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 F26: General Wall Bounded Turbulence and Turbulent Boundary LayersBoundary Layers Turbulence

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Chair: Jin Lee, United Technologies Research Center Room: 707 
Monday, November 20, 2017 8:00AM  8:13AM 
F26.00001: Resolventbased modeling of passive scalar dynamics in wallbounded turbulence Scott Dawson, Theresa SaxtonFox, Beverley McKeon The resolvent formulation of the NavierStokes equations expresses the system state as the output of a linear (resolvent) operator acting upon a nonlinear forcing. Previous studies have demonstrated that a lowrank approximation of this linear operator predicts many known features of incompressible wallbounded turbulence. In this work, this resolvent model for wallbounded turbulence is extended to include a passive scalar field. This formulation allows for a number of additional simplifications that reduce model complexity. Firstly, it is shown that the effect of changing scalar diffusivity can be approximated through a transformation of spatial wavenumbers and temporal frequencies. Secondly, passive scalar dynamics may be studied through the lowrank approximation of a passive scalar resolvent operator, which is decoupled from velocity response modes. Thirdly, this passive scalar resolvent operator is amenable to approximation by semianalytic methods. We investigate the extent to which this resulting hierarchy of models can describe and predict passive scalar dynamics and statistics in wallbounded turbulence. [Preview Abstract] 
Monday, November 20, 2017 8:13AM  8:26AM 
F26.00002: Friction velocity estimation using Reynolds shear stress profile data Ralph Volino, Michael Schultz A method for using profiles of the mean streamwise velocity and the Reynolds shear stress to estimate the friction velocity, $u_\tau$, is presented. The Reynolds averaged twodimensional streamwise momentum equation is solved for the Reynolds shear stress term. The remaining terms in the equation are separated into those which depend on the local gradient of the mean streamwise velocity profile and those which do not. Using only the terms retained with the Couette flow assumption, the Reynolds shear stress profile can be matched in the inner ~10 percent of the boundary layer with the appropriate choice of $u_\tau$. Including the other terms which do not depend on the streamwise velocity profile gradient, the fit can be extended to the inner ~30 percent of the boundary layer. Using all terms the full Reynolds shear stress profile can be fit. The method is verified using laminar solutions for zero and nonzero pressure gradient boundary layers, and with ZPG turbulent DNS results. It is then applied to zero, favorable and adverse pressure gradient experimental data from smooth and rough walls. Results obtained for local friction velocities agree well with those obtained by other techniques. The method may prove useful when other methods are not practical or fully appropriate. [Preview Abstract] 
Monday, November 20, 2017 8:26AM  8:39AM 
F26.00003: Implication of Taylor's hypothesis on amplitude modulation Michael Howland, Xiang Yang Amplitude modulation is a physical phenomenon which describes the nonlinear interscale interaction between large and small scales in a turbulent wallbounded flow. The amplitude of the small scale fluctuations are modulated by the large scale flow structures. Due to the increase of amplitude modulation as a function of Reynolds number ($Re_{\tau} = \delta u_{\tau} / \nu$), this phenomenon is frequently studied using experimental temporal 1D signals, taken using hotwire anemometry. Typically, Taylor's frozen turbulence hypothesis has been invoked where the convection by velocity fluctuations is neglected and the mean velocity is used as the convective velocity. At high Reynolds numbers, turbulent fluctuations are comparable to the mean velocity in the near wall region ($y^+\sim O(10)$), and as a result, using a constant global convective velocity systematically locally compresses or stretches a velocity signal when converting from temporal to spatial domain given a positive or negative fluctuation respectively. Despite this, temporal hotwire data from wind tunnel or field experiments of high Reynolds number boundary layer flows can still be used for measuring modulation provided that the local fluid velocity is used as the local convective velocity. [Preview Abstract] 
Monday, November 20, 2017 8:39AM  8:52AM 
