bluuebunny/crossref_metadata_2025 huggingface dataset:
Dynamics of establishment of selective withdrawal of a stratified fluid from a line sink. Part 1. Theory
Authors: Pao Hsien-Ping , Kao Timothy W.
Published: March 2006

An investigation is made of selective withdrawal of a linear stratified fluid from a line sink in a channel of depth d. The flow is characterized by a densimetric Froude number F = Q/Nd2, where Q is the discharge per unit width and N is the Väisälä frequency. The dynamics of establishment of flow are investigated theoretically. Analytic results are obtained from a linearized theory based on a systematic perturbation scheme for small values of F. These results lead to a proper identification of the successive arrival of ‘columnar disturbance modes’ as the mechanism responsible for the development of flow concentration in the withdrawal region. Viscous and diffusive effects are also examined. For larger times and higher discharges (higher values of F), nonlinear effects become important, and the full Navier-Stokes equations are now solved numerically by a finite-difference procedure in a ‘stretched’ co-ordinate system. The solutions indicate that the establishment of the steady flow field is due to the successive arrival and interaction of ‘columnar disturbance modes’. Steady-state solutions are also presented, and a similarity profile is obtained. Comparison of the theoretical findings with experimental results are presented in part 2. Agreement with experimental measurements is found to be excellent.
Dynamics of establishment of selective withdrawal of a stratified fluid from a line sink. Part 2. Experiment
Authors: Kao Timothy W. , Pao Hsien-Ping , Wei Shuang N.
Published: March 2006

Experiments were conducted to examine the development and establishment of the withdrawal current in the selective withdrawal of a stratified fluid from a line sink. The experiments were performed in a Plexiglas channel 30·5 ft long 14 in. wide, and filled with a linearly stratified salt solution to a depth of 18 in. The line sink was located at mid-depth. The flow was symmetric about the middepth. Velocity measurements and flow visualization were obtained by neutrally buoyant liquid droplets and vertical dye lines. Density measurements were made by a salinity probe. The development of the upstream velocity field was found by measurement to be brought about by the successive arrival of ‘columnar disturbance modes’, discussed in part 1. Agreement with the theoretical predictions is excellent. A similarity profile of the steady-state horizontal velocity is obtained, and the Froude number based on the thickness of the flowing zone is found to approach a constant value in the essentially inviscid region. The results are compared with field data from the Tennessee Valley Authority (TVA) reservoirs.
Laminar flow past an abruptly accelerated elliptic cylinder at 45° incidence
Authors: Lugt H. J. , Haussling H. J.
Published: March 2006

Numerical solutions for laminar incompressible fluid flows past an abruptly started elliptic cylinder at 45° incidence are presented. Various finite-difference schemes for the stream-function/vorticity formulation are used and their merits briefly discussed. Almost steady-state solutions are obtained forRe= 15 and 30, whereas forRe= 200 a Kármán vortex street develops. The transient period from the start to the steady or quasi-steady state is investigated in terms of patterns of streamlines and lines of constant vorticity and drag, lift and moment coefficients.
Experimental and theoretical studies of dissolution roughness
Authors: Blumberg Paul N. , Curl Rane L.
Published: March 2006

Periodic dissolution patterns that result from the interaction of a soluble surface and an adjacent turbulent flow have been investigated experimentally and theoretically. They occur at a Reynolds number based on a characteristic wavelength and friction velocity of about 2200. Experimental results for the stable geometry, propagation, mass-transfer distribution, average mass-transfer correlation and friction factor are presented. An interpretation based upon the repetitive transitional nature of the flow structure is advanced to explain aspects of the origin and behaviour of this type of roughness.
The stability of a trailing line vortex. Part 2. Viscous theory
Authors: Lessen Martin , Paillet Frederick
Published: March 2006

In a previous paper, the inviscid stability of a swirling far wake was investigated, and the superposition of a swirling flow on the axisymmetric wake was shown to be initially destabilizing, although all modes investigated eventually become more stable at sufficiently large swirl. The most unstable disturbances were non-axisymmetric modes with negative azimuthal wavenumber n representing helical wave paths opposite in sense to the wake rotation. The disturbance growth rate appeared to increase continuously with |n|, while all modes with |n| > 1 represented disturbances which are completely stable for the non-swirling wake. In the present analysis, both timewise and spacewise growth rates are calculated for the lowest three negative non-axisymmetric modes (n = −1, −2 and −3). Vortex intensity is characterized by a swirl parameter q proportional to the ratio of the maximum swirling velocity to the maximum axial velocity defect. The large wavenumbers associated with the disturbances at large |n| allow the n = −1 mode to have the minimum critical Reynolds number of 16 (q ≃ 0·40). The other two modes investigated have minimum Reynolds numbers on the neutral curve of 31 (n = −2, q = 0·60) and 57 (n = −3, q = 0·80). For each mode, the neutralstability curve is shown to shift rapidly towards infinite Reynolds numbers once the swirl becomes sufficiently large. Some of the most unstable swirling flows are shown to possess spacewise amplification factors almost ten times that for the most unstable wavenumber for the non-swirling wake at moderate Reynolds numbers.
Kelvin-Helmholtz instability of a slowly varying flow
Authors: Drazin P. G.
Published: March 2006

