bluuebunny/crossref_metadata_2025_split huggingface dataset:
On source-sink flows in a rotating fluid
Authors: Hide R. 
Published: March 2006

An incompressible fluid fills a container of fixed shape and size and of uniform cross-section in the (x, y)-plane, themrigid side walls and the two rigid end walls being in contact with the fluid. Here (x, y, z) are the Cartesian co-ordinates of a general point in the frame of reference in which the container is stationary. Fluid is withdrawn from the container atQcm3/sec via certain permeable parts of the side walls and replaced at the same steady rate via other permeable parts of the side walls. As, by hypothesis, the vorticity of the entering and leaving fluid relative to the container is zero, the concomitant fluid motion within the container, Eulerian velocityu= −∇ϕ − ∇ ×A, is irrotational when the container is stationary in an inertial frame. The present paper is concerned with the effects onuof uniform rotation of the whole system with angular velocity Ω about thez-axis when the normal component ofuon the side walls is independent ofz.In the simplest conceivable case,D≡zu−zlis infinite (butD/Qremains finite). End effects are then negligible anduis everywhere independent ofz.The solenoidal component ofu, − ∇ ×A, corresponds tojgyres, one for each of thejirreducible sets of circuits across which the net flow of fluid does not vanish that can be drawn within them-ply connected region bounded by the side walls. While ∇ϕ, which satisfies ∇2ϕ = 0, depends onQbut not on Ω,jandv(the coefficient of kinematic viscosity), ∇ ×Adepends on all these quantities but vanishes identically whenjΩ = 0. WhenjΩ ≠ 0 butv→ 0, ∇2A+ 2Ω, the absolute vorticity, tends to zero everywhere except in certain singular regions near the bounding surfaces, where boundary layers form.End effects cannot be ignored whenDis finite. WhenDis independent ofxandyand equal toD0(say) and Ω is sufficiently large for the boundary layers on the end walls to be of the Ekman type, 95% thickness δ = 3(v/Ω)½(δ [Lt ]D0), the end effects that then arise are only confined to these boundary layers whenj= 0. Whenj≠ 0 boundary-layer suction influences the flow everywhere; thus ∇2Aand ∇ϕ (but not ∇ ×A) are reduced to zero in the main body of the fluid, the regions of non-zero ∇ϕ and ∇2Abeing the Ekman boundary layers on the end walls and boundary layers of another type, 95% thickness δs(typically greater than δ), on the side walls. A theoretical analysis of the structure of these boundary layers shows that non-linear effects, though unimportant in the end-wall boundary layers, can be significant and even dominant in the side-wall boundary layers. The analysis of an axisymmetric system, whose side walls are two coaxial cylinders, suggests an approximate expression for Δs. WhenDis not everywhere independent ofxandy,non-viscous end effects arise which produce relative vorticity in the main body of the fluid even whenj= 0.Experiments using a variety of source-sink distribution generally confirm the results of the theory, show that instabilities of various kinds may occur under certain circumstances, and suggest several promising lines for future work.
An overlooked aspect of the wind-driven oceanic circulation
Authors: Pedlosky Joseph 
Published: March 2006

The wind-driven circulation of a simple model of the oceanic circulation (linear and homogeneous) is investigated in detail to delineate the role of the Ekman layer mass flux in driving hitherto overlooked components of the oceanic circulation.The role of upwelling boundary-layer regions in driving interior geostrophic circulations is discussed in detail. Several interesting circulations hidden in the earlier transport theories are described.
Finite amplitude convection with changing mean temperature. Part 2. An experimental test of the theory
Authors: Krishnamurti Ruby 
Published: March 2006

