Shear Fluctuations Research Articles

Shear viscosity, heat capacity, and fluctuations of liquid water, all at constant molal volume

Shear viscosity, heat capacity, and fluctuations of liquid water, all at constant molal volume

On the frequency response of wall transfer probes

The time response of wall transfer probes may significantly affect the interpretation of the physical phenomena involved. The transfer function between the heat or mass flux at the probe surface and the wall shear is analysed in the frequency domain. Space variation induced by the finite propagation velocity of a fluctuating wall shear is considered, as frequently encountered in various two-phase flow systems. The analysis indicates that the response is determined by two parameters—the non-dimensional frequency and the non-dimensional fluctuation velocity. The amplitude and phase corrections, which are to be applied to pseudosteady model calculations are numerically calculated. It is found that as the wall shear fluctuation is slowed down the probe frequency response significantly deteriorates. The sensitivity of the response to the fluctuation velocity reduces as the Prandtl or Schmidt numbers increase, indicating a superiority of electrochemical probes over themal probes.

Instability of a viscous liquid jet surrounded by a viscous gas in a vertical pipe

The instability of a cylindrical liquid jet encapsulated by a viscous gas in a pipe is analysed in a parameter space spanned by the Reynolds number, the Froude number, the Weber number, the density ratio, the viscosity ratio, and the diameter ratio. A convergent solution of the problem is constructed by a Galerkin projection with two orthogonal sets of functions. Two distinctively different modes of instability are obtained. The first is the Rayleigh mode which tends to break up the jet into drops of diameter comparable with the jet diameter. The amplification rate of the disturbance belonging to this mode depends weakly on all parameters except the Weber number which represents the ratio of the surface tension force to the inertia force at the interface. The mechanism of the instability remains that of capillary pinching even in the presence of a viscous gas and gravity. However, the surface tension is stabilizing in the other mode termed the Taylor mode. The Taylor mode instability is due to the pressure and shear fluctuations at the interface. This mode tends to produce droplets of diameters much smaller than that of the jet. It is shown that the former mode appears when the Weber number is much larger than the gas to liquid density ratio. When this ratio is of order one, the instability can be due to either modes depending on the values of the rest of the parameters. When the density ratio is much larger than the Weber number, Taylor's atomization mode replaces the Rayleigh mode.

Improvement in the frequency response of the electrochemical wall shear stress meter

One of the very few disadvantages of the mass-transfer transducer when compared with the hot-film sensor, is a slightly diminished frequency-response due to the higher Prandtl number encountered. Mass or thermal balance and transfer equations were solved first by Fortuna and Hanratty (1971) for small fluctuations of the wall shear. The solutions allow to make accurate corrections on the frequency spectra and the power of the fluctuations, but in different time. In this paper, the author deduces the frequency response of split rectangular electrodes and shows how a combination of signals improves the response at higher frequencies and makes it comparable to the thermal transducer with the same size, in the same fluid. Two experimental devices are described and compared. With these devices, the measurement of the wall shear fluctuations is improved in real time. Accurate determinations of turbulent power fluctuations and probability density spectra are feasible and illustrate the subject.

Piezo-electric foils as a means of sensing unsteady surface forces

The experimental determination of steady and unsteady surface forces is an elementary problem in experimental fluid dynamics, e.g., in experimental aerodynamics. Up to now, unsteady forces such as pressure or shear fluctuations have been detected by means of special plug-in probes (e.g., miniature pressure transducers). An alternative and attractive technique of monitoring unsteady surface forces has become possible through the development of piezoelectric foils. With this novel type of sensor, which simply can be glued onto a surface, the piezoelectric effect of polarized plastic foils is used to register time-dependent pressure or shear loads. First of all, the paper concentrates on the fundamentals of this new measuring technique. Furthermore, some practical applications in experimental aerodynamics are outlined.

