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 QB: Turbulent Boundary Layers IX |
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Chair: Daniel Sabatino, Lafayette College Room: Long Beach Convention Center 101B |
Tuesday, November 23, 2010 12:50PM - 1:03PM |
QB.00001: Scale-separation effects on the mechanisms of turbulent inertia Caleb Morrill-Winter, Paththage Priyadarshana, Joseph Klewicki The wall-normal gradients of the Reynolds stress and turbulent kinetic energy have direct connection to the transport mechanisms of turbulent boundary layers. Moreover, these gradients can be shown to arise from the correlation between specific velocity and vorticity components. Importantly, these correlations must remain non-zero at indefinitely high Reynolds numbers if turbulent transport is also to remain a non-negligible dynamical mechanism. Such considerations motivate the investigation of the relevant velocity vorticity products under the condition of increasing scale separation. In the boundary layer, this condition occurs with increasing $y^+$ (at fixed Reynolds number), and more importantly, with increasing Reynolds number. In this study we continue to interrogate data from the SLTEST site in Utah's west desert to explore the behavior of the relevant velocity and vorticity component interactions at high Reynolds number, while making use of existing well-resolved laboratory data to quantify distance from the wall effects. Pre-multiplied power spectra and the associated cospectra are interpreted in the context of the known momentum source and sink behaviors of the Reynolds stress gradient. [Preview Abstract] |
Tuesday, November 23, 2010 1:03PM - 1:16PM |
QB.00002: Coherent enstrophy production and turbulent dissipation in two-dimensional turbulence with and without walls Romain Nguyen Van Yen, Marie Farge, Kai Schneider In the fully-developed turbulent regime dissipation becomes independent on the molecular viscosity of the fluid for three-dimensional incompressible flows when Reynolds number becomes large enough. We inquire if incompressible two-dimensional turbulent flows may exhibit a similar behaviour in the vanishing viscosity limit. For this we examine the viscosity dependence of the solutions of two-dimensional Navier-Stokes equations in both periodic and wall-bounded domains, for Reynolds numbers varying from 10$^3$ to 10$^7$. The vorticity field is split into coherent and incoherent parts by applying the wavelet filter used for CVS [1]. We find that for Reynolds larger than 10$^5$ the coherent enstrophy dissipation rate tends to become independent of Reynolds, while the total enstrophy dissipation rate decays to zero logarithmically with Reynolds. In the wall-bounded case, we observe an additional production of enstrophy at the wall. As a result, coherent enstrophy diverges when Reynolds tends to infinity, but its time derivative seems to remain bounded independently of Reynolds. [1] M. Farge, K. Schneider and N. Kevlahan, 1999. Non-Gaussianity and Coherent Vortex Simulation for two-dimensional turbulence using an adaptative orthogonal wavelet basis. {\it Phys. Fluids.}, {\bf 11}(8), 2187-2201. [Preview Abstract] |
Tuesday, November 23, 2010 1:16PM - 1:29PM |
QB.00003: Markovian properties of velocity increments in a high Reynolds number turbulent boundary layer Maren Fredbo, Murat Tutkun Statistics of velocity increments in a flat plate turbulent boundary layer are investigated using the theory of Markov processes (J. Fluid Mech., Vol. 433, pp. 383-409, 2001). The database analyzed here is a subset of data taken in the 20 m long wind tunnel of Laboratoire de M\'{e}canique de Lille (LML) using a hot-wire rake of 143 single wire probes. The Reynolds number based on momentum thickness, Re$_{\theta}$, tested in this study was $19\:100$. The freestream velocity of the tunnel and the boundary layer thickness at the measurement location were 10 m s\textsuperscript{-1} and 30 cm respectively. Our analysis on the increments of longitudinal velocities at different wall-normal positions show that the flow exhibits Markovian properties when the separation ($\Delta$r) between different scales is on the order of the Taylor microscale, $\lambda$. Initial results indicate that smallest $\Delta r/\lambda$, where the process can be defined as Markovian, decreases from wall to the inertial layer. As the probe moves inside the inertial layer, however, a constant $\Delta r/\lambda$ is observed. The ratio starts growing in the outer layer once the probe leaves the inertial layer. [Preview Abstract] |
Tuesday, November 23, 2010 1:29PM - 1:42PM |
