Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session B30: Instabilities and Turbulence |
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Sponsoring Units: DFD Chair: Robert Ecke, Los Alamos National Laboratory Room: Colorado Convention Center 304 |
Monday, March 5, 2007 11:15AM - 11:27AM |
B30.00001: Lagrangian statistics in two-dimensional turbulence Michael Rivera, Robert Ecke Using data obtained from a stably stratified shallow layer of fluid, we generate Lagrangian trajectories from which a number of statistical quantities can be calculated. Of particular interest are the Lagrangian structure functions of the velocity difference and the acceleration statistics. We find Kolmogorov like scaling in the Lagrangian structure functions (when plotted using ESS) in the direct enstrophy cascade range, and deviations from Kolmogorov in the inverse energy cascade range. This is somewhat surprising because there is a marked lack of intermittency in the inverse energy range. Intermittency is associated with deviations from Kolmogorov scaling in three-dimensional experiments. [Preview Abstract] |
Monday, March 5, 2007 11:27AM - 11:39AM |
B30.00002: Pressure Fluctuations in Two-dimensional Turbulence Yonggun Jun, X.L. Wu We investigate pressure fluctuations in two-dimensional (2D) turbulence driven electromagnetically in a freely suspended soap film. The reduced probability distribution function (PDF), $P(p/\sigma_{p})$, is found to be universal for different Reynolds numbers and consists of asymmetrical exponential wings, where $\sigma_{p}\equiv\langle p^{2}\rangle^ {1/2}$ is the standard deviation. The calculated pressure skewness $S_{p}=\langle p^{3}\rangle/\sigma_{p}^{3}\simeq-0.5$ is significantly smaller than predictions by simple 2D models (Holzer and Siggia, Phys. Fluids A5, 2525 (1993)) but surprisingly close to 3D calculations using a random velocity field with a Kolmogorov energy spectrum $E(k)\propto k^{-5/3}$. The pressure spectrum $E_{pp}(k)$ scales approximately as $E_ {pp}(k)\propto k^{-7/3}$ in the energy inverse-cascade subrange and $k^{-5}$ in the enstrophy cascade subrange. These observations suggest that pressure fluctuations is essentially a large-scale phenomenon and the presence of an enstrophy cascade has no effect on the tails of $P(p/\sigma_{p})$. [Preview Abstract] |
Monday, March 5, 2007 11:39AM - 11:51AM |
B30.00003: ABSTRACT WITHDRAWN |
Monday, March 5, 2007 11:51AM - 12:03PM |
B30.00004: Three regularizations as turbulent subgrid models Jonathan Pietarila Graham, Darryl Holm, Pablo Mininni, Annick Pouquet Geophysical and astrophysical phenomena involve a huge range of scales. The number of degrees of freedom are inconceivable for numerical simulations to achieve, and truncation of the omitted scales removes important physics. Regularization subgrid models for this closure problem have recently emerged. Unlike many Large Eddy Simulations (LES), these models have guarantees on the computability of their solutions, conserve energy, and recover the physical equations as the filter width vanishes. Three regularizations can be viewed as LES with successively more complex subgrid-stress terms: the Clark, Leray, and alpha models. Comparing these, we establish the affects of each term. As each has different small-scale energy spectra this can shed light on the link between small-scale properties of the flows and their intermittent behavior. We find that Leray fails to recover large-scale anisotropy in our flow and the time scale for the development of turbulence. The Clark and alpha models both perform well in these regards but require extra dissipative for adequate computational gains. We also test the helicity of vortex tubes, Beltramization of the flow, and statistical properties for the subgrid models. [Preview Abstract] |
Monday, March 5, 2007 12:03PM - 12:15PM |