It has been found in part 1 (Krishnamurti 1968) that when the mean temperature of a fluid layer is changing at a constant rate η, hexagonal flows are stable in a range of Rayleigh numbers near the critical. The direction of flow depends upon the sign of η. The static state is unstable to finite amplitude disturbances at Rayleigh numbers below the critical point predicted by linear theory.The validity of this theory is tested in an experiment in which the heat flux is measured as a function of η and Rayleigh number. The horizontal plan form is determined from the side by continuously exposing a photographic film moving in a vertical direction as tracers in different regions of the fluid are illuminated. Finite amplitude instability and hexagonal cells are indeed observed.
On the equations of motion for mixtures of liquid and gas bubbles
Authors: Wijngaarden L. Van 
Published: March 2006

On the basis of previous work by the author, equations are derived describing one-dimensional unsteady flow in bubble-fluid mixtures. Attention is subsequently focused on pressure waves of small and moderate amplitude propagating through the mixture. Four characteristic lengths occur, namely, wavelength, amplitude, bubble diameter and inter-bubble distance. The significance of their relative magnitudes for the theory is discussed. It appears that for high gas content the dispersion is weak and then the conservation of mass and momentum lead to equations similar to the Boussinesq equations, describing long dispersive waves of finite amplitude on a fluid of finite depth. For waves propagating in one direction only, the corresponding equation is similar to the Korteweg–de Vries equation.It is shown that for mixtures of low gas content the frequency dispersion is in most cases not small. Finally, solutions of the Korteweg–de Vries equation representing cnoidal and solitary waves in a bubble–liquid mixture are given explicitly.
Two-dimensional bubbles in slow viscous flows
Authors: Richardson S. 
Published: March 2006

The representation of a biharmonic function in terms of analytic functions is used to transform a problem of two-dimensional Stokes flow into a boundary-value problem in analytic function theory. The relevant conditions to be satisfied at a free surface, where there is a given surface tension, are derived.A method for dealing with the difficulties of such a free surface is demonstrated by obtaining solutions for a two-dimensional, in viscid bubble in (a) a shear flow, and (b) a pure straining motion. In both cases the bubble is found to have an elliptical cross-section.The solutions obtained can be shown to be unique only if certain restrictive assumptions are made, and if these are relaxed the same methods may give further solutions. Experiments on three-dimensional inviscid bubbles (Rumscheidt & Mason 1961; Taylor 1934) demonstrate that angular points appear in the bubble surface, and an analysis is presented to show that such a discontinuity in a two-dimensional free surface is necessarily a genuine cusp and the nature of the flow about such a point is examined.
Role of viscosity stratification in the stability of two-layer flow down an incline
Authors: Kao Timothy W. 
Published: March 2006

The stability of the flow of two layers of viscous liquids down an incline is investigated. The problem is governed by two competing long-wavelength modes associated with the surfaces. One mode, calling it the first mode, is faster than the second one. When the two layers have the same coefficient of dynamic viscosity, the second mode was found earlier by the author to be the governing mode for most cases. The situation is greatly altered when viscosity is not the same for the two layers. The second mode is dramatically stabilized for the range of viscosity ratio, m, less than unity, and the first mode is now generally the governing mode in that range. The overall effect is stabilizing compared with m = 1.A relative stability index is also introduced to compare the result with that of the homogeneous case. It is found that the presence of the upper layer is generally destabilizing compared with that of a homogeneous fluid of the same total depth.
Asymptotic solutions for the distribution function in non-equilibrium flows. Part 1. The weak shock
Authors: Narasimha Roddam 
Published: March 2006

