists have traditionally deduced statistical models by generating a hierarchy of moment equations and invoking some closure rules to truncate the hierarchy. In this talk a conceptually different approach to model reduction and statistical closure will be presented, and its implications for coarse-graining fluid turbulence will be indicated. The author has developed this method in the context of nonequilibrium statistical descriptions of Hamiltonian systems with many degrees of freedom. With respect to a chosen parametric statistical model, the lack-of-fit of model paths to the full dynamics is minimized in a time-integrated, mean-squared sense. This optimal closure method is applied to coarse-grain spectrally-truncated inviscid dynamics, including the Burgers-Hopf equation and incompressible two-dimensional flow, using the means and/or variances of low modes as resolved variables. The derived reduced dynamics for these test cases contain (1) scale-dependent dissipation which is not a local eddy viscosity, (2) modified nonlinear interactions between resolved modes, and (3) coupling between the mean and variance of each resolved mode. These predictions are validated against direct numerical simulations of ensembles for the fully resolved dynamics. [Preview Abstract] |
Monday, November 23, 2015 8:13AM - 8:26AM |
G20.00002: Backward two-particle dispersion in turbulence: asymptotic behaviors at high Reynolds number Pui-Kuen Yeung, D. Buaria, B.L. Sawford Backward relative dispersion of fluid elements and diffusing substances or property markers is central to a Lagrangian view of turbulent mixing, but data are not readily available. Recently we have devised a numerical approach based on massively parallel processing of the trajectories of many billions of particle pairs, and have used it to obtain results in simulations of stationary isotropic turbulence up to $4096$ in size and Taylor-scale Reynolds number up to 1000, with a wide range of initial separations. Backward dispersion is faster than forward, especially at intermediate times after the ballistic range and before long-time diffusive behavior is reached. Richardson scaling is demonstrated for the mean-squared separation, with forward and backward Richardson constants estimated to be 0.55 and 1.5 respectively, which are close to or comparable to other estimates. However, because of persistent dissipation sub-range effects no corresponding scaling was observed for higher order moments. An effort is made to analyze theoretically several key characteristics such as asymmetry in time and exponential growth of third and fourth moments at early times. Related results for marked entities that diffuse relative to the fluid will also be briefly addressed. [Preview Abstract] |
Monday, November 23, 2015 8:26AM - 8:39AM |
G20.00003: A Multiscale Morphing Continuum Description for Turbulence James Chen, Louis Wonnell Turbulence is a flow physics phenomena invlolving multiple length scales. The popular Navier- Stokes equations only possess one length/time scale. Therefore, extremely fine mesh is needed for DNS attempting to resolve the small scale motion, which comes with a burden of excessive computational cost. For practical application with complex geometries, the research society rely on RANS and LES, which requre turbulence model or subgrid scale (SGS) model for closure problems. Different models not only lead to different results but usually are invalidated on solid physical grounds, such as objectivity and entropy principle.The Morphing Continuum Theory (MCT) is a high-order continuum theory formulated under the framework of thermalmechanics for physics phenomena involving microstructure. In this study, a theoretical perspective for the multiscale nature of the Morphing Continuum Theory is connected with the multiscale nature of turbulence physics. The kinematics, balance laws, constitutive equations and a Morphing Continuum description of turbulence are introduced. The equations were numerically implemented for a zero pressure gradient flat plate. The simulations are compate with the laminar, transitional and turbulence cases. [Preview Abstract] |
Monday, November 23, 2015 8:39AM - 8:52AM |
