Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session A26: Turbulent Boundary Layers I |
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Chair: Julio Soria, Monash University Room: 2007 |
Sunday, November 23, 2014 8:00AM - 8:13AM |
A26.00001: A unified theory for wall turbulence via a symmetry approach Zhen-Su She, Xi Chen, Fazle Hussain First principle based prediction of mean flow quantities of wall-bounded turbulent flows (channel, pipe, and turbulent boundary layer - TBL) remains a great challenge from both physics and engineering standpoints. Physically, a non-equilibrium physical principle governing mean properties in turbulent flows is yet unknown. Here, we outline a recently developed symmetry-based approach which derives analytic expressions governing the mean velocity profile (MVP) from an innovative Lie-group analysis. In analogy to the order parameter in Landau's (1937) mean-field theory, we develop a concept of order functions which are assumed to satisfy a dilation group invariance - representing the effects of the wall on fluctuations - allowing us to construct a set of new invariant solutions of the (unclosed) mean momentum equation (MME). The theory is validated by recent experimental and numerical data, and identifies a universal bulk flow constant 0.45 for all three canonical wall-bounded flows, which asymptotes to the true Karman constant at large Reynolds numbers. The theory equally applies to the quantification of the effects of roughness (She et al. 2012), pressure gradient, compressibility, and buoyancy, and to the study of Reynolds-averaged Navier-Stokes (RANS) models, such as k-$\omega $model, with significant improvement of the prediction accuracy. These results affirm that a simple and unified theory of wall-bounded turbulence is viable with appropriate symmetry considerations. [Preview Abstract] |
Sunday, November 23, 2014 8:13AM - 8:26AM |
A26.00002: Correspondences between self-similar mean dynamics and streamwise velocity behaviors in the inertial region of the turbulent boundary layer Ang Zhou, Joseph Klewicki Self-similar mean dynamics are analytically known to exist over a well-defined inertial domain of turbulent wall-flows [Klewicki 2013, \textit{J. Fluid Mech}. \textbf{718}, 596]. Well-resolved streamwise velocity measurements up to $\delta^{+} = $ 20,000 are used to investigate three measures of self-similarity in turbulent boundary layers, and compare their behaviors with those determined via analysis of the mean momentum equation. The measures include the Kullback-Leibler divergence (KLD) [Tsuji et al. 2005, \textit{Fluid Dyn. Res}. \textbf{37}, 293], the logarithmic decrease of even statistical moments [Meneveau {\&} Marusic 2013, J. Fluid Mech. \textbf{719}, R1], and the so-called diagnostic plot [Alfredsson {\&} Orlu 2010, \textit{Euro. J. Mech. B/Fluids} \textbf{42}, 403]. The present findings indicate that the approximately constant KLD profiles and the approximately logarithmic moment profiles follow the same scaling but reside interior to the bounds of the self-similar inertial domain associated with the mean dynamics. Conversely, the bounds of the self-similar region on the diagnostic plot correspond closely to the theoretically estimated bounds. A self-consistent physical interpretation is briefly discussed. [Preview Abstract] |
Sunday, November 23, 2014 8:26AM - 8:39AM |
A26.00003: Symmetry-based theory for mean velocities in the flat plate turbulent boundary layer Xi Chen, Fazle Hussain, Zhen-Su She A major difference from channel and pipe flow in zero-pressure-gradient turbulent boundary layer --ZPG-TBL is the streamwise development of the mean velocity components. We report a symmetry-based theory for ZPG-TBL, which yields a complete prediction for both the streamwise and vertical mean velocities, i.e. U(x,y) and V(x,y). A significant result is the identification of a bulk flow constant$\kappa_{b}$, which achieves a highly accurate description of U above y$^{+}$ $\sim$ 150; for a set of DNS data (Schlatter et al. 2010); the relative error is bounded within 0.1{\%}. It is found that $\kappa_{b}$ has a non-trivial streamwise development, and asymptote to 0.45 for large\textit{ Re's}; the latter is consistent with the true Karman constant recently discovered for channel and pipe flows. The theory assumes a fractional scaling for the total stress, which yields, for the first time, an analytical prediction for V, Reynolds stress profile, friction coefficient and shape factor in ZPG-TBL, in good agreement with both DNS and experimental data. In conclusion, a complete analytical theory is viable for both laminar (i.e. Blasius) and turbulent boundary layers. [Preview Abstract] |
