Showing papers on "Velocity gradient published in 1984"

Study of turbulent structure with hot wires smaller than the viscous length

Abstract: The small-scale structure of the streamwise velocity fluctuations in the wall region of a turbulent boundary layer is examined in a new wind-tunnel facility using hot-wires smaller than any previously constructed (typical dimensions: l = 25 μm, d = 0.5 μm). In the boundary layer in which the measurements were made, the ratio of the hot-wire length to the viscous length is 0.3. The turbulent intensity measured with the small hot wires is larger than that measured with longer wires owing to the better spatial resolution of the small wires. The velocity fluctuations measured by the small hot wires are also analysed to determine the burst frequency at two Reynolds numbers and at various distances from the wall. The dimensionless burst frequency does not depend on the Reynolds number when scaled with wall parameters. However, it increases with Reynolds number when scaled with outer variables. Velocity fluctuations measured by two hot wires, less than two viscous lengths apart, are analysed to reveal the small-scale features present during a burst and in the absence of a burst. The main conclusions are: (1) intermittent small-scale shear layers occur most frequently when bursts are present, less frequently just after a burst, and even less frequently just before a burst; and (2) on occasion the velocity gradient of the small-scale shear layers is as large as the mean-velocity gradient at the wall.

Observations on the response of human spermatozoa to gravity, boundaries and fluid shear

Abstract: Human sperm motility response to three mechanical stimuli, gravity, fluid flow shear and rigid boundaries, was measured in a tube of 310 X 400 microns calibre. Data were gathered by cine recordings at various focussing levels d across the tube and analysed with a computerized image analysis system. The most influential stimulus was the tube wall near (more than 'at') which the swimmers tended to accumulate, leaving the fluid beyond 100 microns from the wall (d = 100) vacant of motile spermatozoa. The boundary effect was evident as soon as the spermatozoa could be viewed after loading, and accumulation, measured as frequency, as a function of d did not change with time t. This response was not significantly altered by the addition of laminar flow with a centre line velocity of about 400 microns/sec. In flow shear, spermatozoa aligned positively (in the flow direction) at the wall but negatively by about 30 microns from the wall where the velocity gradient (= shear rate) was about 3.5 sec-1. The response to gravity was relatively weak with 11 spermatozoa positive (swimming downwards) for each 9 negative. Neither the boundary effect nor the 'rheotaxic' effect were influenced by gravity as there was no statistical difference in orientation or distribution patterns between vertically and horizontally flowing suspensions. It is suggested that the boundary effect cannot be ignored in in-vitro manipulations, particularly when spermatozoa are observed or extracted. Its importance in vivo lies in the degree to which the tubes transporting motile spermatozoa seem to have mechanisms for reversing the wall accumulation tendency.

Practical synthetic seismograms for laterally varying media calculated by asymptotic ray theory

Abstract: A fast, efficient algorithm based on asymptotic ray theory has been developed for the calculation of synthetic seismograms through two-dimensional media. The routine is economical and easy to run, and is intended for use as a practical tool in the interpretation of seismic refraction data. The velocity structure is represented by large polygonal blocks, and within each block the velocity gradient is uniform and of arbitrary orientation. Simple analytical expressions are thus used for both ray tracing and amplitude computations. For reflected and refracted rays, amplitudes are determined by using zero-order asymptotic ray theory. For calculating the geometrical spreading function, the width of the ray tube in the in-plane direction is determined by shooting two closely spaced rays for every receiver location. This enables an estimate of the partial derivative of range with respect to starting angle to be made. The ray tube width in the out-of-plane direction is evaluated using expressions valid for the specific case of two-dimensional models with linear velocity gradients. Head wave amplitudes are determined using first-order asymptotic ray theory. Each block of the model is reparameterized as a series of thin homogeneous layers perpendicular to the direction of the velocity gradient. Amplitudes are then determined by analytic expressions valid for models of homogeneous layers with plane dipping boundaries. The reparameterized model also may be used in an alternative method of calculating amplitudes for reflected rays and for refracted rays with no turning points.