This paper is the first part of an investigation of the molecular velocity distribution function in non-equilibrium flows. In this part, the general features of the distribution are discussed and illustrated by a detailed study of its asymptotic expansions in different velocity domains for a weak shock, employing a simple relaxation model for the collisions. Using the strength of the shock as a small parameter, the Chapman–Enskog distribution is derived, in a less restrictive way than in previous analyses, as the first two terms in a suitable ‘inner’ asymptotic expansion of the distribution in velocity space, valid only for not very high velocities. It is shown that the consideration of two further limits, called the intermediate and outer, is necessary for a complete description of the distribution in velocity space. The uniformly valid composite expansion demonstrates the slow approach to equilibrium of fast molecules. The outer solution depends on integrals over the flow and is in general ‘global’, in contrast to the inner solution which is essentially local; this introduces certain asymmetries on a fine scale even in a weak shock. It is shown, for example, that fast molecules moving towards the hot side accumulate by collisionless streaming, whereas those moving towards the cold side attenuate like a molecular beam and represent essentially a ‘precursor’ of the hot side. A simple approximation for the distribution in the precursor is derived, and found to contain, in the outer limit, a large perturbation on the local Maxwellian; this results in an approach to equilibrium like $\exp (-|x|^{\frac{2}{3}})$ on the cold side.A heuristic extension of the argument to the true Boltzmann equation leads to the result that for molecules with an interparticle potential varying as the inverse m-power of the distance, the approach to equilibrium through the precursor is like $\exp (-|x|^l)$, where l = m/(m + 2).
An integral-transform method for shock–shock interaction studies
Authors: Arora N. L. 
Published: March 2006

An analytic solution is obtained for the head-on collision of strong shock waves with supersonically moving, axisymmetric, slender bodies. A new method of the solution is developed using integral transforms. Pressure distributions on the surface of a cone illustrate the effects of shock strength and body speed. The results are compared with those of Blankenship (1965), which were obtained by numerical methods.It is also shown that the same analysis can, with certain modifications, be adapted for treating the shock-shock interaction on thin two-dimensional aerofoils of arbitrary shape at small incidence.
Stability of towed, totally submerged flexible cylinders
Authors: Paidoussis M. P. 
Published: March 2006

A general theory is presented to account for the small, free, lateral motions of a flexible, slender, cylindrical body with tapered ends, totally submerged in liquid and towed at steady speedU. For particular shapes of the ends and length of tow-rope, it is shown that the body may be subject to oscillatory and non-oscillatory instabilities forU> 0; at smallU, these instabilities correspond to those of a rigid body. At higherU, the system generally regains stability in the above modes, but may be subject to higher-mode, flexural oscillatory instabilities. The critical conditions of stability are calculated extensively and the effect on stability of a number of dimensionless parameters is discussed. It is shown that optimum stability is achieved with a streamlined nose, a blunt tail and a short tow-rope.Some experiments are described which were designed to test the theory. Rubber cylinders of neutral buoyancy were held in vertical water flow by a nylon ‘tow-rope’. Provided the tail was streamlined and the tow-rope not too short, ‘criss-crossing’, non-flexural oscillations developed at very low flow. Increasing the flow, these oscillations ceased and the cylinder buckled like a column; subsequently higher-mode flexural oscillations developed. However, for a sufficiently blunt tail and short tow-rope, the system was completely stable.The experimental observations are generally in qualitative agreement with theory. Quantitative comparison of the various instability thresholds and stable zones between experiment and theory, based on estimated values of some of the theoretical dimensionless parameters, is also fairly good.
The spectrum of temperature fluctuations in turbulent flow
Authors: Grant H. L. , Hughes B. A. , Vogel W. M. , Moilliet A. 
Published: March 2006

Temperature and velocity fluctuations have been recorded in the open sea and in a tidal channel, and power spectra have been determined from the records. The one-dimensional spectra of temperature fluctuations are found to have an inertial subrange. At larger wave-numbers the data can be fitted by Batchelor's spectrum function for the viscous-convective range. The spectra are inconsistent with the form proposed by Pao for the viscous-convective range.Estimates are given for the constants in Batchelor's spectrum function, but these depend upon knowledge of the rate of dissipation of kinetic energy, which is determined from the velocity spectra. There is doubt about the validity of some of the velocity spectra, and in other cases there is reason to suspect that the turbulence is not locally isotropic.
Resonant gravity-wave interactions in a shear flow
Authors: Craik Alex. D. D. 
Published: March 2006

