Showing papers on "Velocity gradient published in 2000"
TL;DR: In this article, the kinematics, dynamics, and scales of turbulence are discussed and the importance of small-scale structures to the overall dynamics of the turbulence by visualizing the motions they induce and the stresses they impose both on other smallscale vortices and on the larger-scale field.
Abstract: Methods of analyzing and interpreting velocity-field data (both two- and three-dimensional) to understand the kinematics, dynamics, and scales of turbulence are discussed. Reynolds decomposition and vorticity are traditionally used; however, several other methods, including Galilean (constant convection velocity) and LES decompositions (low-pass filtering), in conjunction with critical-point analysis of the local velocity gradient tensor, reveal more about the structure of turbulence. Once the small-scale structures have been identified, it is necessary to assess their importance to the overall dynamics of the turbulence by visualizing the motions they induce and the stresses they impose both on other small-scale vortices and on the larger-scale field.
826 citations
TL;DR: The particle dynamics and shear forces of granular matter in a Couette geometry are determined experimentally and agree with a locally Newtonian, continuum model, where the granular medium is assumed to behave as a liquid with a local temperature [deltaV(y)](2) and density dependent viscosity.
Abstract: The particle dynamics and shear forces of granular matter in a Couette geometry are determined experimentally. The normalized tangential velocity $V(y)$ declines strongly with distance $y$ from the moving wall, independent of the shear rate and of the shear dynamics. Local rms velocity fluctuations $\ensuremath{\delta}V(y)$ scale with the local velocity gradient to the power $0.4\ifmmode\pm\else\textpm\fi{}0.05$. These results agree with a locally Newtonian, continuum model, where the granular medium is assumed to behave as a liquid with a local temperature $[\ensuremath{\delta}V(y){]}^{2}$ and density dependent viscosity.
230 citations
TL;DR: In this article, the late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamicaly consistent lattice Boltzmann method.
Abstract: The late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamicaly consistent lattice Boltzmann method. We combine results from simulations with different numerical parameters to obtain an unprecendented range of length and time scales when expressed in reduced physical units. Using eight large (256^3) runs, the resulting composite graph of reduced domain size l against reduced time t covers 1 < l < 10^5, 10 < t < 10^8. Our data is consistent with the dynamical scaling hypothesis, that l(t) is a universal scaling curve. We give the first detailed statistical analysis of fluid motion, rather than just domain evolution, in simulations of this kind, and introduce scaling plots for several quantities derived from the fluid velocity and velocity gradient fields.
197 citations
TL;DR: In this paper, a linear theory of wave propagation in saturated, unconsolidated granular materials, including marine sediments, is developed based on two types of shearing, translational and radial, which occur at grain contacts during the passage of a wave.
Abstract: A linear theory of wave propagation in saturated, unconsolidated granular materials, including marine sediments, is developed in this article. Since the grains are unbonded, it is assumed that the shear rigidity modulus of the medium is zero, implying the absence of a skeletal elastic frame. The analysis is based on two types of shearing, translational and radial, which occur at grain contacts during the passage of a wave. These shearing processes act as stress-relaxation mechanisms, which tend to return the material to equilibrium after the application of a dynamic strain. The stress arising from shearing is represented as a random stick-slip process, consisting of a random succession of deterministic stress pulses. Each pulse is produced when micro-asperities on opposite surfaces of a contact slide against each other. The quantity relevant to wave propagation is the average stress from all the micro-sliding events, which is shown to be a temporal convolution between the deterministic stress, h(t), from a single event and the probability, q(t), of an event occurring between times t and t+dt. This probability is proportional to the velocity gradient normal to the tangent plane of contact between grains. The pulse shape function, h(t), is derived by treating the micro-sliding as a strain-hardening process, which yields an inverse-fractional-power-law dependence on time. Based on two convolutions, one for the stress relaxation from translational and the other from radial shearing, the Navier–Stokes equation for the granular medium is derived. In a standard way, it is split into two equations representing compressional and shear wave propagation. From these wave equations, algebraic expressions are derived for the wave speeds and attenuations as functions of the porosity and frequency. Both wave speeds exhibit weak, near-logarithmic dispersion, and the attenuations scale essentially as the first power of frequency. A test of the theory shows that it is consistent with wave speed and attenuation data acquired recently from a sandy sediment in the Gulf of Mexico during the SAX99 experiment. If dispersion is neglected, the predicted expressions for the wave speeds reduce to forms which are exactly the same as those in the empirical elastic model of a sediment proposed by Hamilton. On this basis, the concept of a “skeletal elastic frame” is interpreted as an approximate, but not equivalent, representation of the rigidity introduced by grain-to-grain interactions.
