Showing papers on "Velocity gradient published in 2010"

Designing large-eddy simulation of the turbulent boundary layer to capture law-of-the-wall scalinga)

Abstract: Law-of-the-wall (LOTW) scaling implies that at sufficiently high Reynolds numbers the mean velocity gradient ∂U/∂z in the turbulent boundary layer should scale on u∗/z in the inertia-dominated surface layer, where u∗ is the friction velocity and z is the distance from the surface. In 1992, Mason and Thomson pointed out that large-eddy simulation (LES) of the atmospheric boundary layer (ABL) creates a systematic peak in ϕ(z)≡(∂U/∂z)/(u∗/z) in the surface layer. This “overshoot” is particularly evident when the first grid level is within the inertial surface layer and in hybrid LES/Reynolds-averaged Navier–Stokes methods such as “detached-eddy simulation,” where the overshoot is identified as a “logarithmic layer mismatch.” Negative consequences of the overshoot—spurious streamwise coherence, large-eddy structure, and vertical transport—are enhanced by buoyancy. Several studies have shown that adjustments to the modeling of the subfilter scale (SFS) stress tensor can alter the degree of the overshoot. A com...

Effect of Polymer Additives on the Wetting of Impacting Droplets

Abstract: When a droplet of water impacts a hydrophobic surface, the drop is often observed to bounce. However, for about 10 years it has been known that the addition of very small quantities (approximately 100 ppm) of a flexible polymer such as poly-(ethylene oxide) can completely prevent rebound. This effect has for some time been explained in terms of the stretching of polymer chains by a velocity gradient in the fluid, resulting in a transient increase in the so-called "extensional viscosity." Here we show, by measuring the fluid velocity inside the impacting drop, that the extensional viscosity plays no role in the antirebound phenomenon. Using fluorescently labeled lambda DNA we demonstrate that the observed effect is due to the stretching of polymer molecules as the droplet edge sweeps the substrate, retarding the movement of the receding contact line.

Characterizing the 410 km discontinuity low-velocity layer beneath the LA RISTRA array in the North American southwest

Abstract: [1] Receiver functions recorded by the 54-station 920 km long Program for Array Seismic Studies of the Continental Lithosphere–Incorporated Research Institutions for Seismology Colorado Plateau/Rio Grande Rift Seismic Transect Experiment (LA RISTRA) line array display a pervasive negative polarity P to S conversion (Pds) arrival preceding the positive polarity 410 km discontinuity arrival These arrivals are modeled as a low-velocity layer atop the 410 km discontinuity (410-LVL) and are inverted for a velocity profile via a grid search using a five-parameter linear gradient velocity model Model parameter likelihood and correlations are assessed via calculation of one- and two-dimensional marginal posterior probability distributions The maximum likelihood model parameter values found are top velocity gradient thickness of 00 km with a 46% (−022 km/s) shear velocity reduction, a 198 km constant velocity layer, and bottom gradient thickness of 250 km with a 35% (+017 km/s) shear velocity increase The estimated mean thickness of the 410-LVL is 323 km The top gradient of the 410-LVL is sharp within vertical resolution limits of P to S conversion (<10 km), and the diffuse 410 km velocity gradient is consistent with hydration of the olivine-wadsleyite phase transformation The 410-LVL is interpreted as a melt layer created by the Transition Zone Water Filter model Two secondary observations are found: (1) the 410-LVL is absent from the SE end of the array and (2) an intermittent negative polarity P525s arrival is observed We speculate that upper mantle shear velocity anomalies above the 410 km discontinuity may manifest Rayleigh-Taylor instabilities nucleated from the 410-LVL melt layer that are being shed upward on time scales of tens of millions of years

Active and hibernating turbulence in minimal channel flow of newtonian and polymeric fluids.

