bluuebunny/crossref_metadata_2025_split huggingface dataset:
Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows
Authors: Chwang Allen T. , Wu T. Yao-Tsu 
Published: March 2006

The present study further explores the fundamental singular solutions for Stokes flow that can be useful for constructing solutions over a wide range of free-stream profiles and body shapes. The primary singularity is the Stokeslet, which is associated with a singular point force embedded in a Stokes flow. From its derivatives other fundamental singularities can be obtained, including rotlets, stresslets, potential doublets and higher-order poles derived from them. For treating interior Stokes-flow problems new fundamental solutions are introduced; they include the Stokeson and its derivatives, called the roton and stresson.These fundamental singularities are employed here to construct exact solutions to a number of exterior and interior Stokes-flow problems for several specific body shapes translating and rotating in a viscous fluid which may itself be providing a primary flow. The different primary flows considered here include the uniform stream, shear flows, parabolic profiles and extensional flows (hyper-bolic profiles), while the body shapes cover prolate spheroids, spheres and circular cylinders. The salient features of these exact solutions (all obtained in closed form) regarding the types of singularities required for the construction of a solution in each specific case, their distribution densities and the range of validity of the solution, which may depend on the characteristic Reynolds numbers and governing geometrical parameters, are discussed.
The viscous nonlinear symmetric baroclinic instability of a zonal shear flow
Authors: Walton I. C. 
Published: March 2006

The stability of a baroclinic zonal current to symmetric perturbations on a meridionally unboundedf-plane is considered. The lower boundary is at rest but the upper one moves with a constant velocity in keeping with the velocity of the zonal current. Following Stone (1966) a horizontal length scaleO(Ro) is taken, whereRois the Rossby number, with the Richardson numberRi=O(1). Instability sets in when the wavelength isO(E1/3), whereEis the Ekman number based on the distance between the rigid horizontal boundaries, which corresponds to Stone's inviscid value zero, and to McIntyre's (1970) value infinity on a length scaleO(E½).A nonlinear analysis about the point of onset of instability yields the result that for the monotonic mode zonal momentum is convected polewards. The possible implications of this result for the dynamics of Jupiter's atmosphere are discussed.
The buckling and stretching of a viscida
Authors: Buckmaster J. D. , Nachman A. , Ting L. 
Published: March 2006

We consider the deformation of a thin thread of viscous liquid (viscida) as its ends are slowly moved together. Equations are deduced which are capable of describing the motion of the thread when the displacement of the axis from a straight line is either on the scale of the thread thickness (problem 1) or on the much larger scale of the thread length (problem 2). In the former case it is shown analytically that an arbitrary initial displacement evolves in such a way that, as the appropriately scaled time τ becomes large, the first mode of the disturbance emerges in a dominant role with an amplitude that is proportional to τ½ and independent of the initial amplitude. This provides the initial condition for problem 2, for which a numerical description is obtained.In addition, we analyse the situation when the ends of the viscida are slowly pulled apart. In this case the high frequency end of the spectrum dominates as an arbitrary disturbance decays.
Experiments on the instability waves in a supersonic jet and their acoustic radiation
Authors: Mclaughlin Dennis K. , Morrison Gerald L. , Troutt Timothy R. 
Published: March 2006

An experimental investigation of the instability and the acoustic radiation of the low Reynolds number axisymmetric supersonic jet has been performed. Hot-wire measurements in the flow field and microphone measurements in the acoustic field were obtained from different size jets at Mach numbers of about 2. The Reynolds number ranged from 8000 to 107000, which contrasts with a Reynolds number of 1·3 × 106for similar jets exhausting into atmospheric pressure.Hot-wire measurements indicate that the instability process in the perfectly expanded jet consists of numerous discrete frequency modes around a Strouhal number of 0·18. The waves grow almost exponentially and propagate downstream at a supersonic velocity with respect to the surrounding air. Measurements of the wavelength and wave speed of theSt= 0·18 oscillation agree closely with Tam's theoretical predictions.Microphone measurements have shown that the wavelength, wave orientation and frequency of the acoustic radiation generated by the dominant instability agree with the Mach wave concept. The sound pressure levels measured in the low Reynolds number jet extrapolate to values approaching the noise levels measured by other experimenters in high Reynolds number jets. These measurements provide more evidence that the dominant noise generation mechanism in high Reynolds number jets is the large-scale instability.
Experimental results for the transpired turbulent boundary layer in an adverse pressure gradient
Authors: Andersen P. S. , Kays W. M. , Moffat R. J. 
Published: March 2006