F26.00004: Selfconsistent determination of attached eddies in rotating plane Couette flow Bruno Eckhardt, Marina Pausch, Martin G Lellep, Stefan Zammert The formation of ever thinner boundary layers near a surface requires the presence of ever smaller structures in the flow, ideally organized in a hierarchical manner. We here show how exact coherent structures that have figured prominently in studies on the transition to turbulence can selforganize to provide such a cascade of structures to smaller scales. The flow studied is rotating Couette flow restricted to two spatial degrees of freedom, which is essentially equivalent to 2d RayleighBenard flow. Within the quasilinear approximation to the NavierStokes equation, all transverse modes obey separate equations that depend on the mean velocity profile. The mean profile, on the other hand, is composed of contributions from all transverse modes. The hierarchy of modes that represent attached eddies then follows from a selfconsistent solution to the coupled equations. As the Reynolds number increases, so does the number of contributing modes. Scaling properties of the modes and of the profile can be derived. The study provides a mechanism by which the hypothesized attached eddies emerge selfconsistently from interactions in the NavierStokes equation. [Preview Abstract] 
Monday, November 20, 2017 8:52AM  9:05AM 
F26.00005: On the existence of selfsimilar structures in turbulent pipe flow Leo Hellström, Tyler Van Buren, John Vaccaro, Alexander Smits Townsend's attached eddy hypothesis assumes the existence of a set of geometrically selfsimilar eddies in the logarithmic layer in wallbounded turbulent flows that scale with their distance from the wall. Although there is statistical evidence to support the scaling of the attached eddies in the wallnormal and spanwise directions, there is little evidence to support the existence of fully threedimensional selfsimilar coherent motions in the loglayer. Here we present experimental results of a study of coherent motions in pipe flow using two synchronized stereo PIV systems, to resolve threecomponent velocity data simultaneously in two pipe crosssections with streamwise spacing spanning from $0$ to $9.97R$, at $Re_\tau = 2390$. The data reveal a set of structures with selfsimilar behavior in all three dimensions. Interestingly, the resolved eddies show some geometrical variations among structures of different physical sizes where, for instance, the smaller structures have a more stable streamwise repetition mechanism compared to their larger counterparts. [Preview Abstract] 
Monday, November 20, 2017 9:05AM  9:18AM 
F26.00006: Instantaneous structure of a boundary layer subjected to freestream turbulence R. Jason Hearst, Charitha de Silva, Eda Dogan, Bharathram Ganapathisubramani A canonical turbulent boundary layer (TBL) has a distinct turbulent/nonturbulent interface (TNTI) separating the rotational wallbounded fluid from the irrotational freestream. If an intermittency profile is constructed separating the flow above and below the TNTI, this profile can be described by an errorfunction. Within the turbulent region, the flow is separated by interfaces that demarcate uniform momentum zones (UMZs). We observe that these characteristics of a TBL change if there is freestream turbulence (FST). First, the entire flow is rotational, and thus a distinct TNTI does not exist. Nonetheless, it is possible to identify an interface that approximately separates the flow with mean zero vorticity from the distinctly wallsigned vorticity. This turbulent/turbulent interface is shown to be closer to the wall than the traditional TNTI, and the resulting intermittency profile is not an errorfunction. Also, UMZs appear to be masked by the freestream perturbations. Despite these differences, a velocity field of a TBL with homogeneous, isotropic turbulence superimposed and weighted with the empirical intermittency profile, qualitatively reproduces the 1st and 2ndorder statistics. These findings suggest that a TBL subjected to FST may be described by a simple model. [Preview Abstract] 
(Author Not Attending)

F26.00007: TimeSeries Analysis of Intermittent Velocity Fluctuations in Turbulent Boundary Layers Mohsen Zayernouri, Mehdi Samiee, Mark M. Meerschaert, Joseph Klewicki Classical turbulence theory is modified under the inhomogeneities produced by the presence of a wall. In this regard, we propose a new time series model for the streamwise velocity fluctuations in the inertial sublayer of turbulent boundary layers. The new model employs tempered fractional calculus and seamlessly extends the classical 5/3 spectral model of Kolmogorov in the inertial subrange to the whole spectrum from large to small scales. Moreover, the proposed timeseries model allows the quantification of data uncertainties in the underlying stochastic cascade of turbulent kinetic energy. The model is tested using wellresolved streamwise velocity measurements up to friction Reynolds numbers of about 20,000. The physics of the energy cascade are briefly described within the context of the determined model parameters. [Preview Abstract] 