G20.00004: Dynamics of the tetrad-based velocity gradient in turbulent flows Haitao Xu, Alain Pumir, Eberhard Bodenschatz We investigate the structure and evolution of turbulent flows with the help of the perceived velocity-gradient, determined from four fluid particles initially forming a regular tetrad of size $r_0$. The main feature of the turbulent dynamics can be conveniently captured by a reduced description, in terms of two invariants of the velocity gradient. When $r_0$ is in the inertial range of scales, the evolution of averaged quantities can be parametrized by two dimensionless parameters, which vary slowly with $r_0$. We also characterize the fluctuations around the conditional mean, which represent the dynamics at scales below $r_0$. Using data from both Lagrangian particle tracking experiments and DNS, we show that the behavior qualitatively follows some earlier theoretical prediction, but with interesting new features. [Preview Abstract] |
Monday, November 23, 2015 8:52AM - 9:05AM |
G20.00005: Realizable Closure Model for the Reynolds Stress in Rotating Frames Charles Petty, Andre Benard The Reynolds-averaged Navier-Stokes equation for constant property Newtonian fluids is unclosed due to the explicit appearance of the normalized Reynolds stress and the turbulent kinetic energy. A non-negative algebraic mapping of the normalized Reynolds stress into itself provides a practical closure for a wide class of flows. Unlike eddy viscosity closure models, the theory predict the redistribution of the turbulent kinetic energy among the three components of the fluctuating velocity field for statistically stationary spanwise rotating channel flows as well as the Coriolis re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity field in rotating homogeneous decay. The results partially support the conjecture that the index-of-refraction of the troposphere is anisotropic at all scales. [Preview Abstract] |
Monday, November 23, 2015 9:05AM - 9:18AM |
G20.00006: Filtering on the Sphere Hussein Aluie, Matthew Hecht, Geoffrey Vallis The filtering approach is a natural and valuable framework for analyzing and modeling turbulence, especially within the subject of Large-Eddy Simulation. However, the mathematical development of the approach has been mostly limited to flows in Euclidean (flat) spaces and generalizations to non-Euclidean (curved) manifolds suffer from several shortcomings, such as dependence on the choice of coordinate system, commutation errors, or not preserving volume. Motivated by geophysical flows, we define a new generalized filtering operation on the Sphere which is free from the aforementioned problems. We prove that our filter commutes with spatial derivatives, yielding simple and exact coarse-grained equations for flow on the Sphere. We demonstrate these tools with a-priori tests on flows from high-resolution Ocean simulations. [Preview Abstract] |
Monday, November 23, 2015 9:18AM - 9:31AM |
G20.00007: Turbulent Particle Pair Diffusion Using Kinematic Simulations Nadeem Malik Sweeping errors in Kinematic Simulations (KS) [1] have been shown to be negligible in turbulent flows with extended inertial subranges up to at least \textit{1\textless k\textless 10}$^{6} (k$ is the wavenumber) [2]. The departure from locality scaling observed in the pair diffusivity $K=$\textit{\textless }$\Delta \cdot $\textit{v\textgreater } in KS may therefore be a genuine effect, challenging previous assumptions [3] that in turbulence with generalized power-law energy spectra, $E(k) \sim k^{-p}$ for \textit{1\textless p}$\le $\textit{3}, locality would lead to, $K \sim \sigma_{\Delta }^{\gamma }$, where $\sigma_{\Delta }=$[ \quad \textless $\Delta ^{\mathrm{2}}$\textgreater ]$^{\mathrm{\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} }}$, $\Delta $ is the pair separation, $v$ is the pair relative velocity, \textless \textgreater is the ensemble average, and $\gamma_{\thinspace }=$\textit{(1}$+$\textit{p)/2}. For Kolmogorov turbulence this gives, $K \sim \sigma_{\Delta }^{4/3}$. A new analysis, supported by KS [4] confirms that both local and non-local effects govern the pair diffusion process, leading to, $K \sim \sigma _{\Delta }^{\gamma p}$, where now $\gamma_{p\thinspace }$\textit{\textgreater }$\gamma_{\thinspace }$; for Kolmogorov turbulence, $K \sim \sigma _{\Delta }^{1.53}$. Thus non-local diffusional processes cannot be neglected, and this may have important consequences for the general theory of turbulence. REFERENCES: [1] Fung, J. C. H., Hunt, J. C. R., Malik, N. A., {\&} Perkins, R. J. \textit{J. Fluid Mech. 236, 281 (1992).} [2] Malik, N. A. \textit{Under Review, Physics of Fluids (2015).} [3] Richardson, L. F. \textit{Proc. Roy. Soc. Lond. A 100, 709 (1926).} [4] Malik, N. A. On Turbulent Particle Pair Diffusion. \textit{Under review, Physics of Fluids (2015).} [Preview Abstract] |