186 citations
TL;DR: In this paper, the rotational properties of numerical models of centrally condensed, turbulent molecular cloud cores with velocity fields characterized by Gaussian random fields are investigated, and it is shown that the observed line width-size relationship can be reproduced if the velocity power spectrum is a power law with P(k) ∝ kn and n = -3 to -4.
Abstract: The rotational properties of numerical models of centrally condensed, turbulent molecular cloud cores with velocity fields that are characterized by Gaussian random fields are investigated. It is shown that the observed line width-size relationship can be reproduced if the velocity power spectrum is a power law with P(k) ∝ kn and n = -3 to -4. The line-of-sight velocity maps of these cores show velocity gradients that can be interpreted as rotation. For n = -4, the deduced values of angular velocity Ω = 1.6 km s-1 pc-1×(R/0.1 pc)-0.5, and the scaling relations between Ω and the core radius R are in very good agreement with the observations. As a result of the dominance of long-wavelength modes, the cores also have a net specific angular momentum with an average value of J/M = 7 × 1020 × (R/0.1 pc)1.5 cm2 s-1 with a large spread. Their internal dimensionless rotational parameter is β ≈ 0.03, independent of the scale radius R. In general, the line-of-sight velocity gradient of an individual turbulent core does not provide a good estimate of its internal specific angular momentum. We find however that the distribution of the specific angular momenta of a large sample of cores which are described by the same power spectrum can be determined very accurately from the distribution of their line-of-sight velocity gradients Ω using the simple formula j = pΩR2, where p depends on the density distribution of the core and has to be determined from a Monte Carlo study. Our results show that for centrally condensed cores the intrinsic angular momentum is overestimated by a factor of 2-3 if p = 0.4 is used.
141 citations
TL;DR: In this paper, a Monte Carlo method is used to synthesize the coda envelope of a local and regional earthquake, which has several advantages over previous methods in terms of flexibility of the numerical calculation to incorporate various factors required to construct realistic seismogram envelopes.
Abstract: The analysis of the seismogram coda envelopes of local and regional earthquakes is one of the most effective strategies for investigating the heterogeneous lithospheric structure characterized by the seismic scattering and attenuation. In order to synthesize the coda envelope we introduce a numerical scheme called the direct simulation Monte Carlo method, which has been used in the field of the kinetic theory of gases. Because of the simplicity of the algorithm the method has several advantages over previous methods in terms of the flexibility of the numerical calculation to incorporate various factors required to construct realistic seismogram envelopes. On the basis of coda envelope simulations, including multiple scattering, we show that an increase of seismic velocity with depth severely affects the shape of the coda envelope. The effects of ray bending due to the velocity increase at the Moho and the reflection at the free surface are clearly found in the synthesized envelope for a shallow earthquake. Our simulation demonstrates that the amplitude of the envelope is magnified by stagnation of seismic energy at shallow depths due to the positive velocity gradient with depth. Because of this effect, for an a priori assumption of a homogeneous velocity model the measurement of the scattering coefficient by conventional methods may be overestimated.
111 citations
TL;DR: In this article, a spectral method called normal mode analysis was used for filtering high-resolution data like HF radar observations, even when open boundary flow information is unavailable, and the nowcast velocity gradient fields were much less noisy than the observations, this may be an effective method for preconditioning high resolution observation sets for assimilation into a numerical model.
