Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session Q28: Turbulence: WallBounded Flows  Model & TheoryBoundary Layers Turbulence

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Chair: Elie BouZeid, Princeton University Room: 207 
Tuesday, November 21, 2017 12:50PM  1:03PM 
Q28.00001: Universality of the logarithmic velocity profile restored Paolo Luchini The logarithmic velocity profile of wallbounded turbulent flow, despite its widespread adoption in research and in teaching, exhibits discrepancies with both experiments and numerical simulations that have been repeatedly observed in the literature; serious doubts ensued about its precise form and universality, leading to the formulation of alternate theories and hindering ongoing experimental efforts to measure von K\'arm\'an's constant. By comparing different geometries of pipe, planechannel and planeCouette flow, here we show that such discrepancies can be physically interpreted, and analytically accounted for, through an equally universal higherorder correction caused by the pressure gradient. Inclusion of this term produces a tenfold increase in the adherence of the predicted profile to existing experiments and numerical simulations in all three geometries. Universality of the logarithmic law then emerges beyond doubt and a satisfactorily simple formulation is established. Among the consequences of this formulation is a strongly increased confidence that the Reynolds number of presentday direct numerical simulations is actually high enough to uncover asymptotic behaviour, but research efforts are still needed in order to increase their accuracy. [Preview Abstract] 
Tuesday, November 21, 2017 1:03PM  1:16PM 
Q28.00002: Linear response theory for one point statistics in the loglaw region of wall bounded turbulence Yukio Kaneda, Yoshinobu Yamamoto, Yoshiyuki Tsuji The idea of linear response theory developed in statistical mechanics for irreversible phenomena is applied to onepoint statistics in the socalled loglaw region, or strictly speaking the constant Reynolds stress region, of wall bounded turbulence. The onepoint statistics include the Reynolds stress and the r.m.s's of the velocity fluctuations in the stream wise, span wise and wall normal directions. In the application of the idea, a similarity between (i) the KarmanHowarth equation for homogeneous isotropic turbulence and (ii) the conservation equation of the Reynolds averaged momentum in turbulence with parallel mean flow plays a key role. Both of (i) and (ii) are exact, and they respectively represent the energytransfer from large to small scales, and the momentumtransfer in the wall normal direction. In the limit of infinite Reynolds number, (i) reduces to Kolmogorov's 4/5law in the inertial subrange, while (ii) results in the constancy of the Reynolds stress in a certain range. The theory gives an estimate on the influence of finite Reynolds number on the statistics. The theoretical conjectures are compared with data of a series of direct numerical simulations of turbulent channel flow with Re\textunderscore tau up to 8000. [Preview Abstract] 
Tuesday, November 21, 2017 1:16PM  1:29PM 
Q28.00003: Improved upper bounds on energy dissipation rates in plane Couette flow with boundary injection and suction Harry Lee, Baole Wen, Charles Doering The rate of viscous energy dissipation $\epsilon$ in incompressible Newtonian planar Couette flow (a horizontal shear layer) imposed with uniform boundary injection and suction is studied numerically. Specifically, fluid is steadily injected through the top plate with a constant rate at a constant angle of injection, and the same amount of fluid is sucked out vertically through the bottom plate at the same rate. This setup leads to two control parameters, namely the angle of injection, $\theta$, and the Reynolds number of the horizontal shear flow, $Re$. We numerically implement the ‘background field’ variational problem formulated by Constantin and Doering with a onedimensional unidirectional background field $\phi(z)$, where $z$ aligns with the distance between the plates. Computation is carried out at various levels of $Re$ with $\theta = 0, 0.1^{\circ}, 1^{\circ}$ and $2^{\circ}$, respectively. The computed upper bounds on $\epsilon$ scale like $Re^0$ as $Re >20,000$ for each fixed $\theta$, this agrees with Kolmogorov’s hypothesis on isotropic turbulence. The outcome provides new upper bounds to $\epsilon$ among any solution to the underlying NavierStokes equations, and they are sharper than the analytical bounds presented in Doering et al (2000). [Preview Abstract] 
Tuesday, November 21, 2017 1:29PM  1:42PM 
Q28.00004: Quantifying wall turbulence via a symmetry approach: A Lie group theory. ZhenSu She, Xi Chen, Fazle Hussain We present a symmetrybased approach which yields analytic expressions for the mean velocity and kinetic energy profiles from a Liegroup analysis. After verifying the dilationgroup invariance of the Reynolds averaged NavierStokes equation in the presence of a wall, we select a stress and energy length function as similarity variables which are assumed to have a simple dilationinvariant form. Three kinds of (local) invariant forms of the length functions are postulated, a combination of which yields a multilayer formula giving its distribution in the entire flow region normal to the wall. The mean velocity profile is then predicted using the mean momentum equation, which yields, in particular, analytic expressions for the (universal) wall function and separate wake functions for pipe and channel  which are validated by data from direct numerical simulations (DNS). Future applications to a variety of wall flows such as flows around flat plate or airfoil, in a RayleighBenard cell or TaylorCouette system, etc., are discussed, for which the dilation group invariance is valid in the wallnormal direction. [Preview Abstract] 
