Session R34: Turbulence

Measurements of the Multifractal Dimension of Lagrangian Turbulence

We report experimental measurements of the Lagrangian multifractal dimension spectrum in an intensely turbulent laboratory water flow by the optical tracking of tracer particles. These measurements are compared with three model dimension spectra. The Legendre transform of the measured spectrum is compared with measurements of the scaling exponents of the Lagrangian structure functions, and excellent agreement between the two measurements is found.   

Multifractal particle distribution in compressible turbulence on a free surface.

The distribution of particles in compressible turbulence on a free surface is inhomogeneous. The floaters flee regions of fluid up-wellings and cluster into ridge-like structures near fluid down-wellings. The concentration of floaters is measured on the surface of a large tank of turbulently stirred water. The multifractal structure of the clusters is reflected in the moments of particle concentration. The results are compared with recent work of Bec $et. al.$ [J. Bec, K. Gawedzki and P. Horvai, Phys. Rev. Lett., 92, 224501 (2004)] conducted on synthetic velocity fields that follow the compressible Kraichnan model.   

Velocity and Scalar intermittency in restricted Euler dynamics

A long standing problem in turbulence is to predict the intermittency from Navier-Stokes equation. Recently, by adopting a Lagrangian point of view and using the restricted Euler dynamics, we derived a simple nonlinear dynamical system, called advected delta-vee system, for the time evolution of longitudinal and transverse velocity increments, from which we showed that the non-Gaussian tails in turbulence originate from the inherent self-amplification of longitudinal velocity increments, and cross amplification of transverse velocity increments. Here, after reviewing previous results, the analysis is generalized to the increments of a passive scalar. A simple nonlinear equation is derived for the time evolution of scalar increments. The equation is coupled to the advected delta-vee system through the squeezing effect of the longitudinal velocity increment. Numerical integration of the equations starting from Gaussian initial conditions shows rapid development of non-Gaussian tails in the PDF of scalar increments, suggesting the system captures important trends in the original Navier-Stokes and scalar transport dynamics.   

How Gaussian is the Velocity Gradient Tensor at Large Scales in Hydrodynamic Turbulence?

Fully developed turbulent flows exhibit a continuous range of exited scales, from the finest (dissipative range) towards the integral scale where energy is injected. Many theoretical approaches use the assumption that at large scales the fluctuations display Gaussian statistics. This has also been repeatedly confirmed based on measurements of longitudinal velocity increments in the Eulerian framework and temporal velocity increments in the Lagrangian framework. When the separation is comparable to integral scales of the flow, the PDFs of these velocity increments display Gaussian statistics, in contrast to the elongated tails and non-Gaussian statistics at smaller scales. Motivated by recent insights gained from Restricted Euler dynamics, we examine the statistics of the full velocity gradient tensor and several of its invariants relevant to the transfer of energy from large to small scales. Using Direct Numerical Simulations, we study the coarse-grained and band-pass Eulerian velocity gradient tensor. Among other features, we show that even at the integral length scale, the gradient statistics deviate from Gaussianity.   

Quantum Fluid Mechanical Theory of Turbulence

Turbulence has been called the last great unsolved problem of classical physics. The difficulty of solving the turbulence problem classically (even with the help of recent large scale computer simulations) may be that the problem is not classical. Turbulence will here be described as due to the non-commuting nature of the components of the Landau quantum fluid velocity field. The formation of fractal dimensional regions of quantum vortex strings in fully developed turbulence will be discussed along with the implied Kolmogorov scaling functions.   

Counter-gradient transport in the atmospheric boundary layer

Counter-gradient transport in turbulent flows, also called negative viscosity, has been theorized and observed over the past century at a variety of spatial scales. More than one mechanism may be responsible for the process of transferring momentum from slower moving fluid to faster moving fluid depending on the scale of the flow and other flow properties. Horizontal divergence is presented as a possible mechanism for counter-gradient momentum transport observed in the atmospheric boundary layer.   