Abstract: Nowcasts of the surface velocity field in Monterey Bay are made for the period August 1–9, 1994, using HF radar observations blended with results from a primitive equation model. A spectral method called normal mode analysis was used. Objective spatial and temporal filtering were performed, and stream function, velocity potential, relative vorticity, and horizontal divergence were calculated over the domain. This type of nowcasting permits global spectral analysis of mode amplitudes, calculation of enstrophy, and additional analyses using tools like empirical orthogonal functions. The nowcasts reported here include open boundary flow information from the numerical model. Nowcasts using no open boundary flow information, however, still provide excellent results for locations within the observation footprint. This method, then, is useful for filtering high-resolution data like HF radar observations, even when open boundary flow information is unavailable. Also, since the nowcast velocity gradient fields were much less noisy than the observations, this may be an effective method for preconditioning high-resolution observation sets for assimilation into a numerical model.
82 citations
TL;DR: In this article, the statistical properties of the velocity and velocity gradient distributions in barotropic turbulence have been studied and shown to be non-Gaussian inside coherent vortices, due to the spatial velocity correlations associated with the ordered flow in the vortex cores.
Abstract: We study the statistical properties of the velocity and velocity gradient distributions in barotropic turbulence. At large enough Reynolds number, the velocity distribution becomes non-Gaussian outside the vortex cores, and its characteristics are completely determined by the properties of the far field induced by the coherent vortices. The velocity gradients are always non-Gaussian inside coherent vortices, due to the spatial velocity correlations associated with the ordered flow in the vortex cores, and become non-Gaussian also in the background turbulence at large enough Reynolds number.
71 citations
TL;DR: In this article, a statistical theory for the stochastic Burgers equation in the inviscid limit is developed for the probability density functions of velocity, velocity difference, and velocity gradient.
Abstract: A statistical theory is developed for the stochastic Burgers equation in the inviscid limit. Master equations for the probability density functions of velocity, velocity difference, and velocity gradient are derived. No closure assumptions are made. Instead, closure is achieved through a dimension reduction process; namely, the unclosed terms are expressed in terms of statistical quantities for the singular structures of the velocity field, here the shocks. Master equations for the environment of the shocks are further expressed in terms of the statistics of singular structures on the shocks, namely, the points of shock generation and collisions. The scaling laws of the structure functions are derived through the analysis of the master equations. Rigorous bounds on the decay of the tail probabilities for the velocity gradient are obtained using realizability constraints. We also establish that the probability density function Q() of the velocity gradient decays as jj 7=2 as !1 . c 2000 John Wiley & Sons, Inc.
67 citations
01 Jan 2000
TL;DR: In this paper, the effects of the Lewis number of the fuel on the front velocity of premixed flames along the near-wall low-velocity region at the bases of a laminar boundary layer of a reactive mixture has been studied numerically.
Abstract: The flashback or propagation of premixed flames along the near-wall low-velocity region at the bases of a laminar boundary layer of a reactive mixture has been studied numerically. The analysis, carried out using the constant density approximation for an Arrhenius overall reaction, accounts for the effects of the Lewis number of the fuel. The flow field, as seen by an observer moving with the front, includes the unknown flame front velocity U relative to the wall and the linear velocietygradient A at the base of the boundary layer. Due to this gradient, the flame front is curved with a radius of curvature lF=SLA, proportional to the planar flame velocity SL. The front velocity is changed from SL by a factor which depends on the Karlovitz number, or non-dimensional wall velocity gradient,defined as the ration between the thickness of the planar flame and the front curvature lF. The front velocity has been calculated in the limiting cases of adiabatic and isothermal walls. The front velocity changes from negative to positive when the Karlovitz number decreases below a critical value, determining the onset of flashback. This critical value, which decreases when the Lewis, number of the fuel increases, is smaller for isothermal than for adiabatic walls. In this second case, when the flame is not quenched close to the wall, flashback is prevented by flame stretch associated with flame curvature.
60 citations
TL;DR: In this paper, the shear-thickening transition observed in dilute aqueous solutions of cetyltrimethylammonium tosylate (CTAT) at concentrations is investigated.