Sunday, November 23, 2014 8:39AM - 8:52AM |
A26.00004: Statistical structure and scaling behaviors of spanwise vorticity in smooth-wall turbulent boundary layers Joseph Klewicki, Caleb Morrill-Winter, Ivan Marusic Within the canonical turbulent boundary layer the spanwise component of vorticity, $\omega_z$, is the only component that has a non-negligible mean value. For this and other reasons, the motions bearing $\omega_z$ play a central role in boundary layer dynamics. A compact four element (`Foss-style') hotwire probe was used to acquire well-resolved $\omega_z$ fluctuation time series over an unprecedented Reynolds number range, $1,500 \le \delta^+ = \delta u_{\tau}/\nu \le 15,000$. Very good spatial resolution ($\le 9$ viscous units) was maintained over the entire $\delta^+$ range by leveraging the low speed and large scale attributes of the HRNBLWT and FPF wind tunnels at Melbourne and New Hampshire, respectively. The present talk documents the behaviors of the statistical moments and frequency spectra of the $\omega_z$ fluctuations, and further explores the self-similarity between the mean and rms profiles seen at low Reynolds number. The observed $\omega_z$ behaviors are discussed relative to mean dynamical structure and the asymptotic properties of the boundary layer vorticity field. [Preview Abstract] |
Sunday, November 23, 2014 8:52AM - 9:05AM |
A26.00005: Phase relations of triadic scale interactions in turbulent flows Subrahmanyam Duvvuri, Beverley McKeon The quadratic nature of non-linearity in the Navier-Stokes (NS) equations dictates the coupling between scales in a turbulent flow to be of triadic form. An understanding of the triadic coupling affords good insights into the dynamics of turbulence, as demonstrated by Sharma \& McKeon (\emph{J. Fluid Mech.}, 2013) through analysis of the NS resolvent operator; a set of three triadically consistent spatio-temporal modes was shown to produce complex structures such as modulating packets of hairpin vortices observed in wall-bounded turbulent flows. Here we interpret Skewness ($Sk$) of velocity fluctuations and the Amplitude Modulation coefficient ($R_{am}$), proposed by Mathis, Hutchins \& Marusic (\emph{J. Fluid Mech.}, 2009), to be a measure of the large- and small-scale phase relationship. Through a simple decomposition of scales, both $Sk$ and $R_{am}$ are shown to be amplitude weighted (and normalized) measures of phase between scales that have direct triadic coupling. An analytical relationship is established between the two quantities and the result is demonstrated using experimental data from canonical and dynamically forced turbulent boundary layers presented in Duvvuri and McKeon (\emph{AIAA} 2014-2883). [Preview Abstract] |
Sunday, November 23, 2014 9:05AM - 9:18AM |
A26.00006: Uniform momentum zones in turbulent boundary layers Charitha de Silva, Ivan Marusic, Nicholas Hutchins We examine the properties of large regions of uniform streamwise momentum in turbulent boundary layers using databases obtained from particle image velocimetry that extend over 2.3 $\delta$ (where $\delta$ denotes the boundary layer thickness) in the streamwise direction and 1.2 $\delta$ in the wall-normal direction. The investigation covers a large range of Reynolds numbers, spanning more than an order of magnitude ($Re_\tau = 10^3-10^4$), but with adequate spatial resolution to resolve most structural features. This enables accurate descriptions of the structural evolution of the uniform momentum zones (UMZs) as a function of Reynolds numbers. Our analysis reveals evidence of a hierarchical length scale distribution of structures within turbulent boundary layers, leading to zonal-like organisations. The Reynolds number dependence of these features is also investigated. Interpretation of these results is aided by employing synthetic velocity fields generated by using the attached-eddy model. Comparisons between the model and experimental results show that the widely proposed packet model would lead to a distribution of UMZs that conforms closely to those observed experimentally in this study. [Preview Abstract] |