Among a triad of gravity waves in a uniform shear flow, a remarkably powerful second-order resonant interaction may take place. This interaction is characterized by large growth rates of waves which propagate in directions oblique to that of the primary flow, and by a systematic transfer of energy from the primary flow to such waves. Most of the energy transfer takes place in the vicinity of a ‘critical layer’, where viscous forces are dominant.Provided the resonance condition may be satisfied, a uniform shear flow which is perturbed by a two-dimensional wave of small but finite amplitude may be unstable, owing to the growth of two initially infinitesimal oblique waves which complete the resonant triad.
Equilibrium-range spectra of sand waves formed by flowing water
Authors: Hino Mikio 
Published: March 2006

Based on a dimensional consideration, the ‘−3 power law’ on the spatial spectrum of sand waves formed by flowing water Sηη(k) is derived for a large wave-number equilibrium subrange,
\[
S_{\eta\eta}(k)\sim \alpha k^{-3},
\]
where α is a constant depending on the angle of repose of sand particles and k denotes the wave-number.Likewise, the frequency spectrum is shown to have the ‘−3 power law’ range for higher frequencies as well as the ‘−2 power law’ range for frequencies near a spectral peak.These spectra are shown to agree with experimental data from various sources.
Reflexion and stability of waves in stably stratified fluids with shear flow: a numerical study
Authors: Jones Walter L. 
Published: March 2006

A numerical examination has been made of the reflectivity of critical levels with low Richardson number to internal gravity waves propagating in stratified fluids with shear. At sufficiently low positive Richardson numbers the reflected wave may actually be stronger than the incident.The normal mode instabilities of three simple models have also been computed. The results are presented in three dimensions: Richardson number, horizontal wave scale and real wave frequency.
The stability of the laminar natural convection boundary layer
Authors: Knowles C. P. , Gebhart B. 
Published: March 2006

This paper concerns the stability characteristics of laminar natural convection in external flows. Until recently, very little was known about such stability because of the inherent complexity of temperature-coupled flows and because of the complicated mechanisms of disturbance propagation. In this work the stability of the laminar natural convection boundary layer is examined more closely in an attempt to predict the experimental results recently obtained. In particular, it is shown that an important thermal capacity coupling exists between the fluid and the wall which generates the flow. This thermal capacity coupling is shown to have a first-order effect for particular Grashof-number wave-number products. Solutions are obtained for a Prandtl number of 0·733 and several values of relative wall thermal capacity. These solutions indicate the important role of this wall coupling. In particular, the results predict the experimental data previously obtained.In addition, solutions with ‘zero wall storage’ are obtained for a range of Prandtl numbers from 0·733 to 6·9. The relative disturbance u-velocity and temperature amplitudes and their phases are shown for Pr = 0·733 and several wall-storage parameters, and for Pr = 6·9 with zero wall storage. A comparison between the disturbance temperature distribution and the data obtained from a recent experimental investigation shows close agreement when the thermal capacity of the wall is taken into account.In the appendix, it is shown that for temperature-coupled flows and wall-coupled boundary conditions the flow is unstable at a lower Grashof number for two-dimensional disturbances than it is for three-dimensional disturbances. This result has been supported by the recent experimental observations.
On the stability against shear waves of steady flows of non-linear viscoelastic fluids
Authors: Coleman Bernard D. , Gurtin Morton E. 
Published: March 2006

A shear-acceleration wave is a propagating singular surface across which the velocity vector and the normal component of the acceleration are continuous, while the tangential component$\dot{v}$of the acceleration suffers a jump discontinuity [$\dot{v}$]. We here discuss plane-rectilinear shearing flows of general, non-linear, incompressible simple fluids with fading memory. Working within the framework of such planar motions, we derive a general and exact formula for the time-dependence of the amplitudea= [$\dot{v}$] of a shear-acceleration wave propagating into a region undergoing a steady but not necessarily homogeneous shearing flow. When this expression is specialized to the case in which the velocity gradient is constant in space ahead of the wave, it assumes a form familiar in the theory of longitudinal acceleration waves in compressible materials with fading memory (cf., e.g., Coleman & Gurtin 1965, equation (4.12)).In earlier work (1965) we observed that a planar shear-acceleration wave cannot grow in amplitude if it is propagating into a fluid in a state of equilibrium. It is clear from our present results that if the fluid ahead of the wave is being sheared, |a(t)| not only increases, but can approach infinity in a finite time, provideda(0) is of proper sign and |a(0)| exceeds a certain critical amplitude. We expect this critical amplitude to decrease as the rate of shear ahead of the wave is increased.
Acoustic energy flux from shock-turbulence interaction
Authors: Ribner H. S. 
Published: March 2006