Abstract: We report on the shear-thickening transition observed in dilute aqueous solutions of cetyltrimethylammonium tosylate (CTAT) at concentrations \(\). We have re-examined the kinetics of the shear-thickening transition using start-up experiments at rates above the critical shear rate \(\). Using simple well-defined protocols, we have found that the transient mechanical response depends dramatically on the thermal and on the shear histories. Using the same protocols, flow birefringence experiments were carried out. The gap of a Couette cell containing the sheared solution has been visualized between crossed polarizers in steady shear conditions, as well as in start-up experiments. We show that the birefringent shear-induced phase starts from the inner cylinder and grows along the velocity gradient direction, as in a shear banding situation. However, around \(\) we have not observed a regime of phase coexistence (isotropic and birefringent).
TL;DR: In this article, the theory of linear viscoelasticity of rod-like cholesteric liquid crystals subjected to small-amplitude oscillatory shear flow is formulated and applied to the cholesterics helix along the flow, velocity gradient, and vorticity directions.
Abstract: The theory of linear viscoelasticity of rod-like cholesteric liquid crystals subjected to small-amplitude oscillatory shear flow is formulated and applied to the cholesteric helix along the flow, velocity gradient, and vorticity directions. Expressions for the zero- and infinite-frequency viscosities are derived and their ordering is predicted. Based on the classical ordering of the Miesowicz shear viscosities and anisotropies of torque coefficients, it is found that the largest (smallest) zero-frequency viscosity obtains with the helix along the flow (gradient) direction. In addition, the difference between the zero- and infinite-frequency viscosities is found to be sensitive to the helix orientation, such that it is largest (smallest) when the helix is along the flow (gradient) direction. The complex viscosity corresponds to a viscoelastic material with a single relaxation time. The relaxation time depends on the Frank elastic constants involved in the deformation, such that when the helix is along the vorticity it is twist dependent, and splay–bend otherwise. The strength of the viscoelasticity is largest (smallest) when the helix is along the flow (gradient) direction. The hard-rod theory of Doi is used to confirm the predicted dependence of the strength of the viscoelastic response on the cholesteric helix orientation.
Journal Article•
TL;DR: Localized jets, steep velocity gradients, high vorticity and vortex recirculation have been observed in vitro near model MHV surfaces in vivo, and PIV of fully transparent models is a promising method for evaluating lumenal flows.
Abstract: BACKGROUND AND AIM OF THE STUDY Our previous studies of bileaflet mechanical heart valves (MHV) explanted from sheep revealed patterns of localized platelet aggregation on valve surfaces, which may have clinical relevance. Since flow phenomena may promote localized platelet aggregation, an evaluation of flow within a valve lumen was conducted. METHODS Phase-locked particle image velocimetry (PIV) measurements were obtained within the lumen of a 'mitral' model bileaflet MHV with transparent acrylic leaflets and housing, in a pulsatile flow loop. Instantaneous, two-dimensional flow maps of a central plane, perpendicular to the flow and leaflet pivot axes, were obtained at discrete times during the simulated cardiac cycle. Flow conditions were cardiac output, 3.5 l/min; rate, 72 beats/min; and systolic duration, 300 ms, using blood analog fluid refractive index-matched to acrylic. Leaflet closing velocities and angles were found using double-exposure imagery, and maximum leaflet closing velocity was extrapolated from regression analysis. RESULTS During full opening, flow within the three lumenal orifices formed a three-peak axial velocity profile. Vorticity was concentrated in shear layers adjacent to downstream leaflet surfaces and in downstream wakes. Forward flow peak velocity was 90 cm/s, with a steep velocity gradient in the central orifice. During closing, the central-gap regurgitant flow formed a jet (peak velocity, 144 cm/s). High vorticity occurred near leaflet leading and trailing edges. During full closure, first a transient (<3 ms) 'stopping vortex' developed near the leaflet trailing edge, followed by a wall jet which formed at the leaflet-housing junction. Maximum leaflet closing velocity was 1.4 m/s. CONCLUSION Localized jets, steep velocity gradients, high vorticity and vortex recirculation have been observed in vitro near model MHV surfaces. In vivo, each of these flow phenomena, when occurring near valve surfaces, may promote localized platelet aggregation. For the acrylic leaflets, maximum velocity was comparable with results reported for pyrolytic carbon leaflets. PIV of fully transparent models is a promising method for evaluating lumenal flows.
