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 H25: Turbulence Theory: Wall-Bounded Flows |
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Chair: Javier Jimenez, Universidad Politecnica de Madrid Room: 2005 |
Monday, November 24, 2014 10:30AM - 10:43AM |
H25.00001: A minimal support for turbulence in a restricted nonlinear (RNL) model Vaughan Thomas, Dennice F. Gayme, Brian Farrell, Petros Ioannou In this work we explore the range of streamwise varying perturbations that can support self-sustaining turbulence in a restricted nonlinear (RNL) model of plane Couette flow. The RNL model partitions the dynamics of the flow field into a streamwise averaged mean flow and streamwise varying perturbations about that mean. The resulting system is a minimal representation of self-sustaining turbulence in which only a small number of streamwise varying perturbations interact with the mean flow. In the current work, we show that there is a minimum and maximum streamwise wavelength associated these streamwise perturbations. We also demonstrate that RNL turbulence can also be supported when the dynamics are further restricted to a single streamwise varying perturbation. This minimal RNL system possesses an upper and lower limit on the wavelengths associated with the single streamwise varying perturbation that is able to support RNL turbulence, i.e. when restricted to a perturbation whose wavelength is outside of this range, the RNL system returns to a laminar state. [Preview Abstract] |
Monday, November 24, 2014 10:43AM - 10:56AM |
H25.00002: Structure and spectra of self-sustaining turbulence in a restricted nonlinear model Dennice F. Gayme, Vaughan Thomas, Brian Farrell, Petros Ioannou In this work we study a restricted nonlinear (RNL) model for plane Couette flow. This model is derived directly from the Navier Stokes equations and permits higher resolution studies of the dynamical system associated with the stochastic structural stability theory (S3T) model, which is a second order approximation of the statistical state dynamics of the flow. The RNL system was previously shown to exhibit self-sustaining turbulence that closely resembles DNS of turbulence but has the computational advantage of being supported by a small number of streamwise modes. Here, we further examine the structures underlying RNL turbulence. In particular, we focus on the roll and streak structures that are known to be critical in the self-sustaining process of wall-turbulence. We compare the RNL structures to those obtained from DNS by examining the temporal spectra of their streak and roll energies as well as the spectral densities of these structures at different wall-normal positions. The results show close correspondence between the structure and spectra of the rolls and streaks as well as agreement between the mean velocity profiles obtained from RNL simulations and DNS. [Preview Abstract] |
Monday, November 24, 2014 10:56AM - 11:09AM |
H25.00003: Using Synchronization to study the self-sustaining process in plane Couette flow turbulence Brian Farrell, Petros Ioannou, Dennice Gayme, Vaughan Thomas We show that separate realizations of turbulence in restricted nonlinear (RNL) simulations of plane Couette flow can be synchronized by linearly relaxing only the stream wise averaged components of the flow. The RNL system is obtained directly from the Navier-Stokes (NS) system by decomposing the dynamics into stream wise mean and perturbation equations and neglecting the perturbation-perturbation nonlinearity in the latter. Previous work demonstrated that the RNL system self-sustains turbulence with a mean flow as well as structural and dynamical features consistent with DNS. Using synchronization we verify that the self-sustaining process (SSP) operating in the RNL system is the parametric Lyapunov mechanism previously demonstrated to operate in the closely related stochastic structural stability theory (S3T) system. [Preview Abstract] |
Monday, November 24, 2014 11:09AM - 11:22AM |
H25.00004: Approximation of traveling wave solutions in wall-bounded flows using resolvent modes Beverley McKeon, Michael Graham, Rashad Moarref, Jae Sung Park, Ati Sharma, Ashley Willis Significant recent attention has been devoted to computing and understanding exact traveling wave solutions of the Navier-Stokes equations. These solutions can be interpreted as the state-space skeleton of turbulence and are attractive benchmarks for studying low-order models of wall turbulence. Here, we project such solutions onto the velocity response (or resolvent) modes supplied by the gain-based resolvent analysis outlined by McKeon \& Sharma (JFM, 2010). We demonstrate that in both pipe (Pringle et al, Phil. Trans. R. Soc. A, 2009) and channel (Waleffe, JFM, 2001) flows, the solutions can be well-described by a small number of resolvent modes. Analysis of the nonlinear forcing modes sustaining these solutions reveals the importance of small amplitude forcing, consistent with the large amplifications admitted by the resolvent operator. We investigate the use of resolvent modes as computationally cheap ``seeds'' for the identification of further traveling wave solutions. [Preview Abstract] |
Monday, November 24, 2014 11:22AM - 11:35AM |
H25.00005: A restricted nonlinear-dynamics model for turbulent channel flows Adri\'an Lozano-Dur\'an, Javier Jim\'enez, Brian F. Farrell, Petros J. Ioannou, Marios A. Nikolaidis, Navid C. Constantinou The dynamics of the formation of very-large scale structure in turbulent plane Poiseuille flow is studied by restricting the nonlinearity in the Navier--Stokes (NS) equations to interactions between the streamwise-averaged flow and perturbations. Using comparisons with DNS, we show that this restricted nonlinear dynamics (RNL) supports essentially realistic turbulence at $Re_\tau=900$, despite the naturally occurring severe reduction in the set of streamwise wavenumbers supporting the turbulence. Using statistical diagnostics we verify that there are similar self-sustaining processes (SSP) underlying turbulence in the RNL and in the NS dynamics, separate manifestations of which operate in the buffer and outer layers. In the buffer layer, the SSP supports the familiar roll-streak mechanism of wall-bounded turbulence, while the outer-layer streaks in the RNL are probably the streamwise elongated structures referred to as VLSI. It is argued that the formation of the roll-streak structure is a universal mechanism that can be fruitfully studied in the minimal dynamics of RNL. [Preview Abstract] |