Fascinating polymeric liquids

Abstract: Fluid dynamics is an old subject. In 1687, Isaac Newton wrote a simple equation defining the viscosity of a fluid as the coefficient of proportionality between the shear stress and the velocity gradient. Newton's equation does well at describing gases and liquids made up of “light” molecules—those of molecular weight less than about 1000. By the middle of the last century the mathematical description of the flow of such “Newtonian” fluids was well established. This description is based on use of the laws of conservation of mass and momentum.

Plastic instability and particulation in stretching metal jets

Abstract: Metal jets (or rods) that are plastically stretching eventually undergo a particulation process that arrests the plastic elongation and thus limits the target penetration that is to be achieved by the jet. The particulation process is found to depend upon the perturbation structure and upon a single dimensionless flow parameter φ. Statistical definitions are introduced for the perturbation magnitudes (jet roughness magnitude, velocity irregularity function, yield strength irregularity function). Then the jet length Lb at breakup is determined as a function of φ0 and these perturbation magnitudes. Jet yield strength σ, density ρ, and initial velocity gradient Ux occur in the definition of φ0 so that the effects of σ, ρ, and Ux upon Lb are also determined.

A study of conformation-dependent friction in a dumbbell model for dilute solutions

Abstract: We consider predictions of rheological behavior in a variety of shear and extensional flows for an elastic dumbbell model with a nonlinear spring, and conformation-dependent hydrodynamic properties. The latter include a conformation-dependent anisotropic bead friction coefficient, and a related conformation-dependent degree of inefficiency for rotation in straining flows. With these features, the dumbbell exhibits hydrodynamic behavior consistent with a particle of finite axis ratio over the complete set of possible polymer conformations, from random-coil to a fully extended thread-like configuration. The predicted rheological behavior in shear flow is improved, relative to data, by the inclusion of anisotropy and strain-inefficiency in the frictional properties of the model, while other desirable features such as the sudden onset of fully extended states at a critical value of the velocity gradient, the presence of a hysteresis-loop in end-to-end dimension as a function of the velocity gradient, and the correlation of end-to-end distance (or birefringence) with the eigenvalue of the velocity gradient tensor for a wide variety of two-dimensional flows, are maintained.

Wave‐current Models for Design of Marine Structures

Abstract: Modifications to vertical velocity profiles of coastal currents due to surface gravity waves were experimentally and theoretically examined. Results on these modifications were used to develop guidelines for approximating the form of current velocity profiles to be used in predictive models of wave kinematics. The validity of the guidelines was established by comparing the experimental data of wave particle velocities with the theoretical predictions of two wave‐current models which approximate the shear current by: (1) A constant vorticity current; and (2) a uniform velocity over the water depth. The results show that opposing waves decrease the current mean velocity close to the bottom and increase the mean velocity and the current shear near the free surface. Following waves increase mean velocity and velocity gradient of the current, close to the bottom, and might cause the shear at the surface to be negative. Models for constant vorticity and uniform velocity approximations are found to yield accurat...

Influence of a velocity gradient on small angle neutron scattering of a sheared solution with rodlike micelles

Abstract: A solution consisting of 20 mM cetylpyridiniumsalicylate (CPS) and 20 mM sodiumsalicylate (NaSal) in which rodlike micelles are present, was sheared and studied in a small angle neutron scattering (SANS) experiment. Without a velocity gradient the scattering curves of constant intensity were circles which reflect an isotropic distribution of the orientation of the scatterers. If a velocity gradient is applied to the solution the curves of constant scattering intensity show a characteristic deviation from the circles due to the partially ordering of the rods. From that deviation the rotational diffusion coefficient can be obtained. A theoretical treatment of this problem is given and applied to the experimental data.

