Showing papers in "Physics of Fluids in 2003"

Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box

Abstract: High-resolution direct numerical simulations (DNSs) of incompressible homogeneous turbulence in a periodic box with up to 40963 grid points were performed on the Earth Simulator computing system. DNS databases, including the present results, suggest that the normalized mean energy dissipation rate per unit mass tends to a constant, independent of the fluid kinematic viscosity ν as ν→0. The DNS results also suggest that the energy spectrum in the inertial subrange almost follows the Kolmogorov k−5/3 scaling law, where k is the wavenumber, but the exponent is steeper than −5/3 by about 0.1.

Spectra of the very large anisotropic scales in turbulent channels

Abstract: The spectra of numerically simulated channels at Reτ=180 and Reτ=550 in very large boxes are described and analyzed. They support a model in which the u-structures can be decomposed in two components. The first one is formed by structures of size λx≳5 h, λz≈2 h, which span most of the channel height, and penetrate into the buffer layer. The second one has maximum intensity in the near-wall region, where it is highly anisotropic and scales in inner units. It widens, lengthens, and becomes more isotropic in the outer layer, where it scales with h. The cospectrum exhibits an analogous quasi-isotropic range, whose width grows linearly with wall distance. At the present Reynolds numbers, nothing can be said about a possible streamwise similarity, due to limited scale separation. An extensive set of statistics from the simulations is downloadable from ftp://torroja.dmt.upm.es/channels.

Apparent slip flows in hydrophilic and hydrophobic microchannels

Abstract: The slip effects of water flow in hydrophilic and hydrophobic microchannels of 1 and 2 μm depth are examined experimentally. High-precision microchannels were treated chemically to enhance their hydrophilic and hydrophobic properties. The flow rates of pure water at various applied pressure differences for each surface condition were measured using a high-precision flow metering system and compared to a theoretical model that allows for a slip velocity at the solid surface. The slip length was found to vary approximately linearly with the shear rate with values of approximately 30 nm for the flow of water over hydrophobic surfaces at a shear rate of 105 s−1. The existence of slip over the hydrophilic surface remains uncertain, due to the sensitivity of the current analysis to nanometer uncertainties in the channel height.

Regularization of Grad’s 13 moment equations: Derivation and linear analysis

Abstract: A new closure for Grad’s 13 moment equations is presented that adds terms of Super-Burnett order to the balances of pressure deviator and heat flux vector. The additional terms are derived from equations for higher moments by means of the distribution function for 13 moments. The resulting system of equations contains the Burnett and Super-Burnett equations when expanded in a series in the Knudsen number. However, other than the Burnett and Super-Burnett equations, the new set of equations is linearly stable for all wavelengths and frequencies. Dispersion relation and damping for the new equations agree better with experimental data than those for the Navier–Stokes–Fourier equations, or the original 13 moments system. The new equations also allow the description of Knudsen boundary layers.

An explicit filtering method for large eddy simulation of compressible flows

Abstract: A method for large eddy simulation (LES) is presented in which the sub-grid-scale modeling is achieved by filtering procedures alone The procedure derives from a deconvolution model, and provides a mathematically consistent approximation of unresolved terms arising from any type of nonlinearity The formal steps of primary filtering to obtain LES equations, approximate deconvolution to construct the subgrid model term and regularization are combined into an equivalent filter This filter should be an almost perfect low pass filter below a cut-off wavenumber and then fall off smoothly The procedure has been applied to a pressure-velocity-entropy formulation of the Navier–Stokes equations for compressible flow to perform LES of two fully developed, turbulent, supersonic channel flows and has been assessed by comparison against direct numerical simulation (DNS) data Mach numbers are 15 and 30, and Reynolds numbers are 3000 and 6000, respectively Effects of filter cut-off location, choice of differentiation scheme (a fifth-order compact upwind formula and a symmetric sixth-order compact formula were used), and grid refinement are examined The effects are consistent with, and are readily understood by reference to, filtering characteristics of the differentiation and the LES filter All simulations demonstrate a uniform convergence towards their respective DNS solutions