Monday, November 23, 2015 9:31AM - 9:44AM |
G20.00008: Electrokinetic turbulence in a microchannel at low Reynolds number Wei Zhao, Fang Yang, Guiren Wang Turbulence is commonly viewed as a type of macroflow phenomenon under a sufficiently high Reynolds number (Re). On the other hand, it has been widely perceived in science, engineering and medicine that there is never any turbulence in low Re flow for Newtonian fluids. There is even difficulty to characterize turbulence in microchannels with current available velocimeters, due to the requirement of simultaneously high spatial and temporal resolution. Recently, we generated micro-electrokinetic (EK) turbulence in a microchannel when a pressure driven flow at low Re on the order of unity is electrokinetically forced. We also developed a novel velocimeter, i.e. laser induced fluorescence photobleaching anemometer (LIFPA) that enables us to measure the velocity fluctuations with simultaneously high spatial and temporal resolution. Here we surprisingly observed with LIFPA that the corresponding micro EK turbulence can also have some features of high Re flows, such as Kolmogorov -5/3 spectrum and the exponential tail of probability density function of velocity fluctuation, and the scaling behavior of velocity structure function. This work could provide a new perspective on turbulence. [Preview Abstract] |
Monday, November 23, 2015 9:44AM - 9:57AM |
G20.00009: Universality at low Reynolds numbers and the emergence of intermittent behavior in isotropic turbulence Diego Donzis, Victor Yakhot, K.R. Sreenivasan Most approaches to understand turbulence have sought universal behavior believed to manifest at high Reynolds numbers ($R_\lambda$). However, recent theory and simulations suggest that universal characteristics, such as the non-trivial anomalous scaling exponents of moments of velocity gradients, emerge even at very low $R_\lambda$ at which no inertial range exists. Furthermore, with decreasing Reynolds numbers, a transition occurs from fully intermittent turbulence to (approximately) Gaussian behavior at an apparently universal critical $R_\lambda$. A potential implication of these observations is that significant information concerning the inertial range (e.g. scaling exponents) is already manifest in the dissipation range at very low $R_\lambda$. Thus, high $R_\lambda$ properties can be studied with well-resolved low-$R_\lambda$ simulations instead of marginally resolved high-Reynolds flows. The focus of this talk is to explore signatures of universality at high-Reynolds numbers in the dissipation range of highly resolved DNS ($k_{max}\eta\sim O(20)$) for $R_\lambda$ up to 90, and decaying simulations close to the critical $R_\lambda$. In addition to statistics of velocity gradients and dissipation we explore evidence of Beltramization as suggested in past theoretical work. [Preview Abstract] |
Monday, November 23, 2015 9:57AM - 10:10AM |
G20.00010: Optimal Energy Dissipation Bounds for 2D and 3D Stress-Driven Shear Flows Giovanni Fantuzzi, Andrew Wynn The background method (Doering \& Constantin, 1995) allows the derivation of rigorous bounds on bulk turbulent quantities in a variety of wall-bounded flows as a function of the governing parameters. A classical example is to bound the energy dissipation $\epsilon$ in surface-driven shear flows as a function of the driving force, expressed by the Grashoff number $Gr$. Of particular interest is to compute the best bounds achievable within this framework. However, the variational problem determining the optimal bounds is difficult to solve when the flow is driven by a boundary flux. Tang et al. (2004) first resolved this difficulty by modelling a surface stress with a localised body force. Instead, we propose a novel numerical approach based on Semidefinite Programming that is able to handle fixed-flux boundary conditions directly, and thereby revisit the bounds on $\epsilon$ for surface-stress-driven shear flows. In the 2D case, we find that $\epsilon>8Gr^{3/2}$, improving the scaling law $\epsilon>4Gr^{3/2}$ proven by Hagstrom \& Doering (2014). In 3D, we confirm the results of Tang et al., suggesting that a surface stress can be modelled accurately by a body force. Finally, a careful analysis ensures that, in principle, our bounds hold analytically for a fixed $Gr$. [Preview Abstract] |
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