Stochastically forced current fluctuations in vertical shear and over topography

The effects of constant vertical shear of zonal velocity, uniform meridional bottom slope, and a deep meridional wall (representing the Mid‐Atlantic Ridge) on the response of a linear two‐layer quasi‐geostrophic ocean to stochastic wind stress curl forcing are investigated. The model is motivated by discrepancies in energy levels and distributions between recent observations and a similar model without shear or topography that predicted remote coherences relatively well. The results indicate that the presence of mean shear can significantly enhance the wind‐generation of surface‐intensified oceanic kinetic energy at frequencies above the zero‐shear cutoff for free baroclinic waves. The primary effect of the sloping topography is enhanced barotropic response near the barotropic topographic Sverdrup resonance, where topographic and planetary potential vorticity gradients cancel. The wall inhibits the barotropic response and increases coherences on the mooring side of the wall. Remote coherences for 49‐day period fluctuations are due to long barotropic waves as in the previous model, so the present model only partially reconciles the previous discrepancies.

Elastic and quasielastic neutron scattering studies in KBr:KCN mixed crystals

Neutron scattering studies in (KBr)1−x(KCN)x mixed crystals are presented utilizing powder diffraction, single crystal diffraction and time-of-flight techniques. Forx>0.6 (KBr)1−x(KCN)x crystals exhibit ferroelastic and ferroelectric low-temperature phases. Crystals withx<0.6 undergo transitions into an orientational glass state. Here we present a detailed phase diagram including new results for x=0.85 and x=0.65. For the latter system a stable rhombohedral low-temperature phase has been detected where the orientational disorder of the plastic phase is only partly removed and quadrupolar relaxations between three body diagonals are still possible. From the powder diffraction experiments we determined further the concentration dependence of the static Debye-Waller factors which can be explained by an interplay of the rotation-translation and the rotation-random strain coupling. With single crystal diffraction techniques we studied the diffuse scattered intensities which are directly related to the order parameter of the glass state. The temperature dependence of the quasielastic intensities near the critical concentration shows a strong increase forT<110K indicative for a freezing-in of shear fluctuations which is a characteristic feature of a non-ergodic instability. This phenomenon appears for ordering (x=0.65) and for non-ordering, glassy compounds. A further anomaly in (KBr)0.43(KCN)0.57 at 75 K is interpreted in terms of a residual elastic ordering process. With high-resolution time-of-flight techniques we analysed the dynamic structure factor for x=0.57. We demonstrate that the central peak consists of a static and a dynamic component. The results are compared with mode coupling theories which describe the glass transition in supercooled liquids.

Soft mode behavior in the orthorhombic to tetragonal transition in the high T c superconductor YBa2Cu3O7−δ

The Young’s modulus and rigidity modulus of the high Tc superconductor YBa2Cu3O7−δ is measured from 300 to 1125 K using a 40-kHz ultrasonic resonant composite oscillator. Marked soft mode behavior occurs in both moduli in the vicinity of the orthorhombic to tetragonal transition, the softening being associated with orthorhombic shear fluctuations. The deep soft mode cusp allows the transition to be precisely determined as a function of oxygen partial pressure. A mechanical damping peak similar to that in Y-ZrO2 occurs at 800 K presumably arising from oxygen ion hopping.

Homogeneous block copolymer systems under shear flow

Effects of shear flow are investigated in melts of diblock copolymers in the homogeneous disordered phase near the microphase separation transition point. Simple approximate expressions are given for the anisotropic scattering intensity in nonlinear regimes under shear. A non-Newtonian effect and a normal stress effect are also examined, which are caused by deformations of the critical fluctuations in shear. An explicit expression is also found for the critical part of the complex shear modulus. This paper is a generalization of recent work by Fredrickson and Larson.