On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence

Abstract: The objective of the present study is to analyze our recent direct numerical simulation (DNS) results to explain in some detail the main physical mechanisms responsible for the modification of isotropic turbulence by dispersed solid particles. The details of these two-way coupling mechanisms have not been explained in earlier publications. The present study, in comparison to the previous DNS studies, has been performed with higher resolution (Reλ=75) and considerably larger number (80 million) of particles, in addition to accounting for the effects of gravity. We study the modulation of turbulence by the dispersed particles while fixing both their volume fraction, φv=10−3, and mass fraction, φm=1, for three different particles classified by the ratio of their response time to the Kolmogorov time scale: microparticles, τp/τk≪1, critical particles, τp/τk≈1, large particles, τp/τk>1. Furthermore, we show that in zero gravity, dispersed particles with τp/τk=0.25 (denoted here as “ghost particles”) modify the spectra of the turbulence kinetic energy and its dissipation rate in such a way that keeps the decay rate of the turbulence energy nearly identical to that of particle-free turbulence, and thus the two-way coupling effects of these ghost particles would not be detected by examining only the temporal behavior of the turbulence energy of the carrier flow either numerically or experimentally. In finite gravity, these ghost particles accumulate, via the mechanism of preferential sweeping resulting in the stretching of the vortical structures in the gravitational direction, and the creation of local gradients of the drag force which increase the magnitudes of the horizontal components of vorticity. Consequently, the turbulence becomes anisotropic with a reduced decay rate of turbulence kinetic energy as compared to the particle-free case.

Homotopy of exact coherent structures in plane shear flows

Abstract: Three-dimensional steady states and traveling wave solutions of the Navier–Stokes equations are computed in plane Couette and Poiseuille flows with both free-slip and no-slip boundary conditions. They are calculated using Newton’s method by continuation of solutions that bifurcate from a two-dimensional streaky flow then by smooth transformation (homotopy) from Couette to Poiseuille flow and from free-slip to no-slip boundary conditions. The structural and statistical connections between these solutions and turbulent flows are illustrated. Parametric studies are performed and the parameters leading to the lowest onset Reynolds numbers are determined. In all cases, the lowest onset Reynolds number corresponds to spanwise periods of about 100 wall units. In particular, the rigid-free plane Poiseuille flow traveling wave arises at Reτ=44.2 for Lx+=273.7 and Lz+=105.5, in excellent agreement with observations of the streak spacing. A simple one-dimensional map is proposed to illustrate the possible nature of ...

Second-order slip laws in microchannels for helium and nitrogen

Abstract: We perform gas flow experiments in a shallow microchannel, 1.14±0.02 μm deep, 200 μm wide, etched in glass and covered by an atomically flat silicon wafer. The dimensions of the channel are accurately measured by using profilometry, optical microscopy and interferometric optical microscopy. Flow-rate and pressure drop measurements are performed for helium and nitrogen, in a range of averaged Knudsen numbers extending up to 0.8 for helium and 0.6 for nitrogen. This represents an extension, by a factor of 3 or so, of previous studies. We emphasize the importance of the averaged Knudsen number which is identified as the basic control parameter of the problem. From the measurements, we estimate the accommodation factor for helium to be equal to 0.91±0.03 and that for nitrogen equal to 0.87±0.06. We provide estimates for second-order effects, and compare them with theoretical expectations. We estimate the upper limit of the slip flow regime, in terms of the averaged Knudsen number, to be 0.3±0.1, for the two gases.

Droplet splashing on a thin liquid film

Abstract: We propose a theory predicting the transition between splashing and deposition for impacting drops. This theory agrees with current experimental observations and is supported by numerical simulations. It assumes that the width of the ejected liquid sheet during impact is precisely controlled by a viscous length l ν . Numerous predictions follow this theory and they compare well with recent experiments reported by Thoroddsen [J. Fluid Mech. 451, 373 (2002)].

The significance of vortex ring formation to the impulse and thrust of a starting jet

Abstract: The recent work of Gharib, Rambod, and Shariff [J. Fluid Mech. 360, 121 (1998)] studied vortex rings formed by starting jets generated using a piston-cylinder mechanism. Their results showed that vortex rings generated from starting jets stop forming and pinch off from the generating jet for sufficiently large values of the piston stroke to diameter ratio (L/D), suggesting a maximization principle may exist for propulsion utilizing starting jets. The importance of vortex ring formation and pinch off to propulsion, however, rests on the relative contribution of the leading vortex ring and the trailing jet (which appears after pinch off) to the impulse supplied to the flow. To resolve the relative importance of the vortex ring and trailing jet for propulsion, a piston-cylinder mechanism attached to a force balance is used to investigate the impulse and thrust generated by starting jets for L/D ratios in the range 2–8. Two different velocity programs are used, providing two different L/D values beyond which pinch off is observed, in order to determine the effect of vortex ring pinch off. Measurements of the impulse associated with vortex ring formation show it to be much larger than that expected from the jet velocity alone and proportionally larger than that associated with a trailing jet for L/D large enough to observe pinch off. The latter result leads to a local maximum in the average thrust during a pulse near L/D values associated with vortex rings whose circulation has been maximized. These results are shown to be related to the nozzle exit over-pressure generated during vortex ring formation. The over-pressure is in turn shown to be associated with the acceleration of ambient fluid by vortex ring formation in the form of added and entrained mass.

Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers

Abstract: Two-dimensional flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers has been numerically investigated in this study. For the study, numerical simulations are performed, using the immersed boundary method, in the ranges of 40⩽Re⩽160 and g*<5, where Re and g* are, respectively, the Reynolds number and the spacing between the two cylinder surfaces divided by the cylinder diameter. Results show that a total of six kinds of wake patterns are observed over the ranges: antiphase-synchronized, in-phase-synchronized, flip-flopping, deflected, single bluff-body, and steady wake patterns. It is found that the characteristics of the flow significantly depend both on the Reynolds number and gap spacing, with the latter much stronger than the former. Instantaneous flow fields, time traces, flow statistics and so on are presented to identify the wake pattern and then to understand the underlying mechanism. Moreover, the bifurcation phenomena where either of two wake patterns can occur ...

Dynamics of turbulence strongly influenced by buoyancy

Abstract: The dynamics of quasi-horizontal motions in a stably stratified fluid have been simulated for Froude numbers of order 1, so that the flows are strongly affected by the stable density stratification, and for a range of Reynolds numbers. It is found that the horizontal scales of the motion grow continuously in time. The vertical scales decrease and the vertical shearing increases with time, maintaining the Richardson number of order 1, as suggested by Lilly [J. Atmos. Sci. 40, 749 (1983)] and Babin et al. [Theor. Comput. Fluid Dyn. 9, 223 (1997)]. Small-scale instabilities and turbulent-like motions are observed to occur in the high shearing regions, while the larger-scale motions appear to evolve somewhat independently of the Reynolds number. The results suggest that the larger-scale, quasi-horizontal motions would be a continuous source of smaller-scale turbulence until the local Reynolds number drops below a critical value, which is estimated. Finally, a Froude number based upon a vertical differential scale and used in previous scaling arguments and theories is estimated in terms of other parameters.

Streamwise turbulence intensity formulation for flat-plate boundary layers

Abstract: A similarity formulation is proposed to describe the streamwise turbulence intensity across the entire smooth-wall zero-pressure-gradient turbulent boundary layer. The formulation is an extension of the Marusic, Uddin, and Perry [Phys. Fluids 9, 3718 (1997)] formulation that was restricted to the outer region of the boundary layer, including the logarithmic region. The new formulation is found to agree very well with experimental data over a large range of Reynolds numbers varying from laboratory to atmospheric flows. The formulation is founded on physical arguments based on the attached eddy hypothesis, and suggests that the boundary layer changes significantly with Reynolds number, with an outer flow influence felt all the way down to the viscous sublayer. The formulation may also be used to explain why the empirical mixed scaling of DeGraaff and Eaton [J. Fluid Mech. 422, 319 (2000)] appears to work.

Effect of turbulence on the drag and lift of a particle

Abstract: A direct numerical simulation (DNS) is used to study the effect of a freestream isotropic turbulent flow on the drag and lift forces on a spherical particle. The particle diameter is about 1.5–10 times the Kolmogorov scale, the particle Reynolds number is about 60–600, and the freestream turbulence intensity is about 10%–25%. The isotropic turbulent field considered here is stationary, i.e., frozen in time. It is shown that the freestream turbulence does not have a substantial and systematic effect on the time-averaged mean drag. The standard drag correlation based on the instantaneous or mean relative velocity results in a reasonably accurate prediction of the mean drag obtained from the DNS. However, the accuracy of prediction of the instantaneous drag decreases with increasing particle size. For the smaller particles, the low frequency oscillations in the DNS drag are well captured by the standard drag, but for the larger particles significant differences exist even for the low frequency components. In...