QB.00004: Time-evolution and time-scales of topological structures in a turbulent boundary layer through conditional mean trajectory analysis Callum Atkinson, Sergei Chumakov, Ivan Bermejo-Moreno, Xiaohua Wu, Julio Soria The Lagrangian evolution of the invariants of the velocity gradient tensor in wall-bounded turbulence is examined using conditional mean trajectories (CMT). Fields from direct numerical simulations of a turbulent boundary layer developing over a flat plate with fully turbulent flow over a Reynolds number range of Re$_{\theta} = 730$ to 1954 are used to extract the CMT in the invariant space of the velocity gradient tensor $(Q_A,R_A)$, the invariant space of the strain-rate tensor $(Q_S,R_S)$ and the invariant space of the rate-of-rotation tensor $(Q_W,R_W)$. CMT are considered for the full boundary layer, the log layer and the log and buffer layers. Results show a cyclic evolution of local topology. Associated time scales are extracted and compared with homogeneous isotropic turbulence. [Preview Abstract] |
Tuesday, November 23, 2010 1:42PM - 1:55PM |
QB.00005: Geometrical structure and topology of pressure Hessian in the turbulent boundary layer Sergei Chumakov, Callum Atkinson, Ivan Bermejo-Moreno, Julio Soria, Xiaohua Wu Pressure Hessian $H_{ij} = P_{,ij}$ plays an important role in the evolution equations for the invariants of the deformation tensor $A_{ij} = u_{i,j}$ and its symmertic part $S_{ij}$. The properties of $H_{ij}$ need to be understood in order to develop a mathematical model for the evolution of invariant quantities. In order to develop a full dynamical model for $H_{ij}$, there is a need to study and understand the full effect of the $H_{ij}$ tensor on the Lagrangian dynamics of the invariants. This type of study requires well-resolved data to evaluate all the right-hand side terms in the evolution equations. Attempts to study the properties of $H_{ij}$ via its invariants for the case of decaying isotropic turbulence and a temporally evolving plane wake can be found in the current literature. We present the a priori study of properties of $H_{ij}$ based on the results from the DNS of the fully developed turbulent boundary layer over a smooth flat plate, originally performed by Wu and Moin. [Preview Abstract] |
Tuesday, November 23, 2010 1:55PM - 2:08PM |
QB.00006: Identification of Lagrangian Coherent Structures in a Turbulent Boundary Layer Zachary Wilson, Murat Tutkun, Raul Bayoan Cal In this study, we identify Lagrangian coherent structures (LCS)
in a flat plate turbulent boundary layer at Re$_{\theta}$ 0f $19\:100$. To detect the
LCS,
we compute direct Lyapunov exponents (DLE) (Haller, G., Physica D, vol 149, pp
248-277, 2001).
Specifically we use the velocity field
obtained from stereo PIV measurements to compute trajectories,
$\mathbf{x} (t,t_{0},\mathbf{x} _{0})$, from initial positions,
$\mathbf{x}_{0}$, at time $t_{0}$. For fixed integration times,
$\left| t-t_{0} \right|$, we numerically differentiate the flow
map, given by $F_{t_{0}}^{t}(\mathbf{x}_{0}) = \mathbf{x}(t,
t_{0}, \mathbf{x}_{0})$, and then compute the deformation
gradient tensor field $\Delta ^{t}_{t_{0}}(\mathbf{x}_{0}) =
\left[ \nabla F_{t_{0}}^{t}(\mathbf{x}_{0}) \right]^{T} \left[
\nabla F_{t_{0}}^{t}(\mathbf{x}_{0}) \right]$. The DLE field is
then found as $\mathrm{DLE}_{t_{0}}^{t}(\mathbf{x_{0}}) = \ln \left(
\lambda _{\mathrm{max}} \left( \Delta _{t_{0}}^{t}(\mathbf{x}_{0})
\right) \right)/ \left (2\left| t-t_{0} \right| \right)$. Two
dimensional gradient climbing is
then used to find points on the locally maximizing, LCS surfaces
of the field, $\mathrm{DLE}_{t_{0}}^{t}(\mathbf{x}_{0})$. To determine
whether these surfaces
truly repel (attract) near by fluid particles, the
\emph{hyperbolicity criterion} is applied (Mathur et al., Phys. Rev. Lett., vol 98, pp
144502, 2007). In particular we compute normal strain rates,
$\langle \mathbf{n},\mathbf{Sn}\rangle$, to locate repelling
surfaces $\left( t>>t_{0} \mathrm{\:and\:
} \langle \mathbf{n},\mathbf{Sn}\rangle >0\right)$ and attracting
surfaces $\left( t< |
Tuesday, November 23, 2010 2:08PM - 2:21PM |
QB.00007: The parametric mechanism maintaining the roll/streak/turbulence complex in boundary layers Brian Farrell Stochastic Structural Stability Theory (SSST) provides an autonomous, deterministic, nonlinear dynamical system for evolving the statistical mean state of a turbulent system. In this presentation SSST is applied to the problem of understanding maintenance of the roll/streak/turbulence complex that supports boundary layer turbulence. In the presence of sufficiently high levels of free stream turbulence roll/streak structures bifurcate from the laminar flow as a linear instability of interaction between the free stream turbulence and the mean flow leading to an essentially time dependent state that is self-maintaining in the absence of external forcing by free stream turbulence. This chaotic state is supported by the universal instability inherent in time dependent non-normal system dynamics. [Preview Abstract] |