Transition and Transport in the Initial Region of a Turbulent Diffusion Flame

Abstract: The initial region of a diffusion flame of 2 H2/N2 fuel issuing from a round jet into a coflowing stream has been studied at Reynolds numbers from 5000 to 30,000 using shadowgraphs and LDV. It is found that in addition to the (velocity) shear layer there is a scalar layer whose maximum gradient lies completely outside the shear layer. The shear layer undergoes transition by means of the classical KelvinHelmholtz instabilities which roll up, pair, and produce three-dimensional turbulence. On the other hand, a completely separate transition of this outer scalar layer can occur without disturbing the transitional process in the inner shear layer. This outer layer transition is thought to be caused by transition of the boundary layer on the outside of the nozzle. Measurements by LDV, although hampered by thermophoretic effects on the seed, confirm that the velocity turbulence is confined to the inner layer when the outer appears laminar. It is also found that the Reynolds stress in the "coherent structures" region closely follows the mean velocity gradient. The results are found to be insensitive to the N2/H2 ratio of the fuel and similar phenomena can be seen in published photographs of hydrocarbon diffusion flames. It is concluded that molecular transport

A comparison of velocity and attenuation between the Nicobar and Bengal Deep Sea Fans

Abstract: The compressional wave velocity and attenuation measurements from a deep source, deep receiver seismic refraction experiment from the Nicobar Fan, Indian Ocean, are presented and compared to a similar set of measurements in the Bengal Fan. The two deep sea fans consist of thick sections of turbidites derived from the same sediment source but have slightly different depositional histories. Travel time inversion of the data into a velocity depth model uses the tau-zeta linear inversion scheme. We present a revised reparameterization of the travel time data and improved error analysis for the inversion process. Although the velocity structures with depth are morphologically similar, there exist discrete differences between the two stations. In the Nicobar Fan, the initial velocity (assumed) is 1.513 km/s, with an initial gradient of 2.32 s−1. The velocity increases smoothly with depth, while the velocity gradient decreases rapidly to a constant 0.81 s−1. The Bengal Fan station showed the same trend, although the velocity gradient at depth was only 0.67 s−1. The attenuation profiles are similar only in gross structure, with the Nicobar Fan values of Q−1 being a factor of 3 to 4 less than the Bengal station. The differences in velocity and attenuation structure can be attributed to a number of causes, including porosity and sedimentation rates (which are related to the distance from the sediment source) and the presence of a normal fault near the Nicobar Fan site. This fault may act as a conduit for water removal in the presence of overburden pressure. It is believed that porosity changes, due to whatever cause, dominate the lateral and vertical variations of velocity, velocity gradients, and (together with intrabed multiples) attenuation in thick sedimentary sections.

A note on a geophysical fluid dynamics variational principle

Abstract: A variational principle for an inviscid stratified fluid on a beta plane is developed for horizontal flows. For the special case of solenoidal flow on an f plane, it is shown that a certain velocity gradient invariant can be used to develop simple solutions to the equations of motion. The solution forms are critically dependent on relative magnitudes of the squared local vorticity and the squared total deformation. DOI: 10.1111/j.1600-0870.1984.tb00241.x

Chapter 7. Field-flow fractionation

Abstract: Publisher Summary This chapter describes a new separation concept based on a coupling of concentration and flow non-uniformities. Separation is caused by differential migration in a narrow channel in which a fluid flows unidirectionally. A physical or chemical field that acts across the channel—for example, temperature gradient, electrical, magnetic or gravitational forces, chemical potential gradient, etc., induces a concentration gradient in the direction across the channel—that is, usually in the direction of the axis of the field gradient. The velocity of the flow of the fluid in the channel also varies in the direction across the channel. This velocity gradient is caused by viscosity and other effects, accompanying flow processes. The method was called field-flow fractionation (FFF). Utilization of this concept—particularly for the separations of macromolecules and particles, is of exceptional significance. FFF is similar to chromatography in many respects—especially as far as both dynamic aspects and experimental equipment and procedures are concerned. All of the processes associated with the separation take place in the fluid phase, and there is no stationary phase that would play an active part in the separation process.