The joint cascade of energy and helicity in three-dimensional turbulence

Abstract: Three-dimensional (3D) turbulence has both energy and helicity as inviscid constants of motion. In contrast to two-dimensional (2D) turbulence, where a second inviscid invariant—the enstrophy—blocks the energy cascade to small scales, in 3D there is a joint cascade of both energy and helicity simultaneously to small scales. It has long been recognized that the crucial difference between 2D and 3D is that enstrophy is a nonnegative quantity whereas the helicity can have either sign. The basic cancellation mechanism which permits a joint cascade of energy and helicity is illuminated by means of the helical decomposition of the velocity into positively and negatively polarized waves. This decomposition is employed in the present study both theoretically and also in a numerical simulation of homogeneous and isotropic 3D turbulence. It is shown that the transfer of energy to small scales produces a tremendous growth of helicity separately in the + and − helical modes at high wave numbers, diverging in the limi...

Control of turbulent boundary layers

Abstract: The objective of this paper is to give an overview of recent progress on boundary layer control made by the author’s research group at University of California, Los Angeles. A primary theme is to highlight the importance of a certain linear mechanism and its contribution to skin-friction drag in turbulent boundary layers—and the implication that significant drag reduction can be achieved by altering this linear mechanism. Examples that first led to this realization are presented, followed by applications of linear optimal control theory to boundary-layer control. Results from these applications, in which the linear mechanism in turbulent channel flow was targeted, indirectly confirm the importance of linear mechanisms in turbulent—and hence, nonlinear—flows. Although this new approach has thus far been based solely on numerical experiments which are yet to be verified in the laboratory, they show great promise and represent a fundamentally new approach for flow control. The success and limitations of various controllers and their implications are also discussed.

Large-eddy simulation of a compressible flow past a deep cavity

Abstract: Large-eddy simulations of the flow over a deep cavity are performed. The computations reproduce identically all the parameters of the experiment by Forestier and co-workers [J. Fluid Mech. (to be published)], including the high Reynolds number ReL=8.6×105. Spectra show an accurate prediction of the peak levels of the fundamental frequency and its first harmonics. Results are also analyzed both in terms of Reynolds and phase averages, the procedure used to compute phase averages being identical to the one used during the experiment. Agreement with the experimental data is found to be excellent. The expansion rate of the shear layer is accurately described, and the temporal physics of the flow, including the dynamics of the coherent structures, is fully recovered. By comparison with an auxiliary computation wherein the wind-tunnel upper wall is not taken into account, the cavity is found to oscillate in a flow-acoustic resonance mode. New values for the γ constant of Rossiter’s model are then proposed for a...

Computing granular avalanches and landslides

Abstract: rock fragments that might range from centimeters to meters in size, are typically O(10 m) deep, and can run out over distances of tens of kilometers. This vast range of scales, the rheology of the geological material under consideration, and the presence of interstitial fluid in the moving mass, all make for a complicated modeling and computing problem. Although we lack a full understanding of how mass flows are initiated, there is a growing body of computational and modeling research whose goal is to understand the flow processes, once the motion of a geologic mass of material is initiated. This paper describes one effort to develop a tool set for simulations of geophysical mass flows. We present a computing environment that incorporates topographical data in order to generate a numerical grid on which a parallel, adaptive mesh Godunov solver can simulate model systems of equations that contain no interstitial fluid. The computational solver is flexible, and can be changed to allow for more complex material models, as warranted. © 2003 American Institute of Physics. @DOI: 10.1063/1.1614253#

Regularization modeling for large-eddy simulation

Abstract: A new modeling approach for large-eddy simulation (LES) is obtained by combining a "regularization principle" with an explicit filter and its inversion. This regularization approach allows a systematic derivation of the implied subgrid model, which resolves the closure problem. The central role of the filter in LES is fully restored, i.e., both the interpretation of LES predictions in terms of direct simulation results as well as the corresponding subgrid closure are specified by the filter. The regularization approach is illustrated with "Leray-smoothing" of the nonlinear convective terms. In turbulent mixing the new, implied subgrid model performs favorably compared to the dynamic eddy-viscosity procedure. The model is robust at arbitrarily high Reynolds numbers and correctly predicts self-similar turbulent flow development.

Evaluating the law of the wall in two-dimensional fully developed turbulent channel flows

Abstract: This article is concerned with the mean velocity distributions of two-dimensional fully developed turbulent plane-channel flows. To yield reliable information, the authors performed detailed hot-wire measurements for more than 12 Reynolds numbers. The experimental investigations covered a wide range of the Reynolds numbers up to Reτ≈5×103, where Reτ is based on the wall friction velocity and the channel half-height. From the distribution of the mean velocity gradient (dU+/dy+)=f(y+) the entire flow field was analyzed, resulting in a logarithmic region for the mean velocity profile in the inertial sublayer, extending almost up to the center of the channel at higher Reynolds numbers. The analysis of the experimental results yield a value of the von Karman constant, κ, close to 0.37(≈1/e) independent of the Reynolds number and the additive constant B=3.70, which is close to 10/e, i.e., U+=e ln y++10/e=(1/0.37)ln y++3.70.