Abstract: Turbulent channel flow of drag-reducing polymer solutions is simulated in minimal flow geometries. Even in the Newtonian limit, we find intervals of "hibernating" turbulence that display many features of the universal maximum drag reduction asymptote observed in polymer solutions: weak streamwise vortices, nearly nonexistent streamwise variations, and a mean velocity gradient that quantitatively matches experiments. As viscoelasticity increases, the frequency of these intervals also increases, while the intervals themselves are unchanged, leading to flows that increasingly resemble maximum drag reduction.

The angular momentum of magnetized molecular cloud cores: a two-dimensional-three-dimensional comparison

Abstract: We study the rotational properties of magnetized and self-gravitating molecular cloud cores formed in 2 very high resolution 3D molecular cloud simulations.The simulations have been performed using the code RAMSES at an effective resolution of 4096^3.One simulation represents a mildly magnetically-supercritical cloud and the other a strongly magnetically-supercritical cloud.A noticeable difference between the 2 simulations is the core formation efficiency (CFE) of the high density cores.In the strongly supercritical simulations the CFE is ~33 % per free-fall time of the cloud tff,cl, whereas in the mildly supercritical simulations this value goes down to ~6%/tff,cl. A comparison of the intrinsic specific angular momentum j3D distributions of the cores with the distribitions of j2D derived using synthetic 2D velocity maps of the cores,shows that the synthetic observations tend to overestimate the true value of j by a factor of ~10.The origin of this discrepancy lies in the fact that contrary to the intrinsic determination which sums up the individual gas parcels contributions to j, the determination of j using the observational procedure which is based on a measurement on the global velocity gradient under the hypothesis of uniform rotation smoothes out the complex fluctuations present in the 3D velocity field. Our results provide a natural explanation for the discrepancy by a factor ~10 observed between the intrinsic 3D distributions of j and the corresponding distributions derived in real observations.We suggest that measurements of j which are based on the measurement of the observed global velocity gradients may need to be reduced by a factor of ~10 in order to derive a more accurate estimate of j in the cores.

The Angular Momentum of Magnetized Molecular Cloud Cores: A 2D-3D Comparison

Abstract: We study the rotational properties of magnetized and self-gravitating molecular cloud cores formed in 2 very high resolution 3D molecular cloud simulations.The simulations have been performed using the code RAMSES at an effective resolution of 4096^3.One simulation represents a mildly magnetically-supercritical cloud and the other a strongly magnetically-supercritical cloud.A noticeable difference between the 2 simulations is the core formation efficiency (CFE) of the high density cores.In the strongly supercritical simulations the CFE is ~33 % per free-fall time of the cloud tff,cl, whereas in the mildly supercritical simulations this value goes down to ~6%/tff,cl. A comparison of the intrinsic specific angular momentum j3D distributions of the cores with the distribitions of j2D derived using synthetic 2D velocity maps of the cores,shows that the synthetic observations tend to overestimate the true value of j by a factor of ~10.The origin of this discrepancy lies in the fact that contrary to the intrinsic determination which sums up the individual gas parcels contributions to j, the determination of j using the observational procedure which is based on a measurement on the global velocity gradient under the hypothesis of uniform rotation smoothes out the complex fluctuations present in the 3D velocity field. Our results provide a natural explanation for the discrepancy by a factor ~10 observed between the intrinsic 3D distributions of j and the corresponding distributions derived in real observations.We suggest that measurements of j which are based on the measurement of the observed global velocity gradients may need to be reduced by a factor of ~10 in order to derive a more accurate estimate of j in the cores.

