On a self-sustained process at large scale in the turbulent channel flow

Large-scale motions, important in turbulent shear flows, are frequently attributed to the interaction of structures at smaller scale. Here we show that, in a turbulent channel at Re_{\tau} \approx 550, large-scale motions can self-sustain even when smaller-scale structures populating the near-wall and logarithmic regions are artificially quenched. This large-scale self-sustained mechanism is not active in periodic boxes of width smaller than Lz ~ 1.5h or length shorter than Lx ~ 3h which correspond well to the most energetic large scales observed in the turbulent channel

Large scale flow effects, energy transfer, and self-similarity on turbulence

The effect of large scales on the statistics and dynamics of turbulent fluctuations is studied using data from high resolution direct numerical simulations. Three different kinds of forcing, and spatial resolutions ranging from 256^3 to 1024^3, are being used. The study is carried out by investigating the nonlinear triadic interactions in Fourier space, transfer functions, structure functions, and probability density functions. Our results show that the large scale flow plays an important role in the development and the statistical properties of the small scale turbulence. The role of helicity is also investigated. We discuss the link between these findings and intermittency, deviations from universality, and possible origins of the bottleneck effect. Finally, we briefly describe the consequences of our results for the subgrid modeling of turbulent flows

Turbulence transition and the edge of chaos in pipe flow

The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the \emph{edge of chaos} which separates perturbations that decay towards the laminar profile and perturbations that trigger turbulence. Using the lifetime as an indicator and methods developed in (Skufca et al, Phys. Rev. Lett. {\bf 96}, 174101 (2006)) we show that superimposed on an overall $1/\Re$-scaling predicted and studied previously there are small, non-monotonic variations reflecting folds in the edge of chaos. By tracing the motion in the edge we find that it is formed by the stable manifold of a unique flow field that is dominated by a pair of downstream vortices, asymmetrically placed towards the wall. The flow field that generates the edge of chaos shows intrinsic chaotic dynamics.Comment: 4 pages, 5 figure

Pattern fluctuations in transitional plane Couette flow

In wide enough systems, plane Couette flow, the flow established between two parallel plates translating in opposite directions, displays alternatively turbulent and laminar oblique bands in a given range of Reynolds numbers R. We show that in periodic domains that contain a few bands, for given values of R and size, the orientation and the wavelength of this pattern can fluctuate in time. A procedure is defined to detect well-oriented episodes and to determine the statistics of their lifetimes. The latter turn out to be distributed according to exponentially decreasing laws. This statistics is interpreted in terms of an activated process described by a Langevin equation whose deterministic part is a standard Landau model for two interacting complex amplitudes whereas the noise arises from the turbulent background.Comment: 13 pages, 11 figures. Accepted for publication in Journal of statistical physic

Hydrodynamic response of rotationally supported flows in the Small Shearing Box model

The hydrodynamic response of the inviscid small shearing box model of a midplane section of a rotationally supported astrophysical disk is examined. An energy functional ${\cal E}$ is formulated for the general nonlinear problem. It is found that the fate of disturbances is related to the conservation of this quantity which, in turn, depends on the boundary conditions utilized: ${\cal E}$ is conserved for channel boundary conditions while it is not conserved in general for shearing box conditions. Linearized disturbances subject to channel boundary conditions have normal-modes described by Bessel Functions and are qualitatively governed by a quantity $\Sigma$ which is a measure of the ratio between the azimuthal and vertical wavelengths. Inertial oscillations ensue if $\Sigma >1$ - otherwise disturbances must in general be treated as an initial value problem. We reflect upon these results and offer a speculation.Comment: 6 pages, resubmitted to Astronomy and Astrophysics, shortened with references adde

Incompressible Turbulence as Nonlocal Field Theory

It is well known that incompressible turbulence is nonlocal in real space because sound speed is infinite in incompressible fluids. The equation in Fourier space indicates that it is nonlocal in Fourier space as well. Contrast this with Burgers equation which is local in real space. Note that the sound speed in Burgers equation is zero. In our presentation we will contrast these two equations using nonlocal field theory. Energy spectrum and renormalized parameters will be discussed.Comment: 7 pages; Talk presented in Conference on "Perspectives in Nonlinear Dynamics (PNLD 2004)" held in Chennai, 200

Toward a structural understanding of turbulent drag reduction: nonlinear coherent states in viscoelastic shear flows

Nontrivial steady flows have recently been found that capture the main structures of the turbulent buffer layer. We study the effects of polymer addition on these "exact coherent states" (ECS) in plane Couette flow. Despite the simplicity of the ECS flows, these effects closely mirror those observed experimentally: Structures shift to larger length scales, wall-normal fluctuations are suppressed while streamwise ones are enhanced, and drag is reduced. The mechanism underlying these effects is elucidated. These results suggest that the ECS are closely related to buffer layer turbulence.Comment: 5 pages, 3 figures, published version, Phys. Rev. Lett. 89, 208301 (2002

The helical decomposition and the instability assumption

Direct numerical simulations show that the triadic transfer function T(k,p,q) peaks sharply when q (or p) is much smaller than k. The triadic transfer function T(k,p,q) gives the rate of energy input into wave number k from all interactions with modes of wave number p and q, where k, p, q form a triangle. This observation was thought to suggest that energy is cascaded downscale through non-local interactions with local transfer and that there was a strong connection between large and small scales. Both suggestions were in contradiction with the classical Kolmogorov picture of the energy cascade. The helical decomposition was found useful in distinguishing between kinematically independent interactions. That analysis has gone beyond the question of non-local interaction with local transfer. In particular, an assumption about the statistical direction of triadic energy transfer in any kinematically independent interaction was introduced (the instability assumption). That assumption is not necessary for the conclusions about non-local interactions with local transfer recalled above. In the case of turbulence under rapid rotation, the instability assumption leads to the prediction that energy is transferred in spectral space from the poles of the rotation axis toward the equator. The instability assumption is thought to be of general validity for any type of triad interactions (e.g. internal waves). The helical decomposition and the instability assumption offer detailed information about the homogeneous statistical dynamics of the Navier-Stokes equations. The objective was to explore the validity of the instability assumption and to study the contributions of the various types of helical interactions to the energy cascade and the subgrid-scale eddy-viscosity. This was done in the context of spectral closures of the Direct Interaction or Quasi-Normal type

Evolution of turbulent spots in a parallel shear flow

The evolution of turbulent spots in a parallel shear flow is studied by means of full three-dimensional numerical simulations. The flow is bounded by free surfaces and driven by a volume force. Three regions in the spanwise spot cross-section can be identified: a turbulent interior, an interface layer with prominent streamwise streaks and vortices and a laminar exterior region with a large scale flow induced by the presence of the spot. The lift-up of streamwise streaks which is caused by non-normal amplification is clearly detected in the region adjacent to the spot interface. The spot can be characterized by an exponentially decaying front that moves with a speed different from that of the cross-stream outflow or the spanwise phase velocity of the streamwise roll pattern. Growth of the spots seems to be intimately connected to the large scale outside flow, for a turbulent ribbon extending across the box in downstream direction does not show the large scale flow and does not grow. Quantitatively, the large scale flow induces a linear instability in the neighborhood of the spot, but the associated front velocity is too small to explain the spot spreading.Comment: 10 pages, 10 Postscript figure