B30.00005: Simultaneous Velocity Discrimination Method of Two-Phase Flows Using Time Resolved Stereo PIV and PTV P.B. Vanderwerker, Y. Chen, M.M. Torregrosa, F.J. Diez, S. Photos, D. Troolin Multiphase jets laden with particles appear in many engineering and environmental processes. Typical examples are sprays containing liquid fuel drops in combustion processes, air jets laden with coal particles in a power plant, and the dispersion of harmful substances like soot and pollutants from steady exhaust flows, among others. Studies of particle-laden turbulent flows suggest that particle distribution is not uniform but preferential. In order to understand the mechanism of particle dispersion, time resolved simultaneous 3D velocity measurements of the disperse phase and of the fluid flow were made. Two-phase discrimination algorithms were developed based upon the filtering methodology proposed by Khalitov {\&} Longmire (2002), allowing for complete separation of the two-phases in stereo PIV images. The different filtering methods studied include separation of the two-phases using: (1) particle size discrimination, (2) particle intensity discrimination, (3) particle size and intensity discrimination, and (4) fluorescent particles for one of the two-phases. This methodology also enables time-resolved instantaneous 3D velocity fields using PTV and PIV on the disperse phase and fluid flow phase respectively. These allow visualization of 3D turbulent coherent structure evolution in the fluid as well as the evolution of the dispersed phase. [Preview Abstract] |
Monday, March 5, 2007 12:15PM - 12:27PM |
B30.00006: Measurement of entrainment and mixing in oceanic overflows Philippe Odier, Jun Chen, Michael Rivera, Robert Ecke The mixing and entrainment processes existing in oceanic overflows, e.g., Denmark Strait Overflow (DSO), affect the global thermohaline circulation. Owing to limited spatial resolution in global climate prediction simulations, the small-scale dynamics of oceanic mixing must be properly modeled. We have built a facility (Oceanic Overflow Facility) allowing the study of a gravity current along an inclined plate, flowing into a steady ambient medium. At small values of the Richardson number, the shear dominates the stabilizing effect of the stratification and the flow at the interface of the current becomes unstable, resulting in turbulent mixing. In addition, the level of turbulence is enhanced by an active grid device. Using PIV and PLIF to measure, respectively, the velocity and density fields, we characterize the statistical properties of the mixing. We also study the entrainment of the ambient fluid by the flow. An accurate parametrization of the mixing and entrainment can be a valuable input for ocean circulation models. [Preview Abstract] |
Monday, March 5, 2007 12:27PM - 12:39PM |
B30.00007: Finite Size Effects in the Quasi-geostrophic Inverse Cascade Colm Connaughton In the standard statistical theory of quasi-geostrophic turbulence forced at intermediate scales, two cascades are produced. Energy flows to large scales and potential enstrophy flows to small scales. The inverse cascade of energy is very similar to that which occurs in purely two-dimensional hydrodynamics. In that case, interesting phenomena occur if the friction between the fluid layer and the substrate is sufficientlyweak to allow the inverse cascade to reach the size of the system. Most striking among these is the spontaneous emergence of very intense coherent vortices which suppress turbulent fluctuations. A similar situation can arise in the quasi-geostrophic inverse cascade if the Ekman damping is weak enough, the scenario which I will describe in this talk. The situation is richer because large scale coherence can be obtained either through the formation of large vortices or through the formation of zonal jets. [Preview Abstract] |
Monday, March 5, 2007 12:39PM - 12:51PM |
B30.00008: Measured oscillations of the velocity and temperature fields in turbulent Rayleigh-B\'{e}nard convection in a rectangular cell Sheng-Qi Zhou, Chao Sun, Ke-Qing Xia We report experimental measurements of the velocity and temperature oscillations in a rectangular cell. The aspect ratios are $\Gamma_x=1$ and $\Gamma_y=1/4$ so that the large scale convective flow is confined in the plane of $\Gamma_x=1$. From particle image velocimetry (PIV) measurement it is found that the large-scale flow plane aligns along the diagonal plane of the cell. The large scale circulation is found to be oscillatory based on analysis of the autocorrelation functions of the velocity and temperature fields. It is well known that oscillations of velocity and temperature exist in cylindrical cells. The fact that they are now also found in a rectangular cell suggests that the oscillation phenomenon is an intrinsic character of the convective flow rather than the geometric character of convection cell. In the range of Ra from $3.5\times10^{10}$ to $9\times10^{11}$, it found that the oscillation frequency of temperature $f_{T}\sim Ra^{0.45}$ and that of the velocity $f_{V}\sim Ra^{0.51}$, which are close to results from previous measurements made in cylindrical cells. [Preview Abstract] |