Factors controlling the field settling velocity of cohesive sediment in estuaries

Abstract: It has long been recognized that the suspended sediment concentration (SSC) is one of the major determinants for the flocculation of cohesive particles into sediment flocs in estuaries. It is furthermore well known that the turbulent shear of the water significantly influences the flocculation process and the equilibrium settling velocity of flocculated sediment in a turbulent flow. A vast number of authors have reported algorithms relating the median settling velocity ( W 50 ) to suspended sediment concentration. However, only a few studies have dealt with the impact of the turbulent shear (in this paper expressed as the root mean square [rms] velocity gradient, [ G ]) in the water on the W 50 in situ. There is a strong need to establish algorithms based on in situ measurements describing the dual impact of both SSC and G on the flocculation process, and hence, W 50 . The present paper addresses this topic. Field settling velocities of suspended cohesive sediment have been measured in micro-, meso-, and macro-tidal estuaries. Regression analyses between the W 50 , SSC and G are presented. It is shown that by including both G and SSC in the regression analyses, a significant increase in the correlation of the description of W 50 and the controlling parameters from each area can be obtained. A generic algorithm describing the data from all the investigated areas is suggested. It works well within specific tidal areas but fails to give a generic description of the field settling velocity.

Velocity gradient invariants and local flow-field topology in compressible turbulence

Abstract: The effect of compressibility on velocity gradient structure and the related flow-field patterns/topology is investigated using direct numerical simulation data. To clearly isolate compressibility effects, the behavior is investigated as a function of local level of dilatation. Importantly, dilatation-conditioned behavior is found to be independent of Mach and Reynolds numbers. Not surprisingly, at low dilatation level, velocity gradient structure and local flow topology are similar to incompressible turbulence. At high dilatation levels, however, the behavior is quite different. A recently developed velocity gradient evolution equation – Homogenized Euler Equation (HEE) – qualitatively captures many of the observed features of compressible turbulence.

Regularity issues in the problem of fluid structure interaction

Abstract: We investigate the evolution of rigid bodies in a viscous incompressible fluid. The flow is governed by the 2D Navier–Stokes equations, set in a bounded domain with Dirichlet boundary conditions. The boundaries of the solids and the domain have Holder regularity C1,α, 0 < α ≦ 1. First, we show the existence and uniqueness of strong solutions up to the collision. A key ingredient is a BMO bound on the velocity gradient, which substitutes to the standard H2 estimate for smoother domains. Then, we study the asymptotic behaviour of one C1,α body falling over a flat surface. We show that a collision is possible in finite time if and only if α < 1/2.

Combined effect of the density and velocity gradients in the combination of Kelvin–Helmholtz and Rayleigh–Taylor instabilities

Abstract: We have derived explicit analytic formulas for the linear growth rate and the frequency in the combination of Kelvin–Helmholtz (KH) and Rayleigh–Taylor (RT) instabilities in fluids with continuous density and velocity profiles. It is found that the density gradient effect (i.e., the density transition layer) decreases the linear growth rate in the RT instability (RTI), especially for the short perturbation wavelength. The linear growth rate for the KH instability (KHI) is increased by the density gradient effect but decreased by the velocity gradient effect (i.e., the velocity transition layer). The frequency in the KHI is reduced by both the density gradient effect and the velocity gradient effect. In most cases, both the linear growth rate and the frequency are decreased by the combination of density and velocity transition layers, i.e., the combined effect of density and velocity gradients stabilizes the KHI. The density gradient effect has an opposite influence on the linear growth rates of the RTI an...

LDA Application Methods : Laser Doppler Anemometry for Fluid Dynamics

Abstract: Specifications of Engineering Turbulent Flows.- LDA Principles and Laser Optics.- LDA Systems.- Basic Data Processing Methods in LDA Measurements.- Linear Transformation of Velocities and Turbulent Stresses.- Tracer Particles and Particle Motion Equations.- Zero Correlation Method (ZCM).- Dual Measurement Method (DMM).- Symmetrical Method of 3D-Velocity Measurements.- Non-stationary Turbulent Flows.- Turbulent Flow with Spatial Velocity Gradient.- Flow Measurements Behind the Plane Window: On-axis.- Flow Measurements Behind the Plane Window: Off-axis.- Flow Measurements in Circular Pipes.- Fringe Distortion Effects.- Velocity Bias Effects.- LDA Application Examples.