Sunday, November 23, 2014 9:18AM - 9:31AM |
A26.00007: A bursting phenomenon in a vortex-gas boundary layer Aarthi Sekaran, Roddam Narasimha, Rama Govindarajan Bursts are a central phenomenon in turbulent boundary layers as they are an integral part of turbulent energy and stress production. They have consequently been a continuing area of interest since the 1970s following the detailed investigations of Kline et al. (1967). Despite several attempts to understand their dynamics, it has been difficult to arrive at a consensus even on the scaling of the burst frequency. The present investigation simulates the outer part of a plane turbulent boundary layer using the vortex-gas model, in a first step towards understanding the role of the outer layer in boundary layer dynamics. Preliminary results indicate the formation of regions of concentrated vorticity near the wall, at a frequency that is independent of the initial vortex configuration but a function of the mean velocity profile. Further, comparisons with existing experimental data indicate a burst frequency which when scaled on outer variables, is within the range of scatter among different studies. Quadrant occupancy statistics are also related to those in conventional boundary layers. It appears as if a bursting phenomenon of some kind may be a general feature of an inviscid, wall-bounded shear flow, and does not necessitate inclusion of either viscosity or three-dimensionality. [Preview Abstract] |
Sunday, November 23, 2014 9:31AM - 9:44AM |
A26.00008: Coherent structures in homogeneous shear turbulence compared with those in channels Siwei Dong, Adri\'an Lozano-Dur\'an, Atsushi Sekimoto, Javier Jim\'enez Three-dimensional vortex clusters and coherent structures responsible for the momentum transfer (Qs) are studied by DNS in homogeneous shear turbulence (HST) at $Re_{\lambda}=50$, 100 and 250, with emphasis on comparisons with channel turbulence (CH). The anisotropic orientation of those structures only appears for volumes larger than $L_c^3$ ($L_c$ is the Corrsin scale). Even in that case, their anisotropy is moderate, similar to the detached structures in the CH. Only strictly attached structures in channels are more anisotropic. The Reynolds stress contained in vortex clusters is mainly associated with Q$^-$s, distributed equally between sweeps (Q4) and ejections (Q2), instead of preferentially with the latter, as in the CH. The average fractal dimension of Qs is roughly 2.1 and that of vortex clusters is 1.8. The relative positions of the structures reveal that they form streamwise trains of groups of a Q2 and a Q4, paired side-by-side in the spanwise direction, with vortex clusters in between, as in the CH. [Preview Abstract] |
Sunday, November 23, 2014 9:44AM - 9:57AM |
A26.00009: Dominant length scale of the ``pure'' turbulent fluctuations in the outer region of wall turbulence Yong Seok Kwon, Jason Monty, Nick Hutchins A new method of decomposing the total velocity in boundary layers, which removes the influence of instantaneous boundary layer thickness variations to the fluctuating velocity component, is proposed. The recent proposition of the quiescent core of turbulent channel flow by Kwon et al. (J. Fluid Mech., vol. 751, 2014, pp. 228--254) permits us to apply the same decomposition to channel flows where the quiescent core is analogous to the free-stream. Using this decomposition, it is observed that the majority of the large-scale streamwise velocity fluctuation within the intermittent region is attributed to the oscillation of the turbulent/non-turbulent interface or the quiescent core. It suggests that the quiescent core and the free-stream play a similar role and the flow nearer to the wall in both flows is more similar than previously thought while the different characteristics of the free-stream and the quiescent core account for the differences in the outer region of two flows. These findings re-affirm the analogy between the quiescent core and the free-stream, which could potentially lead to the unified conceptual model between internal and external flows. [Preview Abstract] |
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