Tuesday, November 21, 2017 1:42PM  1:55PM 
Q28.00005: Modification of a Turbulent Boundary Layer within a Homogeneous Concentration of Drag reducing Polymer Solution. Yasaman Farsiani, Brian Elbing High molecular weight polymer solutions in wallbounded flows can reduce the local skin friction by as much as 80{\%}. External flow studies have typical focused on injection of polymer within a developing turbulent boundary layer (TBL), allowing the concentration and drag reduction level to evolve with downstream distance. Modification of the loglaw region of the TBL is directly related to drag reduction, but recent results suggest that the exact behavior is dependent on flow and polymer properties. Weissenberg number and the viscosity ratio (ratio of solvent viscosity to the zeroshear viscosity) are concentration dependent, thus the current study uses a polymer ocean (i.e. a homogenous concentration of polymer solution) with a developing TBL to eliminate uncertainty related to polymer properties. The nearwall modified TBL velocity profiles are acquired with particle image velocimetry. In the current presentation the mean velocity profiles and the corresponding flow (Reynolds number) and polymer (Weissenberg number, viscosity ratio, and length ratio) properties are reported. Note that the impact of polymer degradation on molecular weight will also be quantified and accounted for when estimating polymer properties [Preview Abstract] 
Tuesday, November 21, 2017 1:55PM  2:08PM 
Q28.00006: Viscous versus inviscid exact coherent states in high Reynolds number wall flows Brandon Montemuro, Joe Klewicki, Chris White, Greg Chini Streamwiseaveraged motions consisting of streamwiseoriented streaks and vortices are key components of exact coherent states (ECS) arising in incompressible wallbounded shear flows. These invariant solutions are believed to provide a scaffold in phase space for the turbulent dynamics realized at large Reynolds number $Re$. Nevertheless, many ECS, including upperbranch states, have a large$Re$ asymptotic structure in which the \emph{effective} Reynolds number governing the streak and roll dynamics is order unity. Although these viscous ECS very likely play a role in the dynamics of the nearwall region, they cannot be relevant to the inertial layer, where the leadingorder mean dynamics are known to be inviscid. In particular, viscous ECS cannot account for the observed regions of quasiuniform streamwise momentum and interlaced internal shear layers (or `vortical fissures') within the inertial layer. In this work, a large$Re$ asymptotic analysis is performed to extend the existing selfsustainingprocess/vortexwaveinteraction theory to account for largely inviscid ECS. The analysis highlights feedback mechanisms between the fissures and uniform momentum zones that can enable their selfsustenance at extreme Reynolds number. [Preview Abstract] 
Tuesday, November 21, 2017 2:08PM  2:21PM 
Q28.00007: Modeling wallbounded flows at transcritical conditions Peter Ma, Xiang Yang, Matthias Ihme At supercritical pressures, the transition of a fluid from a liquidlike state to a gaslike state occurs continuously, during which process all fluid properties change drastically. In this work, we conduct direct numerical simulation of a channel flow at transcritical conditions with two walls kept at temperatures above and below the pseudoboiling temperature, which is defined as the temperature of maximum heat capacity. The density change is up to a factor of 20 from the cooled wall to the heated wall. Using the DNS data, we test the usefulness of the mixing length theory and the Townsend attached eddy hypothesis in the context of variable property flows, both of which have received considerable empirical support at regular conditions. It is found that the mean flow can still be modeled with the conventional mixing length model if the fluid density at the wall is used for computing the eddy viscosity. Besides, the streamwise energy spectrum exhibits the celebrated 1/$k$ scaling across an extended range of scales where $k$ is the streamwise wave number, which provides strong support to the attached eddy model at transcritical conditions. [Preview Abstract] 
Tuesday, November 21, 2017 2:21PM  2:34PM 
Q28.00008: Turbulent Kinetic Energy Budgets in a Planar Channel with a Sudden Expansion and Transverse Jets Nima Moallemi, Luca Chiabò, Sergio Hoyas, Joshua Brinkerhoff Numerical simulations are performed to analyze the development of a planar channel flow through a sudden expansion with transverse jets. The budgets of turbulent kinetic energy (TKE) have been computed downstream of the transverse jets at various velocity ratios. At low velocity ratios, a bifurcation phenomena occurs due to the asymmetric growth of disturbances from the sudden expansion, leading to asymmetry in the reattachment lengths on the upper and lower channel walls. Increasing the velocity ratio causes first a disappearance of bifurcation and then the development of localized turbulence. TKE budgets show that the localized turbulent region experiences high negative production of turbulence energy with two peaks adjacent to the mean trajectory of the transverse jets, resulting in a gradual relaminarization of the turbulent flow. The pressure transport and turbulent diffusion terms are found to dominate the relaminarization process. Validation of the numerical simulations is achieved via comparison with numerical and experimental data available in the literature. [Preview Abstract] 