Output pressure and efficiency of electrokinetic pumping of non-Newtonian fluids

Abstract: Theoretical expressions of the flow rate, output pressure and thermodynamic efficiency of electrokinetic pumping of non-Newtonian fluids through cylindrical and slit microchannels are reported. Calculations are carried out in the framework of continuum fluid mechanics. The constitutive model of Ostwald-de Waele (power law) is used to express the fluid shear stress in terms of the velocity gradient. The resulting equations of flow rate and electric current are nonlinear functions of the electric potential and pressure gradients. The fact that the microstructure of non-Newtonian fluids is altered at solid–liquid interfaces is taken into account. In the case of fluids with wall depletion, both the output pressure and efficiency are found to be several times higher than that obtained with simple electrolytes under the same experimental conditions. Apart from potential applications in electrokinetic pumps, these predictions are of interest for the design of microfluidic devices that manipulate non-Newtonian fluids such as polymer solutions and colloidal suspensions. From a more fundamental point of view, the paper discusses a relevant example of nonlinear electrokinetics.

High resolution Rayleigh wave group velocity tomography in North China from ambient seismic noise

Abstract: This study presents the results of the Rayleigh wave group velocity tomography in North-China performed using ambient seismic noise observed at 190 broadband and 10 very broadband stations of the North-China Seismic Array. All available vertical component time-series for the 14 months span between January, 2007 and February, 2008 are cross-correlated to obtain empirical Rayleigh wave Green functions that are subsequently processed, with the multiple filter method, to isolate the group velocity dispersion curves of the fundamental mode of Rayleigh wave. Tomographic maps, with a grid spacing of 0.25o×0.25o, are computed at the periods of 4.5s, 12s, 20s, 28s. The maps at short periods reveal an evident lateral heterogeneity in the curst of North-China, quite well in agreement with known geological and tectonic features. The North China Basin is imaged as a broad low velocity area, while the Taihangshan and Yanshan uplifts and Ordos block are imaged as high velocity zones, and the Quaternary intermountain basins show up as small low-velocity anomalies. The group velocity contours at 4.5s, 12s and 20s are consistent with the Bouguer gravity anomalies measured in the area of the Taihangshan fault, that cuts through the lower crust at least. Most of the historical strong earthquakes (M≥6.0) are located where the tomographic maps show zones with moderate velocity gradient.

Apparent friction coefficient in straight compound channels

Abstract: In compound open channel flow, the strong interaction between the main channel and the shallow floodplains affects considerably the discharge capacity. Since this phenomenon was identified, many authors have estimated experimentally the flow interaction in terms of an apparent shear stress acting at the vertical interface between the main channel and the floodplains. Empirical formulae have been developed to quantify this apparent shear stress, yet without general applicability. Herein, a dimensionally sound expression, depending on the square of the velocity gradient between the main channel and the floodplains, and on the so called “apparent friction coefficient”, is proposed. Its variation with the geometrical and roughness ratios is analysed herein. A generalized formulation to predict the apparent shear stress is presented and validated for a wide range of laboratory data. These include small-scale flumes and the large-scale flood channel facility, with both smooth and rough floodplains.

Optimal velocity and density profiles for the onset of absolute instability in jets

Abstract: The absolute/convective character of the linear instability of axisymmetric jets is investigated for a wide range of parallel velocity and density profiles. An adjoint-based sensitivity analysis is carried out in order to maximize the absolute growth rate of jet profiles with and without density variations. It is demonstrated that jets without counterflow may display absolute instability at density ratios well above the previously assumed threshold ρ jet /ρ ∞ = 0.72, and even in homogeneous settings. Absolute instability is promoted by a strong velocity gradient in the low-velocity region of the shear layer, as well as by a step-like density variation near the location of maximum shear. A new efficient algorithm for the computation of the absolute instability mode is presented.