01 Jan 2000
TL;DR: In this paper, an analysis for the flow, temperature, and concentration fields in the region of attachment of fuel jet diffusion flames, near the wake of the fuel injector, where upstream heat conduction and diffusion are important.
Abstract: An analysis is presented for the flow, temperature, and concentration fields in the region of attachment of fuel jet diffusion flames, near the wake of the fuel injector, where upstream heat conduction and diffusion are important. The chracteristic scales for the size and velocity in this region are identified as l N = v 0 / A and U N = v 0 A , in terms of the kinematic viscosity of the fuel and the wall value of the fuel velocity gradient. The parameters that characterize the structure of the flame attachment region are identified, and some representative cases are numerically analyzed. There are cases with large activation energy, for which the flame will be attached if the Karlovitz number, v0A/UL2, or non-dimensional velocity gradient, is smaller than a critical value: for larger values, the flame lifts off far from the rim of the injector. For smaller values of the activation energy, the diffusion flame is attached, with its edge near the rim of the injector if the Karlovitz number is small; the distance to the injector of the edge of the flame grows with the Karlovitz number, and the edge takes on a triple-flame structure.
TL;DR: In this article, a finite aspect ratio effect on Couette-Taylor flow was studied by means of three-segment electrodiffusion probes placed at the steady outer wall and at a confining ring between cylinders.
TL;DR: In this article, a comprehensive analysis of shear flow-induced microstructure phenomena exhibited by discotic mesophases is presented using a complete generalized nonlinear theory that takes into account short-range order elasticity, long-range elasticity and viscous flow effects.
Abstract: A comprehensive analysis of shear flow-induced microstructure phenomena exhibited by discotic mesophases is presented using a complete generalized non-linear theory that takes into account short-range order elasticity, long-range elasticity, and viscous flow effects. The following four distinct shear-induced stable planar non-homogeneous microstructure modes are found: (1) long-range elasticity-induced steady state, (2) bulk tumbling-boundary wagging state, (3) bulk wagging state, and (4) viscous flow induced steady state. The stability of the microstructure modes is presented in terms of a rheological phase plane spanned by the Ericksen number Er (ratio of viscous flow to long-range elasticity), and the ratio of short-range to long-range elasticity ( R ). The steady and dynamical features of the various microstructure regimes are thoroughly characterized and analyzed. Two strong surface anchoring conditions, along the velocity gradient direction, and along the flow direction, are employed to investigate their effect on the stability and range of various microstructure regimes on the Er – R phase plane. The average bulk orientation for all the modes is found to be close to the velocity gradient direction. The fixed anchoring along the velocity gradient direction transmits the anchoring conditions into the bulk more strongly than that by the fixed anchoring along the flow direction. The effects of long-range elasticity on the flow-induced microstructure features are characterized. These simulations provide useful information to process carbonaceous mesophases by identifying the principles that govern shear flow-induced orientation in discotic mesophases.
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TL;DR: In this paper, the authors show that short-wavelength random velocity fluctuations of only 0.5-1% superimposed on negative velocity gradients are sufficient for generating Pn phases and this implies that an observed Pn wave does not necessitate a positive upper mantle velocity gradient.