Tuesday, November 23, 2010 2:21PM - 2:34PM |
QB.00008: Classification of critical points in a turbulent boundary layer Max Gibson, Anders Helgeland, Murat Tutkun, Ra\'{u}l Bayo\'{a}n Cal Critical points of the velocity field generated by the direct numerical simulation of turbulent channel flow\footnote{M. Marquillie et al. (2008), J. Turbulence, vol 9, no 1, pp. 1-23.} are studied using the methodology described by Aasen and Furuheim (2008)\footnote{M. Aasen and K. Furuheim (2008), M.Sc. thesis, Department of Informatics, University of Oslo, Oslo, Norway.}. First order critical points inside the field are obtained using a trilinear interpolation scheme. Classification of the critical points found in the three dimensional field is performed by studying individual phase planes of each critical point. Distribution of the critical points and their classifications are compared for different parts of the converging-diverging turbulent channel flow in order to investigate the effect of imposed pressure gradient within the domain. The results obtained from the numerical simulation with $Re_\theta=395$ are compared with three-component two-dimensional stereo PIV data recorded over the decelerating part of a converging-diverging bump placed inside the wind tunnel possessing a significantly higher Reynolds number of 19100. [Preview Abstract] |
Tuesday, November 23, 2010 2:34PM - 2:47PM |
QB.00009: Bayesian Assessment of Mean Velocity Profile Models in Wall-Bounded Turbulence Robert Moser, Todd Oliver The form of the mean velocity profile in high-Reynolds-number wall-bounded turbulent shear flows has been the subject of renewed interest in recent years. A number of questions have been raised regarding the universality of the von Karman constant, the dependence of the over-lap layer on Reynolds number and even the appropriateness of a logarithmic description of the overlap layer. The questions have been difficult to resolve because the models predict subtle differences in the mean velocity profiles at finite Reynolds number. However, these subtle differences are important for scaling to very high Reynolds number and for inferring wall shear stress when direct measurements are not available. In this work, Bayesian inference is used to infer parameters (e.g. the Karman constant) and their uncertainty in a variety of turbulent mean velocity representations using experimental data over a wide range of Reynolds number. Moreover, an information theory-based multi-model formalism is used to rank competing models (e.g., the standard log and power laws and finite Reynolds number refinements of these profiles) by a metric that naturally balances data fit versus model complexity. This work is supported by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615]. [Preview Abstract] |
Tuesday, November 23, 2010 2:47PM - 3:00PM |
QB.00010: Forced Solutions of Streamwise Constant Plane Couette Flow Dennice Gayme, Beverley McKeon, Bassam Bamieh, John Doyle, Antonis Papachristodoulou A two-dimensional, three-velocity component ($2D/3C$) model simulated under small-amplitude Gaussian forcing has been shown to capture salient features of turbulent plane Couette flow (Gayme et. al 2010). Periodic spanwise/wall-normal plane stream functions are used as input to develop forced $2D/3C$ streamwise velocities. The resulting steady-state solutions are qualitatively similar to a fully turbulent spatial field of DNS. Our analysis indicates that the momentum transfer which produces a `turbulent-like' mean profile requires a nonlinear streamwise velocity equation. A system theoretic approach is used to study amplification mechanisms which arise through this $2D/3C$ nonlinear coupling. The forcing required to produce each input is used to define an induced norm. The associated input-output response determines the energy optimal spanwise wavelength over a range of Reynolds numbers. We identify an important tradeoff between the linear amplification mechanism and the nonlinearity required to develop an appropriately shaped turbulent velocity profile. \textbf{Acknowledgements:} The research is supported by Boeing and AFOSR. B.J.M. gratefully acknowledges NSF-CAREER award no. 0747672 (program managers W. W. Schultz \& H. H. Winter). [Preview Abstract] |
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