LES Simulations of Pulsed Gas Jets.

The study of pulsed jets is motivated by their applications which include increasing mixing, enhancing heat transfer, and controlling flow separation and vortex structures. This work investigates the interaction between gas jet pulses in the near-field using large eddy simulation (LES). LES employing the constant coefficient Smagorinsky model is compared to Reynolds-averaged Navier-Stokes (RANS) simulations with a two-equation k-$\varepsilon $ model. RANS predictions indicate faster penetration of subsequent jet pulses caused by the mean flow field from the first pulse, and do not show enhanced mixing due to residual turbulence. LES of the jet near-field includes development of the head vortex ring and transition to turbulence in the jet. LES of the pulsed gas jet predicts interaction of the head vortex with residual turbulence from an earlier pulse. The dominant effect of the mean flow field and the accelerated penetration seen in RANS predictions are not evident in the LES results.   

Vortical structures in a flume

We report the results of statistical spatial characterization of coherent structures in turbulent boundary layer in a flume. The characterization approach is based on the proper orthogonal decomposition (POD) of vorticity, elucidating large-scale coherent patterns in a turbulent boundary layer. The method was successfully applied to the two- and three-dimensional experimental data extracted from particle image velocimetry (PIV), and multi-plane stereoscopic PIV (XPIV) respectively, and the three-dimensional data from direct numerical simulation (DNS) in a channel flow. The large-scale structure was obtained by using linear combination of POD eigenmodes of vorticity. POD allows for methodological analysis of the properties of the educed structure in the different measurement planes (orthogonal in the case of 2D PIV and parallel in the case of XPIV) and in the different cross-sections of the DNS data. Based on the statistical approach we suggest a conceptual model of large-scale coherent structures in a turbulent boundary layer flow that incorporates the experimental and the numerical results. The proposed conceptual model is a spiral vortical structure attached to the wall and expanding in both the spanwise and the wall-normal directions. Its shape resembles a funnel structure and a `double-cone eddy' concept. The relationship of the model to the structures in the near wall region is presented.   

Single-point Velocity Statistics

The single-point (SP) velocity statistics is investigated in forced and decaying two-dimensional turbulence in a flowing soap film. It is shown that the probability distributin functions (PDF) in both cases deviate from a Gaussian distribution, which is normally anticipated in turbulent fluid flows. In the forced turbulence case, the tail of the SP velcoty PDF decays faster than Gaussian and can be correlated with the forcing statistics on small sclaes. In the decaying turbulence case, the SP velocity PDF evolves from a sub-Gaussion to a super- Gaussian behavior as a function of decaying time. In all times, however, the locally averaged vorticity distribution remains approximately Gaussian. While our forcing data may be explained by the instanton model put forward by Falkovich et al., the decaying turbulence data remain unexplained by theory.   

Coherent Structures in Decaying Two-Dimensional Turbulence

We revisit the matter of coherent structures, such as vortices, and their role in decaying two-dimensional turbulence. These experiments take place in an electromagnetically forced stratified layer within a square container with no slip boundaries and a linear dissipation with the container bottom. Results relating the energy and enstrophy of the bulk flow with the number and strength of coherent vortices are compared with earlier numerical and experimental work.   

Multiscale Distribution of Energy Transfer in Two Dimensional Turbulence

In two dimensional turbulence, the mechanisms responsible for energy transfer to larger scales are not well understood. We present results from an experimental system consisting of a square meter of electromagnetically driven thin salt water layer that is used to investigate this inverse energy cascade. A filter technique applied to high resolution velocity fields is used to understand scale to scale energy transfer. An extension of this technique determines the contribution of energy transfer across a given length scale from smaller scales. Expanding the subgrid coupling terms allows for some speculation of the energy transfer mechanisms.   