Tailoring turbulence with an active grid

Abstract: Using an active grid in a wind tunnel, we generate homogeneous shear turbulence and initiate turbulent boundary layers with adjustable properties. Homogeneous shear turbulence is characterized by a constant gradient of the mean velocity and a constant turbulence intensity. It is the simplest anisotropic turbulent flow thinkable, and it is generated traditionally by equipping a wind tunnel with screens which have a varying transparency and flow straighteners. This is not done easily, and the reachable turbulence levels are modest. We describe a new technique for generating homogeneous shear turbulence using an active grid only. Our active grid consists of a grid of rods with attached vanes which can be rotated by servo motors. We control the grid by prescribing the time-dependent angle of each axis. We tune the vertical transparency profile of the grid by setting appropriate angles of each rod such as to generate a uniform velocity gradient, and set the rods in flapping motion around these angles to tailor the turbulence intensity. The Taylor Reynolds number reached was Rλ = 870, the shear rate S = ∂U/∂y = 9.2 s−1, the nondimensional shear parameter S*≡ Sq2/e = 12 and u = 1.4 ms−1. As a further application of this idea we demonstrate the generation of a simulated atmospheric boundary layer in a wind tunnel which has tunable properties. This method offers a great advantage over the traditional one, in which vortex-generating structures need to be placed in the wind tunnel to initiate a fat boundary layer.

Investigation of Grease Flow in a Rectangular Channel Including Wall Slip Effects Using Microparticle Image Velocimetry

Abstract: The grease flow in a rectangular channel is investigated using microparticle image velocimetry. Of certain interest is to study the behavior close to the boundary where wall slip effects are shown to be present. Three greases with different consistencies (NLGI00, NLGI1, and NLGI2) have been used, together with three wall materials (steel, brass, and polyamide) with different surface roughness. The pressure drop is also varied. It is shown that the velocity profile is strongly dependent on the consistency, having a dominating plug flow structure for a stiff grease. Furthermore, it is shown that wall slip effects occur in a thin shear layer close to the boundary where a very large velocity gradient is present. An analytical solution for the velocity across the channel is described using a Herschel-Bulkley rheology model. The model fits well with the measured velocity profile for all three above-mentioned greases.

Orientational order of colloidal disk-shaped particles under shear-flow conditions: a rheological-small-angle X-ray scattering study.

Abstract: The structure of a colloidal dispersion consisting of anisometric natural clay particles (beidellite) was followed under shear-flow conditions by small-angle X-ray scattering (SAXS) measurements in a Couette-type cell. It is shown that in this shear-thinning dispersion an orientational order develops with increasing shear rate. By use of two different geometrical configurations for SAXS measurements, corresponding to incident beam parallel and perpendicular to flow velocity gradient (radial and tangential configurations, respectively), it is observed that SAXS patterns are anisotropic in both geometries, meaning that particles tend to align along a preferred orientation with their normal in velocity gradient direction, and further they partly rotate around flow streamlines. Quantitative interpretation of these results is successfully achieved upon derivation of a probability distribution function accounting for biaxial particle orientation. From this distribution and following geometrical arguments, the v...

Discrete rearranging disordered patterns: prediction of elastic and plastic behavior, and application to two-dimensional foams.

Abstract: We study the elasto-plastic behavior of materials made of individual (discrete) objects such as a liquid foam made of bubbles. The evolution of positions and mutual arrangements of individual objects is taken into account through statistical quantities such as the elastic strain of the structure, the yield strain, and the yield function. The past history of the sample plays no explicit role except through its effect on these statistical quantities. They suffice to relate the discrete scale with the collective global scale. At this global scale, the material behaves as a continuous medium; it is described with tensors such as elastic strain, stress, and velocity gradient. We write the differential equations which predict their elastic and plastic behavior in both the general case and the case of simple shear. An overshoot in the shear strain or shear stress is interpreted as a rotation of the deformed structure, which is a purely tensorial effect that exists only if the yield strain is at least of order 0.3. We suggest practical applications including the following: when to choose a scalar formalism rather than a tensorial one; how to relax trapped stresses; and how to model materials with a low, or a high, yield strain.