Abstract: Pn phases are observed along many refraction seismic profiles and are common in earthquake records. Their velocities usually range from 7.8 to 8.2 km s−1. Classical ray theory used to interpret these observations implies a positive upper mantle velocity gradient. However, a wide spread positive velocity gradient in the lithospheric mantle is not expected from petrological and petrophysical data. Laboratory velocity measurements at elevated temparatures and pressures suggest positive velocity gradients only for very low heat flow values (≤40 mW m−2). Higher heat flow causes negative gradients. Consequently, petrological models of the upper mantle would restrict Pn observations to Precambrian shields and old platforms, contrary to observations. We overcome this contradiction by considering media that contain random velocity fluctuations superimposed on positive or negative velocity gradients. In both cases, these structures generate Pn phases by wide-angle scattered waves. Short-wavelength random velocity fluctuations of only 0.5–1% superimposed on negative velocity gradients are sufficient for generating Pn phases. Consequently, this implies that an observed Pn wave does not necessitate a positive upper mantle velocity gradient. For a peridotitic upper mantle, fluctuations of this size can be explained by slightly varying the relative proportions of its mineralogical constituents. Anisotropy is likely to contribute to the inferred fluctuations.
TL;DR: In this article, a two-dimensional argon-ion laser-Doppler Anemometer was used to obtain three-dimensional velocity measurements in a model mixer with optically clear model fluids (Corn syrup, CMC, and Carbopol-940 seeded with polystyrene DVB microspheres).
TL;DR: In this article, the effect of uniform suction on the steady two-dimensional laminar forced flow of a viscous incompressible fluid of temperature dependent viscosity past a wedge with uniform surface heat flux is considered.
Abstract: The effect of uniform suction on the steady two-dimensional laminar forced flow of a viscous incompressible fluid of temperature dependent viscosity past a wedge with uniform surface heat flux is considered The governing equations for the flow are obtained by using suitable transformations and are solved by using an implicit finite difference method Perturbation solutions are also obtained near the leading edge and in the downstream regime The results are obtained in terms of the local skin friction coefficient and the rate of heat transfer for various values of the pertinent parameters, such as the Prandtl number, Pr, the velocity gradient parameter, m, the local suction parameter, ξ, and the viscosity variation parameter, ɛ Perturbation solutions are compared with the finite difference solutions and are found to be in excellent agreement The effect of ξ, m and ɛ on the dimensionless velocity profiles and viscosity distribution are also presented graphically for Pr = 07 and 70, which are the appropriate values for gases and water respectively
TL;DR: An orthokinetic coagulation model including the effects of agglomeration and local stress-induced aggregate breakup was developed and it was concluded that mass transfer between regions of varying flow strain rate and/or velocity gradient should be included in accurate coagulations modeling.
TL;DR: In this article, a tube-cutting method was used to measure the pressure and Mach number distribution along a microtube of 108.3 μm, and experiments were also performed concerning the average Fanning friction factors of five kinds of microtubes whose diameters range from 80.0 to 166.6 μm.
Abstract: A new tube-cutting method was used to measure the pressure and Mach number distribution along a microtube of 108.3 μm. Experiments were also performed concerning the average Fanning friction factors of five kinds of microtubes whose diameters range from 80.0 to 166.6 μm. It is found that the pressure distribution in a microtube becomes nonlinear at a high Mach number and the product of measured average Fanning friction factors\(\overline C _{_f } \) and Reynolds numberRe is higher than 16. Numerical results show that the gas compressibility leads to a variation of the velocity profile from parabolic, and results in a large velocity gradient at the tube inner wall surface. The transition from laminar to turbulence in microtubes also occurs atRe ≈ 2 300, and the phenomenon of early transition is not observed in the experiments.
TL;DR: In this paper, the authors measured the temporal variations of a two-dimensional distribution of velocities in a nitrogen jet and a methane-jet flame using cross-correlation particle-image velocimetry (PIV).
