Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session LR: Turbulent Boundary Layers: Dynamics |
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Chair: Merideth Metzger, University of Utah Room: Hilton Chicago Stevens 3 |
Tuesday, November 22, 2005 8:00AM - 8:13AM |
LR.00001: Linear Dynamics of Turbulent Structures in the Log Layer Oscar Flores, Javier Jimenez The long streamwise-velocity $u-$structures of the log layer are analyzed using the linearized Navier-Stokes equation for a logarithmic mean velocity profile and an appropriate eddy viscosity. A concentrated wall-normal $v$ velocity diffuses into a $v$-puff which leaves upstream a $u$ ``log layer streak" with an energy maximum in the wall region. The lifetime of $v$ is short and the $u$-streak grows even after $v$ decays, eventually becoming self-similar. These results compare well with the conditionally-averaged structures obtained from turbulent channels by del \'Alamo {\em et al} (2005), except that here there is no wake downstream of the puff. This suggests that the puffs are created at the tails of the streaks, leading to long $u$-structures containing several puffs. This is essentially the same vortex-streak cycle known to be responsible for buffer layer streaks, but acting in the log-layer with larger self-similarly growing structures. The short life of $v$ implies that this process does not always originate at the wall. Indeed, using rough-wall profiles, the wall component weakens but the log-layer one is not affected. [Preview Abstract] |
Tuesday, November 22, 2005 8:13AM - 8:26AM |
LR.00002: Quantitative assessment of low-dimensional POD-ODE models of wall-bounded flows. John Gibson, Dietmar Rempfer, John Lumley We examine low-dimensional ODE models of coherent structures in wall-bounded flows derived from proper orthogonal decomposition and Galerkin projection. We show that POD-ODE models of periodized boundary-layer flow are linearly stable about the mean flow for some parameter values, despite the lack of upper-surface velocity boundary conditions. However, such models are predictively and statistically inaccurate. We compare POD-ODE models of plane Couette flow to direct numerical simulations and find that the convergence rate of the modeled dynamics is very slow --much slower than the convergence of POD expansions to instantaneous velocity fields. Eddy viscosity models do not improve the convergence of POD-ODE dynamics. However, numerical results suggest that Galerkin projection is sub-optimal, and that more accurate models of the low-dimensional dynamics can be derived through empirical modeling. [Preview Abstract] |
Tuesday, November 22, 2005 8:26AM - 8:39AM |
LR.00003: Minimal Requirements for Self-Sustained Turbulence in a Square Duct: a Numerical Investigation Alfredo Pinelli, Markus Uhlmann, Genta Kawahara Direct Numerical Simulations of unsteady square channel flows are performed at low to moderate Reynolds numbers diminishing in a systematic way the streamwise length of the computational domain. The basic motivation of the present study is twofold. On one hand we want to determine the minimal requirements for the self-sustainment of a turbulent flow (J. Jim\'enez \& P. Moin, JFM 225: 213-240, 1991). On the other hand, we wish to characterise the flow system on the verge of re-laminarization. Under this condition it is expected that the secondary corner vortices and the near-wall coherent structures collapse in terms of length scales leading to a global motion with a limited number of degrees of freedom. The eventual existence of this reduced basin of attraction may help in shedding some light on the generation mechanism of the secondary flow and on the mechanisms related with non-linear transitional regime. Another objective of the present work aims at establishing a detailed, highly resolved DNS description of this class of flow that received little attention in the past (S. Gavrilakis, JFM 244, 101-129, 1992, A. Huser \& S. Biringen, JFM 257, 65-95, 1993). [Preview Abstract] |
Tuesday, November 22, 2005 8:39AM - 8:52AM |