3D model of bow shocks

Abstract: Context. Shocks produced by outflows from young stars are often observed as bow-shaped structures in which the H2 line strength and morphology are characteristic of the physical and chemical environments and the velocity of the impact. Aims. We present a 3D model of interstellar bow shocks propagating in a homogeneous molecular medium with a uniform magnetic field. The model enables us to estimate the shock conditions in observed flows. As an example, we show how the model can reproduce rovibrational H2 observations of a bow shock in OMC1.Methods. The 3D model is constructed by associating a planar shock with every point on a 3D bow skeleton. The planar shocks are modelled with a highly sophisticated chemical reaction network that is essential for predicting accurate shock widths and line emissions. The shock conditions vary along the bow surface and determine the shock type, the local thickness, and brightness of the bow shell. The motion of the cooling gas parallel to the bow surface is also considered. The bow shock can move at an arbitrary inclination to the magnetic field and to the observer, and we model the projected morphology and radial velocity distribution in the plane-of-sky. Results. The morphology of a bow shock is highly dependent on the orientation of the magnetic field and the inclination of the flow. Bow shocks can appear in many different guises and do not necessarily show a characteristic bow shape. The ratio of the H2 v = 2-1 S(1) line to the v = 1-0 S(1) line is variable across the flow and the spatial offset between the peaks of the lines may be used to estimate the inclination of the flow. The radial velocity comes to a maximum behind the apparent apex of the bow shock when the flow is seen at an inclination different from face-on. Under certain circumstances the radial velocity of an expanding bow shock can show the same signatures as a rotating flow. In this case a velocity gradient perpendicular to the outflow direction is a projection effect of an expanding bow shock lighting up asymmetrically because of the orientation of the magnetic field. With the 3D model we reproduce the brightness levels in three H2 lines as well as the shape and size of a chosen bow shock in OMC1. The inferred bow inclination and the orientation and strength of the magnetic field fit into the pattern suggested by independent observations.

Criteria of turbulent transition in parallel flows

Abstract: Based on the energy gradient method, criteria for turbulent transition are proposed for pressure driven flow and shear driven flow, respectively. For pressure driven flow, the necessary and sufficient condition for turbulent transition is the presence of the velocity inflection point in the averaged flow. For shear driven flow, the necessary and sufficient condition for turbulent transition is the existence of zero velocity gradient in the averaged flow profile. It is shown that turbulent transition can be effected via a singularity of the energy gradient function which may be associated with the chaotic attractor in dynamic system. The role of disturbance in the transition is also clarified in causing the energy gradient function to approach the singularity. Finally, it is interesting that turbulence can be controlled by modulating the distribution of the energy gradient function.

Fresnel-zone binning: Fresnel-zone shape with offset and velocity function

Abstract: The concept of the Fresnel zone has been explored by many workers; most commonly, their work has involved examining the Fresnel zone in the limiting case of zero offset and constant velocity. I have examined the shape of the Fresnel zone for nonzero offset and in the situation of constant velocity gradient. Finite-offset Fresnel zones are not circular but are elliptical and may be many times larger than their zero-offset equivalents. My derivation takes a largely geometric approach, and I suggest a useful approximation for the dimension of the Fresnel zone parallel to the shot-receiver azimuth. The presence of a velocity gradient (velocity increasing with depth) in the subsurface leads to an expansion of the Fresnel zone to an area that is far larger than may be determined through a more usual straight-ray determination.

