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: Resolvent-based modeling of passive scalar dynamics in wall-bounded turbulence Scott Dawson, Theresa Saxton-Fox, Beverley McKeon The resolvent formulation of the Navier-Stokes equations expresses the system state as the output of a linear (resolvent) operator acting upon a nonlinear forcing. Previous studies have demonstrated that a low-rank approximation of this linear operator predicts many known features of incompressible wall-bounded turbulence. In this work, this resolvent model for wall-bounded 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 low-rank 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 semi-analytic methods. We investigate the extent to which this resulting hierarchy of models can describe and predict passive scalar dynamics and statistics in wall-bounded 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 two-dimensional 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 non-zero 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 non-linear inter-scale interaction between large and small scales in a turbulent wall-bounded 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 hot-wire 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 hot-wire 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: Self-consistent 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 self-organize 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 Rayleigh-Benard flow. Within the quasilinear approximation to the Navier-Stokes 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 self-consistent 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 self-consistently from interactions in the Navier-Stokes equation. [Preview Abstract] |
Monday, November 20, 2017 8:52AM - 9:05AM |
F26.00005: On the existence of self-similar 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 self-similar eddies in the logarithmic layer in wall-bounded 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 wall-normal and spanwise directions, there is little evidence to support the existence of fully three-dimensional self-similar coherent motions in the log-layer. Here we present experimental results of a study of coherent motions in pipe flow using two synchronized stereo PIV systems, to resolve three-component velocity data simultaneously in two pipe cross-sections with streamwise spacing spanning from $0$ to $9.97R$, at $Re_\tau = 2390$. The data reveal a set of structures with self-similar 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 free-stream turbulence R. Jason Hearst, Charitha de Silva, Eda Dogan, Bharathram Ganapathisubramani A canonical turbulent boundary layer (TBL) has a distinct turbulent/non-turbulent interface (TNTI) separating the rotational wall-bounded fluid from the irrotational free-stream. If an intermittency profile is constructed separating the flow above and below the TNTI, this profile can be described by an error-function. 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 free-stream 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 wall-signed 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 error-function. Also, UMZs appear to be masked by the free-stream 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 2nd-order statistics. These findings suggest that a TBL subjected to FST may be described by a simple model. [Preview Abstract] |
(Author Not Attending)
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F26.00007: Time-Series 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 sub-layer 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 time-series model allows the quantification of data uncertainties in the underlying stochastic cascade of turbulent kinetic energy. The model is tested using well-resolved 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 Spatio-temporal frequency response analysis of stochastically-forced linearized Navier-Stokes 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 one-point 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 wall-normal distance. We examine two-point correlations of the fluctuating velocity field and the wall-normal 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 two-point correlations that result from Townsend's attached-eddy hypothesis. [Preview Abstract] |
Monday, November 20, 2017 9:44AM - 9:57AM |
F26.00009: Data-driven spectral filters for decomposing the streamwise turbulent kinetic energy in turbulent boundary layers Woutijn J. Baars, Nicholas Hutchins, Ivan Marusic An organization in wall-bounded turbulence is evidenced by the classification of distinctly different flow structures, including large-scale motions such as hairpin packets and very large-scale 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 wall-normal trend in $\langle u^2\rangle$ and its Reynolds number dependence. Via coherence analyses of two-point data in boundary layers we derive spectral filters for stochastically decomposing the streamwise spectra into sub-components, representing different types of statistical flow structures. It is also explored how the decomposition reflects the spectral break-down following the modeling attempts of Perry \emph{et al.} 1986 and Marusic \& Perry 1995. In the process we reveal a universal wall-scaling for a portion of the outer-region turbulence that is coherent with the near-wall region for $Re_{\tau} \sim O(10^3)$ to $O(10^6)$, which is described as a wall-attached self-similar 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 Morrill-Winter, 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 594-617), 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 (von-Karman) 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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