Tuesday, November 21, 2017 2:34PM  2:47PM 
Q28.00009: The role of returntoisotropy in wallbounded flows with buoyancy Elie BouZeid, Xiang Gao, Gabriel Katul The workings of how buoyancy modifies turbulence in wallbounded flows continues to be a topic with various open fundamental questions and multiple pressing applied needs. Horizontal velocity variance is produced by shear, while buoyancy generates vertical variance. These components then interact through the energy redistribution terms that work to return turbulence to an isotropic state. It is thus reasonable to hypothesize that any changes induced by buoyancy must be communicated by these terms to the horizontal directions. In this talk, a model that connects the budgets of the three velocity variance components and captures how the redistribution terms vary with the flux Richardson number is proposed. The results of this model are first validated against large eddy simulations. The model is then used to inquire about how turbulence transitions between different regimes as the Richardson number varies. By employing a Rottatype closure for the redistribution terms, the model further predicts the velocity anisotropy tensor. Comparisons to LES using only the slow part of the linear Rotta closure are less convincing. However, the framework explains the ‘selfpreservation’ of turbulence even for very large gradient Richardson number in stably stratified flows. [Preview Abstract] 
Tuesday, November 21, 2017 2:47PM  3:00PM 
Q28.00010: Restricted nonlinear large eddy simulations: Investigating RNL dynamics at infinite Reynolds number Dennice F. Gayme, Joel U. Bretheim, Charles Meneveau The restricted nonlinear (RNL) model for wallbounded turbulent flows is a quasilinearization of the NavierStokes equations with a streamwise averaged mean flow; a choice motivated by experimental and analytical evidence of the central role of streamwise elongated coherent structures in these flows. The resulting RNL model is inherently less costly computationally. It has been shown to accurately reproduce key flow features and be useful in studying the dynamics of wallturbulence at low to moderate Reynolds (Re) numbers. This work explores a recent extension of the RNL framework to largeeddy simulations (RNLLES) at infinite Re. This RNLLES system retains certain behaviors previously observed in the low Re context, including an amenability to streamwise Fourier component ``bandlimiting;'' a procedure which improves the accuracy of the RNL turbulence statistics. For the bandlimited RNLLES system, we demonstrate that the small scale band of wavelengths necessary to obtain accurate statistics can be determined using a surrogate dissipation spectra of LES data. Furthermore, we identify two grid size dependent regimes: 1) a smallscale only regime and 2) a bimodal regime where a large scale must be included due to a sufficient separation in scales. [Preview Abstract] 
Tuesday, November 21, 2017 3:00PM  3:13PM 
Q28.00011: Quasilinear models through the lens of resolvent analysis Beverley McKeon, Greg Chini Quasilinear (QL) and generalized quasilinear (GQL) analyses, e.g. Marston et al. (Phys. Rev. Letters, 2016), also variously described as statistical state dynamics models, e.g., Farrell et al. (J. Fluid Mech., 2016), restricted nonlinear models, e.g. Thomas et al. (Phys. Fluids, 2015), or 2D/3C models, e.g. Gayme et al. (J. Fluid Mech., 2010), have achieved considerable success in recovering the mean velocity profile for a range of turbulent flows. In QL approaches, the portion of the velocity field that can be represented as streamwise constant, i.e. with streamwise wavenumber $k_x=0$, is fully resolved, while the streamwisevarying dynamics are linearized about the streamwiseconstant field; that is, only those nonlinear interactions that drive the streamwiseconstant field are retained, and the nonstreamwise constant ``fluctuationfluctuation’’ interactions are ignored. Here, we show how these QL approaches can be reformulated in terms of the closedloop resolvent analysis of McKeon $\&$ Sharma (2010), which enables us to identify reasons for their evident success as well as algorithms for their efficient computation. [Preview Abstract] 
Tuesday, November 21, 2017 3:13PM  3:26PM 
Q28.00012: A vortical step model of the turbulent boundary layer Alireza Ebadi, Juan Cuevas, Christopher White, Gregory Chini, Joseph Klewicki Recent studies indicate that the turbulent boundary layer structure at high Reynolds number is composed of large uniform momentum zones (UMZs) segregated by countable narrow fissures of concentrated vorticity. A dynamic model that reproduces the fundamental elements of this UMZ structure by placing a few vortical fissures across the boundary layer in the wallnormal direction is presented. The number of fissures, their most probable wallnormal locations and their corresponding velocities follow scalings informed by analysis of the mean momentum equation in the inertial domain. Furthermore, an asymptotic length and velocity scaling is explored for the subinertial domain, and a conservation mechanism for momentum exchange throughout the turbulent boundary layer is enforced. An ensemble of statistically independent velocity profiles is created by letting the fissures move in the wallnormal direction, and exchange momentum as they do so. The numerical results shows the dynamic model is able to reproduce the main characteristics of the streamwise velocity field up to the fourth statistical moment. [Preview Abstract] 
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