The analysis of the sound field generated by the passage of isotropic turbulence through a shock of finite strength (Ribner 1953, 1954) has been extended to provide the flux of acoustic energy emanating from unit area on the downstream side of the shock. This is motivated by the problem of estimating the sound power emerging from a supersonic jet containing shock waves. The energy flux is found to vary almost linearly with shock density ratio, reaching a maximum at infinite Mach number of 0[sdot ]062 of the flux of turbulence kinetic energy convected into unit area of the shock.Direct comparison with a result obtained by Lighthill (1953) is misleading. His energy relations, reckoned relative to a frame moving with the fluid, must be converted to the shock-fixed frame used herein. The converted results of his theory (weak shocks) and the results of our theory (arbitrary shocks) appear to show a similar asymptotic behaviour for vanishing shock strength; they diverge with increasing shock strength.
Mixed region collapse with internal wave generation in a density-stratified medium
Authors: Wu Jin 
Published: March 2006

An experiment has been conducted modelling a two-dimensional mixed region collapsing in a continuously density-stratified medium. The process of collapse can be divided into three stages. Empirical formulae have been derived to describe the process of the first two stages, during which gravitational effects determine the modelling criterion. The collapse in the final stage is complicated by viscous effects; a ratio between the Froude number and the Reynolds number seems to provide a probable modification of the time scale.The pattern of internal waves generated by the initial impulsive collapse of this mixed region can be represented by moving rays connecting either wave crests or troughs. These rays move away from the collapse centre and at the same time decrease their slopes from the horizontal. A simpler steady-state wave pattern generated by an oscillating plunger has also been studied. Taken together, these experimental results are interpreted to show that the energy density of the collapse is skewed toward high frequencies and is peaked at 8/10 of the Brunt-Väisälä frequency of the medium.
On fluctuating flow of an elastico-viscous fluid past an infinite plate with variable suction
Authors: Soundalgekar V. M. , Puri Pratap 
Published: March 2006

An exact solution is obtained for the two-dimensional flow of an elastico-viscous (Walters fluid B’) incompressible fluid past an infinite porous wall under the following conditions: (i) the suction velocity normal to the plate oscillates in magnitude but not in direction about a non-zero mean; (ii) the free-stream velocity oscillates in time about a constant mean.The response of the skin-friction to the fluctuating stream and suction velocity is studied for variations in the suction parameter A, the elasticity parameter k and the frequency parameter μ. It is found that the back-flow at the wall is enhanced by k. For the same value of A, the amplitude of the skin-friction decreases with increasing k. Also an increase in k and μ leads to a decrease in the phase of the skin-friction. For moderately large A and k, the phase of the skin-friction may be completely negative.
Reliability of a tympanic thermometer in measuring temperatures in children after minor ear surgery
Authors: Pandey A , Ingrams D R , Jones M , Raman R , Marks N D 
Published: March 2006

Aim: To evaluate the reliability of infrared tympanic thermometry in children who have undergone myringotomy with grommet insertion.Method: Forty children who had undergone myringotomy with at least one grommet insertion had the tympanic temperature of each ear and the axillary temperature measured on admission and 30 minutes post-operatively.Result: No difference was found between the pre- and post-operative temperatures measured by either method (p > 0.05, paired t-test, hypothesized difference of 0).Conclusion: Infrared tympanic thermometry is reliable in monitoring body temperature in children who have had minor ear surgery.