An experimental investigation of the fluid mechanics of the transpired turbulent boundary layer in zero and adverse pressure gradients was carried out on the Stanford Heat and Mass Transfer Apparatus. Profiles of (a) the mean velocity, (b) the intensities of the three components of the turbulent velocity fluctuations and (c) the Reynolds stress were obtained by hot-wire anemometry. The wall shear stress was measured by using an integrated form of the boundary-layer equation to ‘extrapolate’ the measured shear-stress profiles to the wall.The two experimental adverse pressure gradients corresponded to free-stream velocity distributions of the type u∞ ∞ xm, where m = −0·15 and −0·20, x being the streamwise co-ordinate. Equilibrium boundary layers (i.e. flows with velocity defect profile similarity) were obtained when the transpiration velocity v0 was varied such that the blowing parameter B = pv0u∞/τ0 and the Clauser pressure-gradient parameter $\beta\equiv\delta_1\tau_0^{-1}\,dp/dx $ were held constant. (τ0 is the shear stress at the wall and δ1 is the displacement thickness.)Tabular and graphical results are presented.
Stokes flow past a particle of arbitrary shape: a numerical method of solution
Authors: Youngren G. K. , Acrivos A. 
Published: March 2006

The problem of determining the slow viscous flow of an unbounded fluid past a single solid particle is formulated exactly as a system of linear integral equations of the first kind for a distribution of Stokeslets over the particle surface. The unknown density of Stokeslets is identical with the surface-stress force and can be obtained numerically by reducing the integral equations to a system of linear algebraic equations. This appears to be an efficient way of determining solutions for several external flows past a particle, since it requires that the matrix of the algebraic system be inverted only once for a given particle.The technique was tested successfully against the analytic solutions for spheroids in uniform and simple shear flows, and was then applied to two problems involving the motion of finite circular cylinders: (i) a cylinder translating parallel to its axis, for which the local stress force distribution and the drag were determined; and (ii) the equivalent axis ratio of a freely suspended cylinder, which was calculated by determining the couple on a stationary cylinder placed symmetrically in two different simple shear flows. The numerical results were found to be consistent with the asymptotic analysis of Cox (1970, 1971) and in excellent agreement with the experiments of Anczurowski & Mason (1968), but not with those of Harris & Pittman (1975).
Electro-convection in a dielectric liquid layer subjected to unipolar injection
Authors: Lacroix J. C. , Atten P. , Hopfinger E. J. 
Published: March 2006

The problem of electric charge convection in a dielectric liquid layer of high ionic purity, when subjected to unipolar injection, is in many ways analogous to that of thermal convection in a horizontal fluid layer heated from below, although no formal analogy can be established. The problem treated is intrinsically more nonlinear than the thermal problem. We consider two asymptotic states of convection: one where the whole motion is dominated by viscosity, and one where inertial effects dominate. In each state, two or three spatial regions are distinguished. From the approximate equations that hold in the different regions, information about the variation of the different quantities with distance from the injector is obtained, and further approximations permit us to establish the dependence of the current density ratioI/I0(called theelectric Nusselt number) on the stability parameterT=M2R= εϕ0/Kρν, and on 1/R= ν/Kϕ0, which is an equivalent Prandtl number (ε is the permittivity, ρ the fluid density,Kthe mobility, ν the kinematic viscosity, and ϕ0the applied voltage). In the viscous state, the analysis givesI/I0∞T½; in the inertial state the lawI/I0∞ (T/R)1/4=M½is obtained. SinceMis independent of the applied voltage, the latter law shows the saturation in the electric Nusselt number observed in earlier experiments. The transition in the states is associated with a transition number (MR)T[gap ] 30, which is an electric Reynolds number, related to an ordinary Reynolds number of about 10.The experimental results, obtained in liquids of very different viscosities and dielectric constants, verify these theoretical predictions; further, they yield more precise numerical coefficients. As for the transition criteria, the experiments confirm that the viscous and inertial effects are of the same order whenRe[gap ] 10. It was also possible to determine roughly the limits of the viscous and inertial states. The viscous analysis remains valid up to a Reynolds number of about 1; the inertial state can be considered valid down to a Reynolds number of 60. Schlieren observations show that the motion has the structure of very stable hexagonal cells at applied voltages just above the critical voltage, which are transformed into unstable filaments when the voltage is increased further. At even higher voltages, the motion finally breaks down into turbulence. It may be of interest to point out that, whenM< 3, the electric Nusselt number approaches 1, which is equivalent to the situation in thermal convection at low Prandtl numbers.
On double-roll convection in a rotating magnetic system
Authors: Robert P. H. , Stewartson K. 
Published: March 2006