Inversion of Body-Wave Seismograms for Upper Mantle Structure

Abstract: We invert observed long- and short-period body-wave seismograms, travel times, and apparent velocity data to further constrain the compressional velocity structure in the upper mantle beneath northwestern Eurasia and the shear-wave velocity structure beneath western North America. Long- and short-period WWSSN seismograms from nuclear explosions in the Union of Soviet Socialist Republics are incorporated with apparent velocity observations to derive an upper mantle model for northwestern Eurasia. The compressional waves from these explosions have several distinctive features that provide important new information about the character of the upper mantle in the region. The seismograms from 9° to 13° exhibit impulsive first arrivals, P n , implying a smooth positive velocity gradient between depths of 60 and 150 km. There is a consistent pulse arriving about 2s after P n at the distances of 13° to 17°, and at larger ranges there are distinct reflections from two major discontinuities in the mantle. Synthetic seismograms displaying these features indicate a velocity model that correlates with other models from around the world, with a distinctive lid and low-velocity zone. The arrival following P n is modeled by positioning the low-velocity zone between 150 and 200 km. The model is relatively smooth from a depth of 200 km down to 420 km, where a 5% jump in velocity produces a triplication in the travel time curve from 15° to 23°. The observations from 21° to 26° clearly show another discontinuity at a depth of 675 km with a 4% change in velocity. These results suggest that stable continental regions may have a shadow zone that extends beyond 17°. Below 250 km there is no distinguishable difference between the model proposed for northwest Eurasia and models derived for the United States. A systematic inversion technique is proposed to extract the maximum amount of information from these data. We use the WKBJ method to compute approximate synthetic seismograms in a radially heterogeneous earth. Where the WKBJ method breaks down, in low-velocity zones and near discontinuities, a generalized ray expansion is used in a layered model approximation to the velocity structure to isolate the energy that has reflected from these regions. Synthetic seismograms computed using these approximations compare very well to those computed by the more accurate method of summing primary reflections in a generalized ray sum yet require 1/20 the computation time. With this efficiency it is feasible to compute the differential seismograms necessary to pose an inverse problem. With a fast means of computing synthetic seismograms, an inverse problem can be posed to relate the differences between observed and synthetic seismograms to perturbations in the velocity structure. The problem is nonlinear, especially at high frequencies, but at long periods an iterative technique based on a linearized relation between perturbations in the velocity structure and the seismograms is effective if a reasonable initial model is assumed. Some simple tests of the method indicate that convergence to a satisfactory final model is possible even when starting with a model that predicts substantially different seismograms than those observed. We invert long-period SH waves recorded on WWSSN seismographs at distances from 15° to 31° in the western United States and East Pacific Rise to determine the upper mantle shear velocity structure beneath these regions. A high velocity gradient near 400 km produces clear later arrivals from 15° to 17°. We interpret large later phases observed al distances from 23° to 27° as another large velocity gradient at between 600 and 720 km depth. Inversion of these seismograms suggests that the velocity gradient in the upper 200 km of the mantle is small; there is an increase in the velocity gradient around 250 km resulting in a 4% velocity increase by 360 km. The large velocity gradient near 400 km results in a velocity increase of around 8½% between 360 km and 420 km depth. The velocity gradient becomes smaller between 420 and 600 km with a cumulative increase of 5% over these depths. The total increase in velocity from 600 to 750 km is about 14%. Below 750 km the velocity gradient is assumed to be similar to those predicted by global studies of travel times. There are differences in published travel time data and models that have been derived to fit the SS phases and SS-S differential times observed in this region. The discrepancies amount to about 5s in the direct S-wave travel time at distances of 15° to 18°. The discrepancy appears to be on the order of 3 s from 19° to 23° and is not resolvable beyond. These disagreements are probably the manifestation of large velocity heterogeneities in the uppermost mantle; either assumption concerning absolute travel times can be fit by models that are virtually identical below 270 km. Absolute travel times can constrain absolute velocities and, thus, are necessary to constrain the depth to discontinuities. Waveform data can constrain the structural details better. A joint waveform and travel time inversion method is a very useful tool for interpreting seismograms for earth structure.