Light Scattering from Bulk Polymers

Light is scattered by fluctuations in the dielectric tensor e in a material. If the fluctuations are dynamic the scattered light has a spectrum S(q, w) that differs from the incident light and the intensity is a function of time J(q, t). The technique of dynamic light scattering has been applied to many different materials. In this review we report on the application of this technique to the study of bulk polymers. There are many processes that couple to the dielectric tensor and lead to light scattering. For organic liquids and glasses the primary sources oflight scattering are fluctuations in density, mechanical shear, and optical anisotropy. Part of these fluctuations are due to thermal acoustic phonons and lead to inelastically scattered light called Brillouin scattering. Several extensive reviews of Brillouin scattering from polymers have been pub­ lished (1-4). In the present review we focus on developments in this area since 1977. Light scattering from anisotropy fluctuations in bulk polymers has also been treated in detail (3, 4). Here we present a systematic review of all the papers in this field. Near the glass transition in bulk polymers there are fluctuations that relax slowly enough to be analyzed using photon correlation spectroscopy. This subject was recently reviewed (5) in exhaus­ tive detail, but there are so few papers yet published that a summary of the work is given here. The theory of light scattering from a viscoelastic medium was workcd out in detail by Rytov (6). A summary of the results is presented so that the experimental results can be understood in a general framework. Recent experimental advances are also discussed.

Structural relaxation and magnetism in amorphous alloys

Structural relaxation phenomena in amorphous alloys caused by post-quenching heat treatments are discussed in relation to the magnetic properties. It is pointed out that both microscopically irreversible and reversible relaxation processes exist, and are related to the changes in the atomic level density fluctuation and shear fluctuation, respectively. The importance of the microscopic variables in determining the kinetics of the reversible relaxation process is emphasized.

Local structural fluctuations in amorphous and liquid metals: a simple theory of the glass transition

A method of describing the thermal fluctuations in the local atomic structure of liquid and amorphous metals in terms of the fluctuations in the atomic level stresses is proposed. The energy of the system is expressed in terms of these stresses in the elastic approximation. The temperature dependence of the second moments of the stresses is then calculated and shown to be linear with temperature. The glass transition is assumed to take place when the second moments freeze to certain values determined by computer simulation. It is shown that the pressure fluctuations and the shear fluctuations freeze at different temperatures. The glass transition, in the normal sense, is described by the freezing of the pressure fluctuation. This method provides a reasonable estimate of the glass transition temperature, and predicts it to be proportional to the product of atomic volume and bulk modulus. It furthermore provides an explanation of the different relaxation behaviours between the pressure and shear fluctuations.

Nonlinear resonant coupling between shear and heat fluctuations in fluids far from equilibrium

Fluctuating hydrodynamics is used to show that in fluids with large temperature gradients the shear mode couples to the heat mode in a resonant manner that results in a very large increase in the amplitude of the central peak of the spectrum of scattered light, in agreement with the results of Kirkpatrick et al. [Phys. Rev. A 26, 995 (1982)].

Wave‐particle transport by weak electrostatic flow shear fluctuations

This paper presents calculations of transport in a Vlasov plasma due to weak electrostatic microfluctuations driven unstable by a shear in a bulk flow. The flow velocity is parallel to a uniform magnetic field and wave propagation is in the plane perpendicular to the shear direction. A consistent procedure is used to evaluate transport of the momentum and the kinetic energy tensor due to the electrostatic flow shear instability. The transport reduces the free energy driving the instability. The wave‐particle momentum loss rate scales as the cube of the inverse shear scale length, suggesting that it may be difficult to attain an asymptotically large Reynolds number for macroscopic turbulence in a collisionless plasma.

Experimental measurements of the flow-induced shear stress distribution in the vicinity of prosthetic heart valves.

The present study examines the local shear stress distribution occurring during flow through prosthetic valves. The electrochemical technique is a powerful tool for the study of mass transfer related phenomena and was selected for this investigation. The present investigation attempts to establish the viability of the particular application of the technique. Three test section geometries were analyzed: a straight tube, a ball-in-cage valve, and a model disk-in-cage valve, and the tests were conducted at six Reynolds numbers range from 1000 to 6000 under steady-state conditions. The model disk valve provided a base-case check on the validity of the technique since it has been employed in several previous studies and the flow through it is well documented. High shear and low shear regions are clearly evident and their locations can be pinpointed. The ball-in-cage valve was tested over the full range of Reynolds numbers. The shear profiles demonstrate a double peak in the region of the ball, a result which was unexpected. Careful study revealed that this was a result of the test section geometry. The frequency of the fluctuations in wall shear for the ball valve were found to be different than those for the disk valve indicating that the environment at the aortic wall is definitely affected by valve design. This study showed the electrochemical technique to be a valuable tool for the study of the flow through prosthetic heart valves.

