Effect of Froude number on bubble clustering in a hydraulic jump

The study of bubble clustering processes may provide a significant insight into turbulent air–water flows. Previous studies investigated these processes in plunging jets, dropshafts and hydraulic jumps. This research investigates the bubble clustering process in hydraulic jumps using experimental data collected in a rectangular horizontal flume with partially developed inflow conditions for inflow Froude numbers in the range 6.5–14.3. Two criteria for cluster identification were applied: one criterion was based upon a comparison of the local instantaneous water chord time with the median water chord time, whereas the second identified a cluster if the water chord time was smaller than the air chord time of the preceding bubble, i.e. a bubble was in the near-wake of the leading bubble. The results highlight significant patterns in clusters production both over the flow depth and the distance from the jump toe. The effect of the inflow flow Froude number on the clustering process is also discussed. © 2010 International Association for Hydro-Environment Engineering and Researc

The return of the membrane paradigm? Black holes and strings in the water tap

Several general arguments indicate that the event horizon behaves as a stretched membrane. We propose using this relation to understand gravity and dynamics of black objects in higher dimensions. We provide evidence that (i) the gravitational Gregory-Laflamme instability has a classical counterpart in the Rayleigh-Plateau instability of fluids. Each known feature of the gravitational instability can be accounted for in the fluid model. These features include threshold mode, dispersion relation, time evolution and critical dimension of certain phase transitions. Thus, we argue that black strings break in much the same way as water from a faucet breaks up into small droplets. (ii) General rotating black holes can also be understood with this analogy. In particular, instability and bifurcation diagrams for black objects can easily be inferred. This correspondence can and should be used as a guiding tool to understand and explore physics of gravity in higher dimensions.Comment: This essay received an honorable mention in the Gravity Research Foundation Essay Competition, 2007. v2: Published versio

Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity

Dynamical Chern-Simons gravity is an extension of General Relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard General Relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun for Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods.Comment: RevTex4, 12 pages, 8 figures, 3 Tables. v2: minor typos corrected and references added. Published versio

Exact regularized point particle method for multi-phase flows in the two-way coupling regime

Particulate flows have been largely studied under the simplifying assumptions of one-way coupling regime where the disperse phase do not react-back on the carrier fluid. In the context of turbulent flows, many non trivial phenomena such as small scales particles clustering or preferential spatial accumulation have been explained and understood. A more complete view of multiphase flows can be gained calling into play two-way coupling effects, i.e. by accounting for the inter-phase momentum exchange between the carrier and the suspended phase, certainly relevant at increasing mass loading. In such regime, partially investigated in the past by the so-called Particle In Cell (PIC) method, much is still to be learned about the dynamics of the disperse phase and the ensuing alteration of the carrier flow. In this paper we present a new methodology rigorously designed to capture the inter-phase momentum exchange for particles smaller than the smallest hydrodynamical scale, e.g. the Kolmogorov scale in a turbulent flow. In fact, the momentum coupling mechanism exploits the unsteady Stokes flow around a small rigid sphere where the transient disturbance produced by each particle is evaluated in a closed form. The particles are described as lumped, point masses which would lead to the appearance of singularities. A rigorous regularization procedure is conceived to extract the physically relevant interactions between particles and fluid which avoids any "ah hoc" assumption. The approach is suited for high efficiency implementation on massively parallel machines since the transient disturbance produced by the particles is strongly localized in space around the actual particle position. As will be shown, hundred thousands particles can therefore be handled at an affordable computational cost as demonstrated by a preliminary application to a particle laden turbulent shear flow.Comment: Submitted to Journal of Fluid Mechanics, 56 pages, 15 figure

Application of the exact regularized point particle method (ERPP) to particle laden turbulent shear flows in the two-way coupling regime

The Exact Regularized Point Particle method (ERPP), which is a new inter-phase momentum coupling ap- proach, is extensively used for the first time to explore the response of homogeneous shear turbulence in presence of different particle populations. Particle suspensions with different Stokes number and/or mass loading are considered. Particles with Kolmogorov Stokes number of order one suppress turbulent kinetic energy when the mass loading is increased. In contrast, heavier particles leave this observable almost un- changed with respect to the reference uncoupled case. Turbulence modulation is found to be anisotropic, leaving the streamwise velocity fluctuations less affected by unitary Stokes number particles whilst it is increased by heavier particles. The analysis of the energy spectra shows that the turbulence modulation occurs throughout the entire range of resolved scales leading to non-trivial augmentation/depletion of the energy content among the different velocity components at different length-scales. In this regard, the ERPP approach is able to provide convergent statistics up to the smallest dissipative scales of the flow, giving the opportunity to trust the ensuing results. Indeed, a substantial modification of the turbu- lent fluctuations at the smallest-scales, i.e. at the level of the velocity gradients, is observed due to the particle backreaction. Small scale anisotropies are enhanced and fluctuations show a greater level of in- termittency as measured by the probability distribution function of the longitudinal velocity increments and by the corresponding flatness