Capillary driven flow in circular cylindrical tubes

Abstract: Capillary-driven flow of a perfectly wetting liquid into circular cylindrical tubes is studied. Based on an analysis of previous approaches, a comprehensive theoretical model is presented which is not limited to certain special cases. This model considers the meniscus reorientation, the dynamic contact angle as well as inertia, convective, and viscous losses inside the tube and the reservoir. The capillary-driven flow is divided into three successive phases where first inertia then convective losses and finally viscous forces counteract the driving capillary force. This leads to an initial meniscus height increase proportional to the square of time followed by a linear dependence and finally the Lucas–Washburn behavior where the meniscus height is proportional to the square root of time. The three phases are separated by two characteristic transition times which are determined by the Ohnesorge number and the inertia of the liquid. Experiments were carried out under microgravity condition in a carefully chosen range of Ohnesorge numbers and initial liquid heights to cover the complete process from the initial meniscus development to the final Lucas–Washburn behavior. Good agreement of experimental and theoretical data is found throughout the complete range of experiment parameters. The existence of all three flow regimes predicted by the theory is verified by the experiments.

Comment on Cercignani's second-order slip coefficient

Abstract: Cercignani’s second-order slip model has been neglected over the years, perhaps due to Sreekanth’s claim that it cannot fit his experimental data. In this paper we show that Sreekanth’s claim was based on an incorrect interpretation of this model. We also show that Cercignani’s second-order slip model, when modified and used appropriately, is in good agreement with solutions of the Boltzmann equation for a hard-sphere gas for a wide range of rarefaction. Given its simplicity, we expect this model to be a valuable tool for describing isothermal micro- and nanoscale flows to the extent that the hard-sphere approximation is appropriate.

The modeling of turbulent reactive flows based on multiple mapping conditioning

Abstract: A new modeling approach—multiple mapping conditioning (MMC)—is introduced to treat mixing and reaction in turbulent flows. The model combines the advantages of the probability density function and the conditional moment closure methods and is based on a certain generalization of the mapping closure concept. An equivalent stochastic formulation of the MMC model is given. The validity of the closuring hypothesis of the model is demonstrated by a comparison with direct numerical simulation results for the three-stream mixing problem.

Database-analysis of errors in Large-Eddy Simulation

Abstract: A database of decaying homogeneous, isotropic turbulence is constructed including reference direct numerical simulations at two different Reynolds numbers and a large number of corresponding large-eddy simulations at various subgrid resolutions. Errors in large-eddy simulation as a function of physical and numerical parameters are investigated. In particular, employing the Smagorinsky subgrid parametrization, the dependence of modeling and numerical errors on simulation parameters is quantified. The interaction between these two basic sources of error is shown to lead to their partial cancellation for several flow properties. This leads to a central paradox in large-eddy simulation related to possible strategies that can be followed to improve the accuracy of predictions. Moreover, a framework is presented in which the global parameter dependence of the errors can be classified in terms of the “subgrid activity” which measures the ratio of the turbulent to the total dissipation rate. Such an analysis allows one to quantify refinement strategies and associated model parameters which provide optimal total simulation error at given computational cost.

Reduction of flow-induced forces on a circular cylinder using a detached splitter plate

Abstract: Control of flow-induced forces on a circular cylinder using a detached splitter plate is numerically studied for laminar flow. A splitter plate with the same length as the cylinder diameter is placed horizontally in the wake region. Suppressing the vortex shedding, the plate significantly reduces drag force and lift fluctuation; there exists an optimal location of the plate for maximum reduction. However, they sharply increase as the plate is placed further downstream of the optimal location. This trend is consistent with the experimental observation currently available in the case of turbulent wake.

Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow

Abstract: A new boundary-integral algorithm for the motion of a particle between two parallel plane walls in Poiseuille flow at low Reynolds number was developed to study the translational and rotational velocities for a broad range of particle sizes and depths in the channel. Instead of the free-space Green’s function more commonly employed in boundary-integral equations, we used the Green’s function for the domain between two infinite plane walls [Liron and Mochon, J. Eng. Math. 10, 287 (1976)]. This formulation allows us to directly incorporate the effects of the wall interactions into the stress tensor, without discretizing the bounding walls, and use well-established iterative methods. Our results are in good agreement with previous computations [Ganatos et al., J. Fluid Mech. 99, 755 (1980)] and limiting cases, over their range of application, with additional results obtained for very small particle–wall separations of less than 1% of the particle radius. In addition to the boundary-integral solution in the mobility formulation, we used the resistance formulation to derive the near-field asymptotic forms for the translational and rotational velocities, extending the results to even smaller particle–wall separations. The decrease in translational velocity from the unperturbed fluid velocity increases with particle size and proximity of the particle to one or both of the walls. The rotational velocity exhibits a maximum magnitude between the centerline and either wall, due to the competing influences of wall retardation and the greater fluid velocity gradient near the walls. The average particle velocity for a uniform distribution of particles was generally found to exceed the average fluid velocity, due in large part to exclusion of the particle centers from the region of slowest fluid near the walls. The maximum average particle velocity is 18% greater than the average fluid velocity and occurs for particle diameters that are 42% of the channel height; particles with diameters greater than 82% of the channel height have smaller average velocities than does the fluid, due to the retarding effects of the nearby walls. Additionally, the translational and rotational velocities of oblate and prolate ellipsoids were calculated using the boundary-integral algorithm. The proximity of the walls to the ellipsoids was found to have a strong effect on particle velocity, so that a prolate spheroid aligned on the channel centerline moves faster than an oblate spheroid of the same volume, because the edge of the latter spheroid is closer to the channel walls. For off-centerline locations for a prolate spheroid with its major axis at an angle to the walls, a second translational velocity component normal to the walls is present. For each lower-wall gap examined, the maximum normal translational velocity occurs for smaller gaps from the upper wall (i.e., larger angle). The direction of this velocity component changes sign for mid-range angles studied, due to increased interactions with the lower wall that prevent the ellipsoid from rotating upward and, hence, yield a negative velocity perpendicular to the walls. The rotational velocity changes direction for particles at the smallest angles studied, due to the competition between the Poiseuille fluid velocity profile, which pushes the particle clockwise, and the lubrication forces, which impede this rotation.

Granular flow down a rough inclined plane: Transition between thin and thick piles

Abstract: The rheology of granular particles in an inclined plane geometry is studied using three dimensional molecular dynamics simulations. The flow–no-flow boundary is determined for piles of varying heights over a range of inclination angles θ. Three angles determine the phase diagram: θr, the angle of repose, is the angle at which a flowing system comes to rest; θm, the maximum angle of stability, is the inclination required to induce flow in a static system; and θmax is the maximum angle for which stable, steady state flow is observed. In the stable flow region θr<θ<θmax, three flow regimes can be distinguished that depend on how close θ is to θr: (i) θ≫θr: Bagnold rheology, characterized by a mean particle velocity vx in the direction of flow that scales as vx∝h3/2, for a pile of height h, (ii) θ≳θr: The slow flow regime, characterized by a linear velocity profile with depth, and (iii) θ≈θr: Avalanche flow characterized by a slow underlying creep motion combined with occasional free surface events and large ...

Fractal clustering of inertial particles in random flows

Abstract: It is shown that preferential concentrations of inertial (finite-size) particle suspensions in turbulent flows follow from the dissipative nature of their dynamics. In phase space, particle trajectories converge toward a dynamical fractal attractor. Below a critical Stokes number (non-dimensional viscous friction time), the projection on position space is a dynamical fractal cluster; above this number, particles are space filling. Numerical simulations and semi-heuristic theory illustrating such effects are presented for a simple model of inertial particle dynamics.

Flow over a surface with parallel grooves

Abstract: Stokes shear flow over a surface with evenly spaced, finite-depth rectangular grooves is solved analytically by eigenfunction expansions and matching. Macroscopically the rough surface is equivalent to a smooth surface with partial slip. The slip coefficients are determined for shear flow both along and transverse to the grooves. The partial slip condition is then applied to the flow through a channel with nonaligned grooves on the walls.

Effective eddy viscosities in implicit large eddy simulations of turbulent flows

Abstract: We propose a method for computing effective numerical eddy viscosity acting in dissipative numerical schemes used in monotonically integrated large eddy simulations of turbulence. The method is evaluated on an example of a specific nonoscillatory finite volume scheme MPDATA developed for simulations of geophysical flows.