Statistical Properties of 2 Dimensional Turbulence in a Finite Box

In the standard statistical theory of two dimensional hydrodynamics forced at some intermiediate scale, two cascades are produced. Energy flows to large scales, producing Kolmogorov's $k^{-5/3}$ spectrum at small $k$ and enstrophy flows to small scales to produce Kraichnan's $k^{-3}$ spectrum at large $k$. If we consider turbulence in a finite box in the absence of large scale dissipation, the inverse cascade eventually reaches the size of the box and the cascade is blocked. This leads to accumulation of energy in the largest modes, a process which can be qualitatively thought of as a nonequilibrium condensation process. The ``condensate'' in this case is a coherent, large scale vortex dipole. We investigate how the system passes through a series of distinct regimes, leading to the emergence of this large scale structure. We show how it affects the scaling properties of two-dimensional turbulence and explain how the presence of very strong vortices leads to an apparent modification of the small scale statistical properties of the inverse cascade.   

Direct Numerical Simulations of Turbulent Flow in a Wavy Channel

A spectrally preconditioned biconjugate gradient algorithm (Bi-CGSTAB) has been developed that enabled us to perform high accuracy (spectral) efficient Direct Numerical Simulations (DNS) of Newtonian turbulent flow in an undulating channel geometry. The DNS of have been performed in a channel geometry involving a single sinusoidal solid wavy wall with amplitude/half width ratio of 0.1 and a wave length of 2. Two different friction Reynolds numbers have been investigated, Re$_{\tau }$=160 and 220 corresponding to mean Reynolds numbers (based on the channel half width) 1800 and 2480, respectively. The computational domain used was 10x2x5 along the streamwise, shearwise and spanwise direction respectively, with spectral resolutions ranging from 160x257x64 to 320x385x128. The numerical results compare well against Hudson's measurements (Hudson, Ph.D. Thesis, UIUC 1993). In addition, the DNS results allowed us to investigate in detail various turbulence statistics and the vorticity structure and its influence from the wall undulation.   

Non-Boussinesq effects on heat transport in turbulent Rayleigh-B\'enard convection of gases

In turbulent Rayleigh-B\'enard convection large temperature differences often are used in order to reach very high Rayleigh numbers. This can lead to a breakdown of the Boussinesq approximation which assumes temperature-independent fluid properties. We presents quantitative measurements of non-Boussinesq (NB) effects on the heat transport obtained by using Ethane gas at a mean temperature of 40$^\circ$C and pressures up to 40 bars. At the largest temperature differences of about 40$^\circ$C, where the top of the sample approached the vapor-liquid saturation curve, the Nusselt number was {\bf increased} above the Boussinesq value by several percent. This contrasts with NB effects in liquids\footnote{G. Ahlers, E. Brown, D. Funfschilling, S. Grossmann, and D. Lohse, J. Fluid Mech., submitted.} where the heat transport is reduced below the Boussinesq value.   

Lattice Boltzmann studies of drag reduction in turbulent channel flow with polymers.

Massive drag reduction in turbulent flow by dilute addition of polymers has long been a challenging problem in fluid dynamics. In order to study this problem here we use the Lattice Boltzmann method (LBM) to simulate turbulent channel flow. A polymer model, which is macroscopically equivalent to the FENE-P model, is included in LBM to represent polymers. Drag reduction with polymers was observed in the simulations. Although such drag reduction has been demonstrated in laboratory experiments, the mechanisms are not yet clear. In order to understand these results we investigated the role of dilute polymers on Kelvin-Helmholtz instability in the much simpler turbulent mixing layer. Our simulations of the mixing layer show that polymers produce a stabilizing effect and suppress momentum transport due to fluctuating velocity components. The simulations of these two systems together provide a clearer picture of the interaction between polymers and coherent structures in the near-wall region of the turbulent flow and shed light on the mechanism of drag reduction. The addition of polymers primarily modifies turbulent bursts in channel flow, and this phenomenon has several features in common with the effect of polymers on Kelvin-Helmholtz instability in the mixing layer.