Monday, November 20, 2017 9:31AM  9:44AM 
F26.00008: Coherent structures in high Reynolds number turbulent shear flows Armin Zare, Joseph Nichols, Mihailo Jovanovic Spatiotemporal frequency response analysis of stochasticallyforced linearized NavierStokes equations enables efficient computation of the energy amplification as well as estimation of the convection velocity and spatial structure of fluctuations. For a turbulent channel flow with $R_\tau=2003$, we build on recent work by Zare, Jovanovic, and Georgiou (J. Fluid Mech., vol. 812, 2017) to determine the forcing statistics to the linearized model that provide consistency with the result of nonlinear simulations in matching onepoint velocity correlations. The frequency response of the resulting model can be used to estimate the convection velocity for various spatial length scales as a function of the wallnormal distance. We examine twopoint correlations of the fluctuating velocity field and the wallnormal support of the most amplified spatial structures. Our results provide insight into the validity of Taylor's hypothesis as well as the functional forms of twopoint correlations that result from Townsend's attachededdy hypothesis. [Preview Abstract] 
Monday, November 20, 2017 9:44AM  9:57AM 
F26.00009: Datadriven spectral filters for decomposing the streamwise turbulent kinetic energy in turbulent boundary layers Woutijn J. Baars, Nicholas Hutchins, Ivan Marusic An organization in wallbounded turbulence is evidenced by the classification of distinctly different flow structures, including largescale motions such as hairpin packets and very largescale motions or superstructures. In conjunction with less organized turbulence, these flow structures all contribute to the streamwise turbulent kinetic energy $\langle u^2\rangle$. Since different class structures comprise dissimilar scalings of their overlapping imprints in the streamwise velocity spectra, their coexistence complicates the interpretation of the wallnormal trend in $\langle u^2\rangle$ and its Reynolds number dependence. Via coherence analyses of twopoint data in boundary layers we derive spectral filters for stochastically decomposing the streamwise spectra into subcomponents, representing different types of statistical flow structures. It is also explored how the decomposition reflects the spectral breakdown following the modeling attempts of Perry \emph{et al.} 1986 and Marusic \& Perry 1995. In the process we reveal a universal wallscaling for a portion of the outerregion turbulence that is coherent with the nearwall region for $Re_{\tau} \sim O(10^3)$ to $O(10^6)$, which is described as a wallattached selfsimilar structure embedded within the logarithmic region. [Preview Abstract] 
Monday, November 20, 2017 9:57AM  10:10AM 
F26.00010: Scaling of mean inertia and theoretical basis for a log law in turbulent boundary layers Jimmy Philip, Caleb MorrillWinter, Joseph Klewicki Log law in the mean streamwise velocity ($U$) for pipes/channels is well accepted based on the derivation from the mean momentum balance (MMB) equation and support from experimental data. For flat plate turbulent boundary layers (TBLs), however, there is only empirical evidence and a theoretical underpinning of the kind available for pipes/channels in lacking. The main difficultly is the mean inertia (MI) term in the MMB equation, which, unlike in pipes/channels, is not a constant in TBLs. We present results from our paper (JFM – 2017, Vol 813, pp 594617), where the MI term for TBL is transformed so as to render it invariant in the outer region, corroborated with high $Re$ ($\delta^+$) data from Melbourne Wind Tunnel and New Hampshire Flow Physics Facility. The transformation is possible because the MI term in the TBL has a ‘shape’ which becomes invariant with increasing $\delta^+$ and a ‘magnitude’ which is proportional to $1/\delta^+$. The transformed equation is then employed to derive a log law for $U$ with $\kappa$ an order one (vonKarman) constant. We also show that the log law begins at $y^+ = C_1\sqrt{\delta^+}$, and the peak location of the Reynolds shear stress, $y^+_m = C_2 \sqrt{\delta^+}$, where, $C_1\approx 3.6$ and $C_2\approx 2.17$ are from high $Re$ data. [Preview Abstract] 
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