Monday, March 5, 2007 12:51PM - 1:03PM |
B30.00009: A connexion between turbulence in Rayleigh Taylor flows and turbulence in other buoyant flows Olivier Poujade An increasing number of numerical simulations and experiments describing the turbulent spectrum of Rayleigh-Taylor (RT) mixing layers came to light over the past few years. Results reported in recent studies allow to rule out a turbulence {\it \`a la Kolmogorov} as the main mechanism acting on a self similar RT turbulent mixing layer. In this case, the injected power is due to buoyancy motion on a broad range of length scales. We have generalised Lin's spectral equation to buoyant flows and we have shown that this injected power tends to accumulate at large scales so that big whirls can get bigger as the mixing layer thickness increases. Only a small fraction of this power is transferred to small scales through a Kolmogorov cascade and dissipated. This balance between the accumulation of energy at large scales and the buoyancy production can also be applied to Rayleigh-B\'enard instabilities. It explains the Bolgiano-Obukov scaling predicted and experimentally observed for these flows. [Preview Abstract] |
Monday, March 5, 2007 1:03PM - 1:15PM |
B30.00010: Unsteady Kelvin-Helmholtz instability of an inmiscible interface with a large contrast in viscosity Harunori Yoshikawa, Jose-Eduardo Wesfreid We studied a stability problem of two-layer oscillatory flows, especially with an interest in the case of a large contrast in viscosity at the interface. Preceding experimental studies showed that static deformations of the interface, often referred to as ``frozen waves,'' happened beyond a threshold. Theoretically, we examined exhaustively the linear stability of the system for any viscosity contrast. What we found are: (i) destabilizing effect by the viscosity contrast and (ii) frequency dependence of the wave length selected by the linearly most instable mode. Instability is provoked by a smaller excitation in the case of large viscosity contrast within a certain band of frequency. The second point shows a deviation from the classical KHI. For high frequencies, the most instable mode has the capillary wave length, while for low frequencies, a longer one. Within an intermediate frequency range, the most instable mode can have a shorter wave length than the capillary one, depending on the viscosity contrast. We also realized a model experiment in a small-frequency range rarely investigated in the preceding studies. The two fluids were chosen so that the contrast in viscosity was very large ($10^4$ times difference in kinematics viscosity). Interface behavior was determined in detail. Results were in good agreement with our theoretical predictions. [Preview Abstract] |
Monday, March 5, 2007 1:15PM - 1:27PM |
B30.00011: Growth of Convective and Absolute Instabilities in Co-flowing Jets Andrew Utada, Alberto Fernandez-Nieves, David Weitz We have shown recently that the dripping-to-jetting transition in co-flowing liquids is controlled by two non-dimensional numbers: the capillary number (\textbf{\textit{Ca}}$_{out})$ of the outer liquid and the Weber number of the inner liquid (\textbf{\textit{We}}$_{in})$. When jetting is forced by \textbf{\textit{Ca}}$_{out}$, the diameter of the jet narrows in the downstream direction and the drop size scaling is well predicted assuming that the Rayleigh-Plateau instability is convected along the jet to cause its break up. However, when jetting is forced by \textbf{\textit{We}}$_{in}$, the diameter of the jet widens in the downstream direction and the resultant drop size can not be predicted assuming that the Rayleigh-Plateau instability causes the jet to break up. Instead, we believe these jets break due to absolute instabilities. [Preview Abstract] |
Monday, March 5, 2007 1:27PM - 1:39PM |