Abstract: Temporal variations of a two-dimensional distribution of velocities in a nitrogen jet and a methane-jet flame are measured by cross-correlation particle-image velocimetry (PIV). Two different approaches to investigating the turbulence characteristics are demonstrated. One gives the distribution of ensemble-averaged velocities and turbulence intensities by means of repetitive PIV measurements using a double-pulse laser for a longer period. The other provides the detailed motion of velocity profiles for a shorter duration, allowing one to analyse the characteristic scale of turbulence using a high-power continuous laser. The accuracy of measurements of the time-averaged velocity and turbulence intensity is quantitatively assessed on the basis of the agreement with the results from hot-wire-anemometry (HWA) measurement. This indicates the feasibility of the PIV measurement, which may supply information about turbulence characteristics. From the measured results for a jet and a jetting flame, it is shown that the velocity gradient in the shear layer in the reacting zone is increased due to the local acceleration caused by buoyancy, resulting in higher turbulence intensities than those in a non-reacting jet. Also, from the change in the distribution of velocity vectors with time, it is clear that the turbulence eddies are carried downstream along the gas motion with little transformation. The time scale of turbulence at each location in the flow is obtained from the autocorrelation function of the velocity fluctuations. Furthermore, this can afford an estimate of the turbulence length scale if one assumes that the Taylor hypothesis is valid and multiplies the time scale and the time-average velocity. It is shown that the characteristic length scales of a flaming jet are about 1.5 times greater than those of a non-flaming jet. The effects of combustion on the turbulence in a flaming jet are discussed in detail on the basis of these experimental results.
TL;DR: In this paper, it is shown that the three-dimensional, explicit algebraic stress solution for the anisotropy tensor precludes rotational stabilization unless two invariants of the mean velocity gradient vanish.
Abstract: Equilibrium and bifurcation analysis is used to explore algebraic second moment models. It is shown that the three-dimensional, explicit algebraic stress solution for the anisotropy tensor precludes rotational stabilization unless two invariants of the mean velocity gradient vanish. If these vanish the irrotational part of the flow must be a plane strain: essentially the model can only bifurcate and stabilize in two-dimensional mean flow. However, it is also shown that those same two invariants must vanish if the mean flow is steady. The full equilibrium analysis described herein provides a consistent picture of a model with equilibria that respond appropriately to rotation.
TL;DR: In this article, a floating surface element on a pool of liquid, here water, is used to measure surface shear stress in the boundary layer that forms over the salt playa of western Utah.
Abstract: A novel method for measuring shear stress via a floating surface element beneath a turbulent boundary layer has been tested and implemented. The final design is used for measuring the surface shear stress in the boundary layer that forms over the salt playa of western Utah. Wind tunnel model studies were conducted to establish the characteristics of two competing sub-designs, and to determine their sensitivities and potential error sources. The wind tunnel based experiments included independent comparisons with the results of wall velocity gradient based measurements using hot-wire data. Overall, the results show that a floating element on a pool of liquid, here water, provides a more accurately measured surface shear stress than that determined utilizing an air bearing. In addition, the water pool technique is simpler to implement and produces a higher degree of repeatability. The wind tunnel results provided the design criteria needed to build a larger-scale device used to measure the surface shear stresses over the Great Salt Lake Desert in western Utah. This final design has been implemented and field results are presented and compared with sonic anemometer based estimates of the wall shear stress.
TL;DR: In this paper, a generalized mean magnetic field induction equation for differential rotators is derived, including a compressibility, and the anisotropy induced on the turbulent quantities from the mean magnetic fields itself and a mean velocity shear.
Abstract: A generalized mean magnetic field induction equation for differential rotators is derived, including a compressibility, and the anisotropy induced on the turbulent quantities from the mean magnetic field itself and a mean velocity shear. Derivations of the mean field equations often do not emphasize that there must be anisotropy and inhomogeneity in the turbulence for mean field growth. The anisotropy from shear is the source of a term involving the product of the mean velocity gradient and the cross-helicity correlation of the isotropic parts of the fluctuating velocity and magnetic field, (0). The full mean field equations are derived to linear order in mean fields, but it is also shown that the cross-helicity term survives to all orders in the velocity shear. This cross-helicity term can obviate the need for a preexisting seed mean magnetic field for mean field growth: though a fluctuating seed field is necessary for a nonvanishing cross-helicity, the term can produce linear (in time) mean field growth of the toroidal field from zero mean field. After one vertical diffusion time, the cross-helicity term becomes subdominant and dynamo exponential amplification/sustenance of the mean field can subsequently ensue. The cross-helicity term should produce odd symmetry in the mean magnetic field, in contrast to the usually favored even modes of the dynamo amplification in sheared disks. This may be important for the observed mean field geometries of spiral galaxies. The strength of the mean seed field provided by the cross-helicity depends linearly on the magnitude of the cross-helicity.