Phase Doppler anemometry measurements and analysis of turbulence modulation in dilute gas-solid two-phase shear flows

Abstract: Flow velocities of a dilute gas-solid two-phase flow in a vertical sudden expansion were measured using phase Doppler anemometry to study the behaviour of the turbulence modulation for the stronger shear for various particle mass loadings, inlet Reynolds numbers and particle diameters. The measurements show that the particles changed the gas turbulence by elongation of the entire gas flow field in the downstream direction, which displaced the axial profile of the section-averaged fluctuation velocity in comparison with that of the single-phase flow, and by either the particle inertia reducing the local turbulence or the wake eddy effects enhancing the turbulence. Both mechanisms resulted in an apparent turbulence modulation, which has not been referred to in the related literature, and have led to an ambiguous understanding of turbulence modulation. The elongation and inlet effects should be eliminated to estimate whether the gas turbulence was really modified. The linear relationship between the gas mean velocity gradient and the root-mean-square fluctuation velocity, which was found to be similar to that in single-phase flows, gradually disappeared as the flow developed and the shear intensity reduced. The linear relationship also varied with different conditions. Specifically, the turbulence modulation was enhanced by higher particle mass loadings and the linear relationship disappeared with increasing particle mass loading. This linearity can perhaps be regarded as a criterion for determining the effect of stronger turbulence modulation.

Calibrating passive scalar transport in shear-flow turbulence.

Abstract: The turbulent diffusivity tensor is determined for linear shear-flow turbulence using numerical simulations. For moderately strong shear, the diagonal components are found to increase quadratically with Peclet and Reynolds numbers below about 10 and then become constant. The diffusivity tensor is found to have components proportional to the symmetric and antisymmetric parts of the velocity gradient matrix, as well as products of these. All components decrease with the wave number of the mean field in a Lorentzian fashion. The components of the diffusivity tensor are found not to depend significantly on the presence of helicity in the turbulence. The signs of the leading terms in the expression for the diffusion tensor are found to be in good agreement with estimates based on a simple closure assumption.

A new algorithm for extended nonequilibrium molecular dynamics simulations of mixed flow.

Abstract: In this work, we develop a new algorithm for nonequilibrium molecular dynamics of fluids under planar mixed flow, a linear combination of planar elongational flow and planar Couette flow. To date, the only way of simulating mixed flow using nonequilibrium molecular dynamics techniques was to impose onto the simulation box irreversible transformations. This would bring the simulation to an end as soon as the minimum lattice space requirements were violated. In practical terms, this meant repeating the short simulations to improve statistics and extending the box dimensions to increase the total simulation time. Our method, similar to what has already been done for pure elongational flow, allows a cuboid box to deform in time following the streamlines of the mixed flow and, after a period of time determined by the elongational field, to be mapped back and recover its initial shape. No discontinuity in physical properties is present during the mapping and the simulation can, in this way, be extended indefinitely. We also show that the most general form of mixed flow, in which the angle between the expanding (or contracting) direction and the velocity gradient axis varies, can be cast in a so-called canonical form, in which the angle assumes values that are multiples of π (when a mixed flow exists), by an appropriate choice of the field parameters.

Characteristics of the Marangoni Convection Induced in Initial Quiescent Water

Abstract: By means of continuous deposition of the surface tension-lowering solvent at the quiescent water surface, the closed-loop Marangoni convection can be induced as a single convection cell at the air−water interface For this single Marangoni convection cell, its temporal-spatial evolution is visualized by means of the shadowgraph optical method, and its surface radial velocity distribution is measured with the help of the high speed photography technique Meanwhile, an absorption experiment of CO2 into water, a scaling analysis, and a 2-D numerical simulation are conducted, respectively, to investigate mass transfer performance and flow characteristics of the induced Marangoni convection Results show that the induced Marangoni convection has the high surface velocity, the sharp velocity gradient is in the immediate vicinity of the water surface, and the velocity of the Marangoni convection in the bulk of water is much less than that near the interface The high surface velocity of the Marangoni convection