Experimental Analysis on a Low Crested Rubble Mound Breakwater

In the present study, the flow induced by waves around a physical model of a detached low crested rubble mound breakwater is investigated experimentally. The model was designed with a scale factor of 1/30, parallel to the shoreline, in a coast of constant slope 1/15, assuming Froude similarity. For the design of the rock armor layer, the van der Meer\u27s hydraulic stability formula was applied. Two wave conditions were examined: one with an offshore wave height of 2 m (Case A) and one with the maximum annual characteristic offshore wave height (Case B), calculated in prototype scale. Measurements include surface elevation time series, as well as three-dimensional velocity time series of the flow around the model. Results include flow patterns on the seaward and leeward side of the breakwater for both wave conditions, as well as transmission and reflection coefficients. Along the leeward side, the current profiles have an offshore direction close to the bottom and a shoreward direction close to the free surface where the reduction of the water depth induced an acceleration of the flow, influenced by the overtopping. Transmission and reflection coefficients data were compared with literature equations. The comparison revealed that literature equations tended to underestimate the transmission coefficient due to the critical condition represented by a zero free-board breakwater. About the reflection coefficient, it was found that the literature equations tend to overestimate its value, possibly due to the fact that these formulas were obtained by experiments performed with emerged breakwaters

Direct Numerical Simulations of Turbulence Subjected to a Straining and De-Straining Cycle

In many turbulent flows, significant interactions between fluctuations and mean velocity gradients occur in nonequilibrium conditions, i.e., the turbulence does not have sufficient time to adjust to changes in the velocity gradients applied by the large scales. The simplest flow that retains such physics is the time dependent homogeneous strain flow. A detailed experimental study of initially isotropic turbulence subjected to a straining and destraining cycle was reported by Chen et al. [“Scale interactions of turbulence subjected to a straining-relaxation-destraining cycle,” J. Fluid Mech. 562, 123 (2006)] . Direct numerical simulation (DNS) of the experiment of Chen et al. [“Scale interactions of turbulence subjected to a straining-relaxation-destraining cycle,” J. Fluid Mech. 562, 123 (2006)] is undertaken, applying the measured straining and destraining cycle in the DNS. By necessity, the Reynolds number in the DNS is lower. The DNS study provides a complement to the experimental one including time evolution of small-scale gradients and pressure terms that could not be measured in the experiments. The turbulence response is characterized in terms of velocity variances, and similarities and differences between the experimental data and the DNS results are discussed. Most of the differences can be attributed to the response of the largest eddies, which, even if are subjected to the same straining cycle, evolve under different conditions in the simulations and experiment. To explore this issue, the time evolution of different initial conditions parametrized in terms of the integral scale is analyzed in computational domains with different aspect ratios. This systematic analysis is necessary to minimize artifacts due to unphysical confinement effects of the flow. The evolution of turbulent kinetic energy production predicted by DNS, in agreement with experimental data, provides a significant backscatter of kinetic energy during the destraining phase. This behavior is explained in terms of Reynolds stress anisotropy and nonequilibrium conditions. From the DNS, a substantial persistency of anisotropy is observed up to small scales, i.e., at the level of velocity gradients. Due to the time dependent deformation, we find that the major contribution in the Reynolds stresses budget is provided by the production term and by the pressure/strain correlation, resulting in large time variation of velocity intensities. The DNS data are compared with predictions from the classical Launder–Reece–Rodi isoptropic production [ B. E. Launder et al., “Progress in the development of a Reynolds stress turbulence closure,” J. Fluid Mech. 68, 537 (1975) ] Reynolds stress model, showing good agreement with some differences for the redistribution term

Scaling properties in the production range of shear dominated flows

Recent developments in turbulence are focused on the effect of large scale anisotropy on the small scale statistics of velocity increments. According to Kolmogorov, isotropy is recovered in the large Reynolds number limit as the scale is reduced and, in the so-called inertial range, universal features -namely the scaling exponents of structure functions - emerge clearly. However this picture is violated in a number of cases, typically in the high shear region of wall bounded flows. The common opinion ascribes this effect to the contamination of the inertial range by the larger anisotropic scales, i.e. the residual anisotropy is assumed as a weak perturbation of an otherwise isotropic dynamics. In this case, given the rotational invariance of the Navier-Stokes equations, the isotropic component of the structure functions keeps the same exponents of isotropic turbulence. This kind of reasoning fails when the anisotropic effects are strong as in the production range of shear dominated flows. This regime is analyzed here by means of both numerical and experimental data for a homogeneous shear flow. A well defined scaling behavior is found to exist, with exponents which differ substantially from those of classical isotropic turbulence. Contrary to what predicted by the perturbation approach, such a deep alteration concerns the isotropic sector itself. The general validity of these results is discussed in the context of turbulence near solid walls, where more appropriate closure models for the coarse grained Navier-Stokes equations would be advisable.Comment: 4 pages, 4 figure