Electrically and thermally conducting inviscid fluid rotating about a vertical axis is confined between two horizontal plates maintained a t different temperatures, the upper plate being the cooler. The fluid is permeated by a horizontal magnetic field that corotates with the fluid. In an earlier paper (Roberts & Stewartson 1974) the fluid is supposed to be in a state of near-marginal instability to convective overturning and the nonlinear evolution of single rolls is discussed. Inertial terms are neglected. However, if q < 2 and λ < 2/3½, where q and λ may be defined by equation (2.3) below, the principle of the exchange of stabilities holds and there is also a degeneracy in the linear stability problem. There are now two distinct unstable rolls equally possible and their nonlinear interaction leads to a violation of the governing equations. This difficulty has already been noted by Taylor (1963) and it is resolved in this paper by adding a geostrophic motion (the Taylor shear) parallel to the magnetic field and by restoring the inertial terms in the governing equations. We consider particularly instabilities in which one roll predominates and find that, if λ is sufficiently small, each of the rolls that can occur is stable with respect to the other, i.e. an initially weak roll of the other type dies out relative to it. This means that we can expect the fluid motion to consist of single rolls at large times. On the other hand when λ is near 2/3½ both rolls are unstable with respect to the other. The Taylor shear does not then die out and the two rolls become comparable in magnitude and modify each other's structure. At intermediate values of λ one of the rolls is stable in this way and the other unstable.The study is motivated by a desire to understand better the dynamical means by which a large mass of conducting fluid can create its own magnetism. It is argued that these instabilities suggest the existence of a mechanism of self-adjustment preventing λ from either increasing or decreasing indefinitely and noted that, very roughly, λ is of order unity in the earth's core.
Transition to turbulence in oscillating pipe flow
Authors: Merkli P. , Thomann H. 
Published: March 2006

Published results on transition in a Stokes layer indicate a wide range of transition Reynolds numbers. As thermal effects in a resonance tube (Merkli & Thomann 1975) depend on the state of the boundary layer, the transition Reynolds number was determined, and a critical Reynolds numberAc≈ 400 was found. The observations were made with hot wires and with flow visualization by means of smoke, and provide new details on turbulence in a Stokes layer. With this knowledge an explanation of the large discrepancies between some stability theories and the experiments is suggested. The main point is that turbulence occurs in the form of periodic bursts which are followed byrelaminarimtionin the same cycle and donotlead to turbulent flow during the whole cycle.A further, unexpected result of the present investigation is the discovery of vortex patterns superimposed on the normal laminar acoustic motion.
Statistical characteristics of a turbulent jet
Authors: Ribeiro M. M. , Whitelaw J. H. 
Published: March 2006

Velocity probability distributions and autocorrelation functions were measured in the self-preserving region of a round free jet at 57 diameters. On-line digital-sampling procedures were used to interpret the signals from a crossed hot-wire probe. Particular attention was paid to the probabilities of the axial and radial velocity components and of the angle between them at radial locations corresponding to the centre-line and the location of maximum shear stress and at an edge location r/x = 0·087.The results show, for example, that the probability of the axial velocity on the centre-line is slightly non-Gaussian and that, in general, the observed deviations of the probabilities of u depend upon the difference in behaviour of the corresponding distributions for positive and negative ν; outward transport (positive ν) is associated with near-Gaussian u distributions whereas inward transport (negative ν) is associated with skewed u distributions. The probability of the fluctuating vector (u, v) becomes more asymmetric with increasing radius with the dominant direction corresponding to positive $\overline{uv}$. The measured auto-and cross-correlations are shown to be largely independent of radius.
A turbulence velocity scale for curved shear flows
Authors: So Ronald M. C. 
Published: March 2006

Assuming the turbulence length scale to be unaffected by streamline curvature, a turbulence velocity scale for curved shear flows is derived from the Reynolds-stress equations. Closure of the equations is obtained by using the scheme of Mellor & Herring (1973), and the Reynolds-stress equations are simplified by invoking the two-dimensional boundary-layer approximations and assuming that production of turbulent energy balances viscous dissipation. The resulting formula for the velocity scale has one free parameter, but this can be determined from data for non-rotating unstratified plane flows. Consequently there is no free constant in the derived expression. A single value of the constant is found to give good agreement between calculated and measured values of the velocity scale for a wide variety of curved shear flows.The result is also applied to test the validity and extent of the analogy between the effects of buoyancy and streamline curvature. This is done by comparing the present result with that obtained by Mellor (1973). Excellent agreement is obtained for the range −0·21 [les ]Rif[les ] 0·21. Therefore the present result provides direct evidence in support of the use of a Monin–Oboukhov (1954) formula for curved shear flows as proposed by Bradshaw (1969).
Thermal convection in gas–droplet mixtures with phase transition
Authors: Kambe T. , Takaki R. 
Published: March 2006