LR.00004: Large-box DNS of a turbulent channel at $Re_\tau \approx 2000$ Sergio Hoyas, Javier Jim\'enez A DNS of a turbulent channel has been performed at $Re_{\tau}\approx2000$ in a computational box of dimensions $(8\pi\times 2\times 3\pi)h$, using dealiased Fourier expansions in $x-z$, and compact finite differences in $y$. The results broadly confirm lower $Re_\tau$'s, but there is enough scale separation to distinguish some features of the logarithmic layer. At $y^+=15$ the $u$-spectrum has a wall-streak component whose length is $\lambda_x^+=300-5000$ and $\lambda_z sim\lambda_x^{1/3}$, and an outer one with $\lambda_x/h=2-10$ and $\lambda_z \sim\lambda_x$. The former peaks near the wall, and the latter moves outwards across the logarithmic layer as $\lambda_x$ increases. The intensities of the transverse velocity fluctuations collapse well with other Reynolds numbers when expressed in wall units, although the spanwise velocity has an unsuspected near-wall peak. The mean velocity has almost a decade of logarithmic profile. The streamwise velocity fluctuations have a short $k^{-1}$ spectral range, but they don't collapse in wall units. [Preview Abstract] |
Tuesday, November 22, 2005 8:52AM - 9:05AM |
LR.00005: Asymptotic Analysis of the Constant Pressure Turbulent Boundary Layer Thomas Lundgren
Following Mellor (1972), the Navier-Stokes equations are expanded
in the
small parameter $\epsilon (=u_{\tau}/U_{\infty})$ which is
determined as
a function of Reynolds number by the matching process. The
present analysis
differs from previous ones by employing the complete unsteady NS
equations
instead of the unclosed mean equations. The result is an overlap
logarithmic
inertial range with time dependent additive constants. The
specific results
are (with $X=x/\delta, Y=y/\delta, Z=z/\delta,
T=U_{\infty}t/\delta$):
$u/U_{\infty}=1+\epsilon(\kappa^{-1}\ln(Y)+B_0(X-T,Z)); v/U_{\infty}=
\epsilon A_0(X-T,Z);
w/U_{\infty}=\epsilon C_0(X-T,Z)$, where $A_0, B_0, C_0$ are
random functions
of $T$ when $X,Z$ are fixed, and $\epsilon=\kappa/\ln(\epsilon
R_e b), b=cst$
determines the wall friction in terms of the Reynolds number in
the usual way.
Note that the logarithmic part is steady. B.Lindgren et al (PF
{\bf 16},2004)
have shown experimentally that the fluctuations of $u$ about the
mean, i.e.
$B_0- |
Tuesday, November 22, 2005 9:05AM - 9:18AM |
LR.00006: Energy amplification in turbulent channels Juan C. del Alamo, Javier Jimenez, Paulo Zandonade, Robert D. Moser We study the temporal stability of the Orr-Sommerfeld and Squire equations in channels with turbulent mean velocity profiles and turbulent eddy viscosities. All the eigensolutions of this problem are damped, but initial perturbations with wavelengths $\lambda_x > \lambda_z$ can grow temporarily before decaying. For each wavelength, the structure of the most amplified solution agrees with that of the most energetic POD eigenfunction obtained from the available direct numerical simulations ($180 \le Re_\tau \le 1900$). The transient growth has two local maxima at $\lambda_z^+ = 100$ and $\lambda_z/h = 3$, which coincide with the widths of the near-wall streaks and of the largest structures of the outer layer. The dynamics of both the near-wall and the outer solutions are similar. They start with a wall-normal $v$ event which does not grow but which forces streamwise velocity fluctuations by stirring the mean shear ($uv<0$). The resulting $u$ fluctuations grow significantly and last longer than the $v$ ones, containing nearly all the kinetic energy at the instant of maximum amplification. [Preview Abstract] |
Tuesday, November 22, 2005 9:18AM - 9:31AM |
LR.00007: Pod Study of the Coherent Structures within a Turbulent Spot Amy Lang, Pablo Hidalgo, William Thacker In this experimental study, turbulent spots were created in the boundary layer on a flat plate inside a water tunnel using a peristaltic pump. Digital Particle Image Velocimetry (DPIV) obtained velocity vector field plots of turbulent spots and the Proper Orthogonal Decomposition (POD) analysis was used in order to identify and study the coherent structures within turbulent spots. The part of the turbulent spot studied was a 5 x 5 cm region of the trailing edge, since it was impossible to capture the entire spot due to size constraints. This region of the trailing edge was also chosen because it corresponded to the best data obtained from the DPIV system. The POD analysis resulted in eigenvalues, which represent the energy contributed by each coherent structure. The velocity vector fields corresponding to the POD eigenvectors were obtained and plotted in order to visualize each coherent structure. The results revealed the presence of low and high-speed streaks, as well as hairpin vortices within the turbulent spot. [Preview Abstract] |
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