Inertial effects on the rheology of a dilute emulsion

Abstract: The behaviour of an isolated nearly spherical drop in an ambient linear flow is examined analytically at small but finite Reynolds numbers, and thereby the first effects of inertia on the bulk stress in a dilute emulsion of neutrally buoyant drops are calculated. The Reynolds numbers, Re = γa 2 ρ/μ and Re = γa 2 ρ/μ, are the relevant dimensionless measures of inertia in the continuous and disperse (drop) phases, respectively. Here, α is the drop radius, γ is the shear rate, ρ is the common density and μ and μ are, respectively, the viscosities of the drop and the suspending fluid. The assumption of nearly spherical drops implies the dominance of surface tension, and the analysis therefore corresponds to the limit of the capillary number (Ca) based on the viscosity of the suspending fluid being small but finite; in other words, Ca « 1, where Cα = μαγ/T, T being the coefficient of interfacial tension. The bulk stress is determined to O(φRe) via two approaches. The first one is the familiar direct approach based on determining the force density associated with the disturbance velocity field on the surface of the drop; the latter is determined to O(Re) from a regular perturbation analysis. The second approach is based on a novel reciprocal theorem formulation and allows the calculation, to O(Re), of the drop stresslet, and hence the emulsion bulk stress, with knowledge of only the leading-order Stokes fields. The first approach is used to determine the bulk stress for linear flows without vortex stretching, while the reciprocal theorem approach allows one to generalize this result to any linear flow. For the case of simple shear flow, the inertial contributions to the bulk stress lead to normal stress differences (N 1 , N 2 ) at O(φRe), where φ(«1) is the volume fraction of the disperse phase. Inertia leads to negative and positive contributions, respectively, to N 1 and N 2 at O(φRe). The signs of the inertial contributions to the normal stress differences may be related to the O(ReCa) tilting of the drop towards the velocity gradient direction. These signs are, however, opposite to that of the normal stress differences in the creeping flow limit. The latter are O(φCa) and result from an O(Ca 2 ) deformation of the drop acting to tilt it towards the flow axis. As a result, even a modest amount of inertia has a significant effect on the rheology of a dilute emulsion. In particular, both normal stress differences reverse sign at critical Reynolds numbers (Re c ) of O(Ca) in the limit Ca «1. This criterion for the reversal in the signs of N 1 and N 2 is more conveniently expressed in terms of a critical Ohnesorge number (Oh) based on the viscosity of the suspending fluid, where Oh = μ(ρT) 1/2 . The critical Ohnesorge number for a sign reversal in N 1 is found to be lower than that for N 2 , and the precise numerical value is a function of λ. In uniaxial extensional flow, the Trouton viscosity remains unaltered at O(φRe), the first effects of inertia now being restricted to O(φRe 3/2 ). The analytical results for simple shear flow compare favourably with the recent numerical simulations of Li & Sarkar.

Dynamics of an Alfven surface in core collapse supernovae

Abstract: We investigate the dynamics of an Alfven surface (where the Alfven speed equals the advection velocity) in the context of core collapse supernovae during the phase of accretion on the proto-neutron star. Such a surface should exist even for weak magnetic fields because the advection velocity decreases to zero at the center of the collapsing core. In this decelerated flow, Alfven waves created by the standing accretion shock instability (SASI) or convection accumulate and amplify while approaching the Alfven surface. We study this amplification using one dimensional MHD simulations with explicit physical dissipation. In the linear regime, the amplification continues until the Alfven wavelength becomes as small as the dissipative scale. A pressure feedback that increases the pressure in the upstream flow is created via a non linear coupling. We derive analytic formulae for the maximum amplification and the non linear coupling and check them with numerical simulations to a very good accuracy. We also characterize the non linear saturation of this amplification when compression effects become important, leading to either a change of the velocity gradient, or a steepening of the Alfven wave. Applying these results to core collapse supernovae shows that the amplification can be fast enough to affect the dynamics, if the magnetic field is strong enough for the Alfven surface to lie in the region of strong velocity gradient just above the neutrinosphere. This requires the presence of a strong magnetic field in the progenitor star, which would correspond to the formation of a magnetar under the assumption of magnetic flux conservation. An extrapolation of our analytic formula (taking into account the nonlinear saturation) suggests that the Alfven wave could reach an amplitude of B ~ 10^15 G, and that the pressure feedback could significantly contribute to the pressure below the shock.