Thermal convection in a three-component fluid consisting of an inert carrier gas, a condensable vapour and small liquid droplets dispersed throughout the gaseous components has been investigated both theoretically and experimentally. The theoretical study is concerned with the stability of a horizontal fluid layer subject to gradients of both temperature and droplet density. The stability is characterized by four parameters: two material constants, that is, a modified Prandtl number P and a constant Q proportional to Dm − κ (Dm is the mutual mass diffusivity of the two gaseous constituents, κ the thermometric conductivity of the gas phase), a modified Rayleigh number R and a parameter S defined as the ratio of the droplet density gradient to the gas density gradient. It is shown for positive R that, irrespective of the value of R, the system is stable for S > S∞ (S∞ is a constant dependent on P and Q) and unstable for S < Q (Q is normally less than S∞) and that for the intermediate range Q < S < S∞ a transition from stability to instability occurs via an oscillatory state as R is increased through a critical value depending on S. It is shown that the stability is governed largely by both vapour diffusion through the inert gas and droplet growth or decay due to phase changes.In the experiments, thermal convection in a three-component fluid consisting of air, water vapour and water droplets was investigated. The cloud of droplets was mainly formed by injecting cigarette smoke into a horizontal layer of air saturated with water vapour. After the injection several phases of motion were observed successively. Among them there were travelling waves and steady cellular convection. Measurements were made of the critical Rayleigh numbers for the onset of the phases, the scale of the steady convection cells and the speed of the travelling waves. It is found that all the qualitative features of the experiment are explained by the theory.
The influence of shear on mixing across density interfaces
Authors: Long Robert R. 
Published: March 2006

This paper discusses critically observations of mixing processes across density interfaces in laboratory experiments and inferences that have been made and can be made from these observations. Fluxes of heat or salt and entrainment velocities have been found to depend on negative powers of an overall Richardson number Ri* based on the buoyancy jump across the interface, the depth of the homogeneous layer and the intensity of the turbulence near the source. When the Reynolds and Péclet numbers are large, the fluxes or entrainment velocities appear to be proportional to the minus one and minus three-halves powers of Ri* for flows with and without mean shear respectively, and this difference has caused speculation about the accuracy of the experimental data and about the reasons for the two laws if the difference is real. In the present discussion, we accept the accuracy of the two laws and attribute the higher entrainment rate for shear flows to the decrease of r.m.s. velocities near the interface with increasing Ri* in the case of zero shear. A plausible argument yields the unifying result that the entrainment rates in both cases are proportional to Ri−1, where Ri is a Richardson number based on the buoyancy jump and velocities and lengths characteristic of the turbulence near the interface. It is suggested that the $Ri^{-\frac{3}{2}}$ behaviour inferred by Turner is based on an erroneous interpretation of experimental data.In the course of the discussion, it is shown that the drag coefficient in flow of a stratified fluid over a rough surface is independent of the Richardson number (or density jump across the interface or inversion) and depends only on the ratio of the roughness length to the depth of the homogeneous layer. This has obvious implications for problems of parameterizing the momentum flux near the ground in the atmosphere.
Laser-Doppler anemometer measurements in drag-reducing channel flows
Authors: Reischman M. M. , Tiederman W. G. 
Published: March 2006

The objective of this study was to make velocity measurements in drag-reducing flows which would be sufficient in scope and accuracy to test proposed models of drag-reducing flows and to yield new information about the mechanisms of drag reduction. Consequently, measurements of the mean and turbulence intensity of the streamwise velocity component were made in fully developed, turbulent, drag-reducing flow in a two-dimensional channel with a laser-Doppler anemometer. The anemometer was operated in the individual-realization mode and corrections were made to eliminate statistical biasing of the data. Two polyacrylamides and a polyethylene oxide were used to produce seven flows which had drag reductions ranging from 24 to 41 %. Measurements were also made in water to establish the standard characteristics of the flow channel.The data show that the drag-reducing mean velocity profile can be divided into three zones: a viscous sublayer, a buffer or interactive region and a logarithmic region. There is no evidence that the viscous sublayers of the drag-reducing channel flows are thicker than those in the solvent flows. In addition the normalized streamwise fluctuations are essentially the same in both the solvent and drag-reducing sublayers. The changes caused by the polymer addition occur in the buffer region. The drag-reducing buffer region is thicker and the velocity profile in the outer flow region adjusts in order to accommodate this buffer-region thickening. The measurements of the streamwise velocity fluctuations also show that the polymer additives redistribute the primary turbulent activity over a broadened buffer region. The normalized magnitude of these fluctuations is, however, considerably lower in these two-dimensional drag-reducing channel flows than in those previously reported by Rudd (1972), Logan (1972) and Kumor & Sylvester (1973). Moreover, the mean velocity profiles in the buffer region do not confirm the hypothesis of Virk, Mickley & Smith (1970) that the data will follow their proposed ‘ultimate profile’ when the drag reduction is less than that given by the maximum asymptote. The mean velocity measurements also show that the proposed methods for predicting the upward shift in the outer portion of the mean velocity profile are inconsistent and lack universality. However, these results do confirm the previous suggestions of Virk (1971), Tomita (1970) and Lumley (1973) that the buffer region is the area of importance and change in drag-reducing flows.