The Dispersion of Slightly Dense Contaminants

Abstract: Existing theoretical models of dense gas dispersion vary greatly in degree of complexity from simple layer averaged (integral equation) approaches to the use of complex turbulence models, the latter usually employing some form of eddy diffusivity closure approximation. However there remain several aspects of the problem which are poorly understood, and may therefore not be adequately modelled. For example the question of how “entrainment” (however it may be defined) or eddy diffusivities can be related to stability. Evidently a careful look at the dynamics of dense contaminant dispersion is called for. Our research, which we review here, is an attempt to study in some detail one aspect of the dispersion dynamics in particular, namely the effects of stable stratification, which may be set up in dispersing plumes or clouds, on the turbulence. We shall describe three approaches to the problem. Firstly, the use of Rapid Distortion Theory to investigate structural changes to homogeneous turbulence with varying degrees of stable stratification in the presence of a mean velocity gradient. Secondly, a Lagrangian dynamical model of fluid element motions (as previously employed in studies of mixing in homogeneous stratified turbulence) is introduced in the context of the present problem. Finally, an experimental program is described.

Linear inversion of body-wave data; Part III, Model parameterization

Abstract: A velocity gradient model parameterized with the tau‐zeta inversion for seismic refraction data is examined with respect to a synthetic traveltime data set. The velocity‐depth model consists of a stack of laterally homogeneous layers, each with a constant velocity gradient. The free model parameters are the velocities of the layer bounds and the number of layers. The best velocity gradient solutions, i.e., with the least deviation from the true model, were obtained from “constrained” models in which the velocities of the layer bounds are the velocities of the observed refracted waves. An arbitrary selection of layer bound velocities was found to be a suboptimal choice of model parameterization for the tau‐zeta inversion. A trade‐off curve between model resolution and solution variance was constructed with the constrained model parameterization from examination of numerous solutions with a diverse number of layers. A constrained model with as many layers as observed data points represents a satisfactory co...

Run-Up and Decay of Plane Poiseuille Flow

Abstract: An incompressible Newtonian or Maxwellian fluid is contained between two stationary parallel plates. The velocity in the fluid is calculated, which results from the application at some instant of a uniform pressure gradient which is subsequently held constant.

Friction loss in piping

Abstract: This program for the HP-41C with one memory module computes pipe friction loss, velocity, and optimum diameter given pipe ID, flow rate, viscosity and density. Flow can be entered as 1.lb/h, 2.BPH-/sup 0/API, 3. gas mol. wt.-scfh, or 4. gpm-sp.gr. Density can be entered as 1.lb/ft, 2. mol. wt.-psig-/sup 0/F, or 3. /sup 0/API-/sup 0/F. For some standard strength pipes, nominal to actual diameter conversion is provided. A change in gas density with pressure can be taken into account if desired.

Head waves in laterally heterogeneous media

Abstract: Summary. A layer of constant thickness over a half-space is assumed, and the propagation of head waves is considered for the following two cases: (1) the P-wave velocity varies in the layer in the horizontal direction, and is constant in the half-space: (2) the P-wave velocity varies in the half-space in the horizontal direction, and is constant in the layer. In each case the horizontal velocity gradient is assumed to remain constant. The wave propagation is investigated in the direction of the gradient (direct profile), and opposite to it (reverse profile). Formulae for the travel times and the amplitudes are obtained on the basis of ray-theoretical considerations. Conditions are discussed for the discrimination in a field experiment between the case of a sloping boundary separating the homogeneous media, and the case of an intrinsic horizontal velocity gradient.

A canonical ocean bottom sound velocity profile

Abstract: A new canonical sound velocity profile is presented in which the velocity cubed varies linearly with depth and is characterized by two parameters. The ray acoustic equations have exact analytic solutions for this profile, and the expressions for horizontal range, travel time, and intensity are derived. It is shown that the canonical profile can be derived approximately from Hamilton’s profile for bottom sediments obtained from sonobuoy data. The agreement between the two is shown to be excellent for both the velocity and the velocity gradient even for sediment thicknesses of 1 km.