B30.00012: Lattice Boltzmann Model for Two-Dimensional Flow of Immiscible Fluids between Closely-Spaced Plates Alex Fore, Robert Sekerka, Michael Widom We formulate a Lattice Boltzmann (LB) model for simulation of two-dimensional flow of nearly-immiscibile fluids between closely spaced parallel plates. We treat displacement of a more viscous fluid by a less viscous fluid, as in a Hele-Shaw cell. The nearly two dimensional flow leads to the well-known Saffman-Taylor instability. We use a binary (A-B) LB model to simulate the problem. We account for the effects of the thin dimension between the plates via a drag force that we obtain by averaging the equations of motion over the thin dimension. We consider the A-B solution to be a regular solution with a strongly repulsive potential and use the effective potential method, consistent with equilibrium thermodynamics, to model non-ideal solutions. To control the viscosity of each phase we use a mixing rule for the relaxation time that depends linearly on mole fraction. We use a gradient energy on the mole fraction to attain control over the interface width and surface tension. We use this model to simulate viscous fluid displacement in a rectangular Hele-Shaw cell. Preliminary results display the Saffman-Taylor instability which we compare with a classical linear stability analysis. We have also observed time development of nonlinear fingering patterns. [Preview Abstract] |
Monday, March 5, 2007 1:39PM - 1:51PM |
B30.00013: A Numerical Study of Shock-Bubble Multiple Interaction Lingling Wu, Xiaolin Li This paper studies the numerical solution of shock-bubble multiple interactions through reflecting walls. Front tracking method is applied to track the dynamic motion of the interface and FFT method is used to analyze the enstrophy changes during the process. Our results suggest that the enstrophy is a monotonically increasing function of the Mach number and the bubble radius when the density ratio of the two fluids inside and outside the bubble is fixed. Moreover from light-in/heavy-out to heavy-in/light-out, enstrophy is a monotonic function of the Atwood number. The analysis of these different cases provides a quantitative understanding about the vorticity generation in the turbulent mixing as a result of the Richtmyer-Meshkov instability induced by shock-contact interaction. We have also compared numerical solutions with and without tracking of the contact surface. The comparison shows that the untracked solution suffered substantial loss of enstrophy due to numerical diffusion. [Preview Abstract] |
Monday, March 5, 2007 1:51PM - 2:03PM |
B30.00014: Non-Brownian microrheology of a fluid-gel interface Erik K. Hobbie, Sheng Lin-Gibson, Satish Kumar We use stroboscopic video microscopy to study the stability of a planar fluid-gel interface under simple steady shear flow. External mechanical noise plays a role analogous to temperature, with periodic fluctuations associated with the repeated build-up and release of stress. We relate the high frequency motion of the interface to the rheological properties of the underlying gel, pointing toward potential applications in the area of non-Brownian optical microrheology. At low frequency, the data suggest a breakdown of linear response, which we interpret as the emergence of an instability that is intrinsic to the driven interface. [Preview Abstract] |
Monday, March 5, 2007 2:03PM - 2:15PM |
B30.00015: Spin dewetting of wetting and partially wetting fluids Shomeek Mukhopadhyay, Robert Behringer One of the classical results of fluid dynamics is the free-surface flow of a viscous liquid in a vertically rotating cylinder, where the free surface becomes a paraboloid. This solution neglects both viscosity and surface tension, and makes the unphysical prediction that the fluid height can become negative beyond a certain critical angular velocity (for a given fluid height). We perform experiments with completely wetting PDMS oil on silcon wafer, where beyond the critical angular velocity, the central region never dewets, but goes to a nominally flat state over long times. The dynamics of the transition to this final state depends on the angular speed and the initial radius of the dewetting region. There is a marked difference in the spin-up and spin-down dynamics. When the completely wetting liquid is replaced by a partially wetting liquid a dry central spot opens up, occasionally leaving a droplet trail. In both cases the contact line does not develop any azimuthal instabilities. Collaboration with Tom Witelski and Mihaela Froehlich. [Preview Abstract] |
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