TL;DR: In this paper, the orientation of single fibers suspended in a polybutene-based Boger fluid under oscillatory shear was found to be dependent on the amplitude of the fiber rotation during a cycle of the oscillation.
Abstract: Observations of the orientation of single fibers suspended in a polybutene-based Boger fluid under oscillatory shear were made to test a recent theory [O.G. Harlen, D.L. Koch, J. Non-Newtonian Fluid Mech. 73 (1997) 81] that predicts a preferred alignment in the flow direction at strain amplitudes much less than unity. The steady state fiber orientation was found to be dependent on the amplitude of the fiber rotation during a cycle of the oscillation. For large fiber rotations, due to large strain amplitude (e ≥ 1.0) or large fiber projections in the velocity gradient direction, the majority of the fibers drifted slowly towards the vorticity axis, as would be expected for steady shear. A slow rotation towards the flow direction was observed for small strains (e = 0.05), as expected, and for moderate strains with smaller fiber projections in the velocity gradient direction. The theory predicted the correct order of magnitude of this orientational drift. The observations at moderate strains suggest the existence of multiple steady states with both the flow and vorticity directions being stable fixed points.
TL;DR: It is shown that it is possible for a nonuniform velocity gradient to generate a heat flow in the absence of a temperature gradient, and a term representing heat flow due to a gradient in the square of the strain rate is found.
Abstract: We derive the leading terms of a generalized Fourier law for heat conduction in fluids under strong, nonuniform shear by expanding the heat flux vector as a Taylor series about the equilibrium state in powers of the temperature gradient, the velocity gradient (the first spatial derivative of the streaming velocity or the strain rate tensor), and, in an extension of previous work, the second spatial derivative of the streaming velocity (a third rank tensor). This results in a general macroscopic constitutive equation, independent of any microscopic model, and valid for all flow geometries. Assuming that the fluid is isotropic at equilibrium, we find a term representing heat flow due to a gradient in the square of the strain rate. This shows that it is possible for a nonuniform velocity gradient to generate a heat flow in the absence of a temperature gradient. We also find terms corresponding to heat flow parallel to the streamlines that are not present in uniform shear flow.
TL;DR: A scanning acoustic microscope is used to study the distribution of elastic properties in small samples of new hard phases of C60 and the heterogeneous internal structure of the specimen is visualized in the images formed in C- and B-scan modes.
TL;DR: In this article, the effect of the molecular mass of a polymer sample on the dependence of the stationary viscosity on the velocity gradient upon simple shear and uniaxial tension is studied.
Abstract: The effect of the molecular mass of a polymer sample on the dependence of the stationary viscosity on the velocity gradient upon simple shear and uniaxial tension is studied. The model of the dynamics of a suspension of noninteracting dumbbells in the anisotropic medium is used. The theoretical results show that the asymptotic behavior of the shear viscosity does not depend on the molecular mass and corresponds to experimental data.
TL;DR: In this paper, a phase- Doppler anemometer is used for the measurement of axial velocity of entrained air and powder jet, and it is found that the axial velocities of entrainments show the maximum value at the center-line and decreases toward outer edge.
Abstract: In this research, we experimentally and numerically examine the flow characteristics of entrained air and powder jet. A phase- Doppler anemometer is used for the measurement of axial velocity of entrained air and particle. It is found that the axial velocity profiles of the entrained air shows the maximum value at the center-line and decreases toward outer edge. The flow region of entrained air spreads into a particle free space. The center-line velocity of entrained air increases with increasing distance from the orifice and decreases after it takes the maximum value. The spread of the entrained air is very small compared with that of the single-phase turbulent jet. The numerical simulation is performed based on the Lagrangian modeling for particles and Eulerian modeling for air flow. We consider particle-particle collision, drag force, gravity force and transverse force due to the particle spin and to the velocity gradient of air flow, and apply a k-e model. The present simulation qualitatively explains our measurement in terms of particle and air velocity profiles and jet spreading.