Monday, November 24, 2014 11:35AM - 11:48AM |
H25.00006: Identifying structure models in real turbulence Javier Jim\'enez Even when a model for the structures of a turbulent flow makes theoretical sense, it is important to test whether those structures are present in the flow, as well as how approximately and how often they appear. How that can be done is explored by tracking a linear transient-growth model for the logarithmic-layer in medium-size channel simulations ($Re_\tau$=1000--2000). The predicted linearized behavior is found in the evolution of `minimal' Fourier modes of the wall-normal velocity, but only during bursting events accounting for about half of the total elapsed time. In particular, if a wavefront tilt angle is defined for each mode, periods of increasing forward tilt correspond to amplitude bursts. It is mostly during those periods that the tilt is well defined but, even then, the linearly most amplified perturbations do not describe the flow well. The flow evolution is explained by the model, but nonlinear initial conditions remain important for the fluctuation profiles. Quantitative measures for the level of approximation are defined and reported. [Preview Abstract] |
Monday, November 24, 2014 11:48AM - 12:01PM |
H25.00007: Wavenumber-frequency spectra in the logarithmic layer of wall turbulence Michael Wilczek, Richard J.A.M. Stevens, Charles Meneveau We study space-time correlations of wall-bounded turbulence in terms of wavenumber-frequency spectra of the streamwise velocity component. The spectra are obtained from Large Eddy Simulations, which provide a full space-time record of the flow. We find that the frequency distributions exhibit a Doppler shift, which is a consequence of mean flow advection, as well as a considerable Doppler broadening, consistent with the Kraichnan-Tennekes random sweeping hypothesis. For wall-bounded turbulence, both of these effects vary with the wall distance and are closely related to the logarithmic behavior of the mean velocity profile and the velocity fluctuation profiles. We incorporate these observations into a simple analytical model for the wavenumber-frequency spectrum based on an advection equation featuring advection of the small-scale velocity fluctuations with a mean and a large-scale random-sweeping velocity. The model is found to be in very good agreement with the LES data. Potential applications of the model spectrum, e.g., to quantify the spatio-temporal structure of fluctuations in wind energy conversion, will be discussed. [Preview Abstract] |
Monday, November 24, 2014 12:01PM - 12:14PM |
H25.00008: Structures and scaling laws of turbulent Couette flow Martin Oberlack, Victor Avsarkisov, Sergio Hoyas, Andreas Rosteck, Jose P. Garcia-Galache, Andy Frank We conducted a set of large scale DNS of turbulent Couette flow with the two key objectives: (i) to better understand large scale coherent structures and (ii) to validate new Lie symmetry based turbulent scaling laws for the mean velocity and higher order moments. Though frequently reported in the literature large scale structures pose a serious constraint on our ability to conduct DNS of turbulent Couette flow as the largest structures grow with increasing Re\#, while at the same time Kolmogorov scale decreases. Other than for the turbulent Poiseuille flow a too small box is immediately visible in low order statistics such as the mean and limited our DNS to $Re_\tau=550$. At the same time we observed that scaling of the mean is peculiar as it involves a certain statistical symmetry which has never been observed for any other parallel wall-bounded turbulent shear flow. Symmetries such as Galilean group lie at the heart of fluid dynamics, while for turbulence statistics due to the multi-point correlation equations (MPCE) additional statistical symmetries are admitted. Most important, symmetries are the essential to construct exact solutions to the MPCE, which with the new above-mentioned special statistical symmetry led to a new turbulent scaling law for the Couette flow. [Preview Abstract] |
Monday, November 24, 2014 12:14PM - 12:27PM |
H25.00009: ABSTRACT WITHDRAWN |
Monday, November 24, 2014 12:27PM - 12:40PM |
H25.00010: The evolution of the very large scale motions in pipe flow Leo Hellstr\"om, Bharathram Ganapathisubramani, Alexander Smits We present a dual-plane snapshot POD analysis of turbulent pipe flow at a Reynolds number of 94,000. The high-speed PIV data were simultaneously acquired in two planes, a cross-stream plane (2D-3C) and a streamwise plane (2D-2C) on the pipe centerline. The two light sheets were orthogonally polarized, allowing particles situated in each plane to be distinguished. The dual-plane data were conditionally-averaged based on the occurrence/intensity of a given cross-stream snapshot POD mode. The conditionally-averaged modes reveal the streamwise extent and evolution of that particular cross-stream snapshot POD mode. A complex structure consisting of both wall-attached and detached large-scale structures is associated with the most energetic modes. The temporal evolution of these large-scale structures is examined using the time-shifted correlation of the cross-stream snapshot POD coefficients, identifying the low energy intermediate modes responsible for the transition between the large-scale modes. [Preview Abstract] |
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