Assessment of wall shear stress in arteries, applied to the coronary circulation.

Time dependent wall shear rates cannot be directly or accurately measured in arteries using presently available techniques. Here a simple method is presented for calculating them from a single measured velocity waveform (either centreline or cross-sectionally averaged velocity). The method involves only Fourier analysis and the application of given formulae, and it is expected to be approximately valid in any segment of artery which has no branches or sharp curves for a distance of several diameters. It is shown, however, that a frequency response of 30 Hz is required in the velocity measuring device if the resulting wall shear rate waveform is to be accurate throughout the cycle although 10 Hz is adequate if only the rms value is desired. This restriction on accuracy applies to this or any other method of estimating time-dependent wall shear. The method is applied to a prediction of wall shear in the left coronary arteries of the horse, based on measured velocities where they are available and calculated ones where they are not; the results show that in vivo the amplitude of wall shear fluctuations is much greater than the mean. The method is also applied to a scaled down model of the horse coronaries, thought to be representative of man; here the unsteadiness is still important but no longer dominant. The variation of wall shear with distance along the artery is discussed in the context of atherogenesis.

Shear and critical fluctuations: Instantaneous mapping of the velocity gradients

An application of the effect of shear on critical fluctuations (“moustache effect”) is described. The light scattered from a critical mixture (cyclohexane-aniline) under shear flow instantaneously provides: (i) the visualisation of the velocity gradients, (ii) the measurement of these gradients by microdensitometry. Particular interest lies in the study of nonstationary flows.

Wind Shear Fluctuations Downwind of Large Surface Roughness Elements

Abstract Wind measurements in the lowest 50 m of the atmosphere approximately 1 mi downwind of an urban area are examined to provide estimates of the short-term fluctuations of the vertical and lateral shear of the longitudinal component of the wind during six periods of slightly to moderately unstable atmospheric conditions. The fluctuations are described by a Pearson Type IV probability distribution. Models are presented for the standard deviation, skewness and kurtosis of the distributions. The distributions are slightly skewed and more peaked than Gaussian but tend toward Gaussian as separation increases. Time scales for the shear fluctuations are described.

A chaotic cosmology

An anisotropic, inhomogeneous cosmological model is proposed in which the inhomogeneity is generated by shear fluctuations. This is a sufficient condition for dissipative heating by collisional neutrinos to explain the present large heat content of the universe, S(b o) approximately 10(8), together with its isotropy and comparative homogeneity on large scales when the photons were last scattered. The model does not require the chaotic motions to be arbitrarily truncated on large scales and isotropises early enough with high entropy to ensure the synthesis of light elements with the observed abundancies. A population of black holes which arises in a natural way can also provide the necessary ingredients for a theory of galaxy formation and morphology. The 10(15)-g black holes, predicted by some authors, are not necessarily expected to be a feature of chaotic cosmologies.

Observed interaction between oceanic internal waves and mesoscale eddies

Measurements from arrays of moored current meters taken during the Mid-Ocean Dynamics Experiment (MODE) are analyzed, using short-term spectral analysis. A weak variability in space and time is detected in the internal wave continuum, as well as some horizontal anisotropy. It is suggested that the observed anisotropy is induced by the weak interaction between internal waves and mesoscale motions in a manner consistent with the weak interaction theory of >ü (Hamburger Geophysikalische Einzelschriften23, 1974). The interaction appears to be essentially local in space and time. It is shown that the internal wave continuum contributes positively to the horizontal diffusion of mean flow momentum, and is characterized by a relaxation time of the order of 1 to 4 days in the vicinity of the main thermocline. From observed correspondences between the fluctuations in total internal wave energy and square mean vertical shear, an estimate of the vertical eddy viscosity vν induced by internal waves is attempted, suggesting a large value for vν in the mid-ocean thermocline, maybe as high as 103 cm2 s−1.