The linear stability of a basic flow of two homogeneous inviscid incompressible fluids under the action of gravity is treated mathematically. In the basic state, one fluid is at rest below a horizontal planez= 0; and the other flows above in thexdirection, its speed varying slowly with the lateral co-ordinatey. The eigenvalue problem for normal modes is derived; its equation is a partial differential one, the co-ordinatesyandznot being separable. The problem is solved approximately by taking the modeslocallyas if the basic velocity were independent ofy, though the lateral wavenumber is allowed to vary slowly withy. This leads to an ordinary differential equation inywhich is solved by the JWKB method. Detailed calculations are made for a parabolic profile, representing the blowing of air over water in a wide channel, and for other profiles.
Finite amplitude side-band stability of a viscous film
Authors: Lin S. P.
Published: March 2006

The nonlinear stability of a viscous film flowing steadily down an inclined plane is investigated by the method of multiple scales. It is shown that the super-critically stable, finite amplitude, long, monochromatic wave obtained by Lin (1969, 1970, 1971) is stable to side-band disturbances under modal interaction if the bandwidth is less in magnitude than to the ratio of the amplitude to the film thickness. Near the upper branch of the linear neutral-stability curve where the amplification rate ci is O(ε2), the nonlinear evolution of initially infinitesimal waves of a finite bandwidth is shown to obey the Landau-Stuart equation, Near the lower branch of the neutral curve, the nonlinear evolution is stronger. An equation is derived for describing this strong nonlinear development of relatively long waves. In practice, disturbance of this type clusters in the form of a hump which cannot be constructed only by the first few harmonics.
The effect of mean compression or dilatation on the turbulence structure of supersonic boundary layers
Authors: Bradshaw P.
Published: March 2006

It is now well known that the turbulence structure of thin shear layers can be strongly affected by the application of extra rates of strain in addition to the shear velocity gradient. Examples of such extra strain rates include lateral divergence or convergence, and streamline curvature in the plane of the mean shear. The changes in Reynolds stress are an order of magnitude larger than would be expected from the explicit extra terms in the Reynolds-stress transport equations, and therefore an order of magnitude larger than predicted by conventional calculation methods. In the present paper, one of a series on ‘complex’ turbulent flows, we show that bulk compression or dilatation (i.e. an extra strain rate div U) also appears to affect turbulent shear layers, typical values of Reynolds stress being increased by compression and decreased by dilatation. The fractional change in Reynolds stress is an order of magnitude larger than the fractional change in volume of a fluid element. The physical mechanism is probably analogous to that responsible for the large effects of divergence or convergence in incompressible flow. Because the phenomenon seems to be of great practical importance we discuss it in the context of engineering calculation methods. An empirical correction formula, analogous to those used to allow for divergence or curvature effects, greatly reduces the large discrepancies found between recent experiments on supersonic boundary layers and calculations by conventional extensions of successful incompressible-flow methods.
The stability of pendent liquid drops. Part 2. Axial symmetry
Authors: Pitts E.
Published: March 2006

In a drop of liquid which hangs below a horizontal support or a t the end of a tube, the forces due to surface tension, pressure and gravity are in equilibrium. Amongst the many possible equilibrium shapes of the drop, only those which are stable occur naturally. The calculus of variations has been used to determine theoretically the stable equilibria, by calculating the energy change when the liquid in equilibrium experiences axially symmetrical perturbations under physically realistic constraints. If the energy change can be made negative, the drop is unstable. With this criterion, stable equilibria have been identified through which the naturally growing drops evolve until they reach a maximum volume, when they become unstable. These results are illustrated by calculations relating to typical experimental conditions.
Near-resonant forcing in a shallow two-layer fluid: a model for the internal surge in Loch New?
Authors: Thorpe S. A.
Published: March 2006

The form taken by a finite amplitude internal seiche in a shallow two-layer fluid within a long narrow container is akin to a shock wave in a gas-filled tube; an undular bore or surge is present which reflects back and forth along the length of the container. The internal surge in Loch Ness is sometimes observed to retain its amplitude over several seiche periods, and a resonance with the wind appears possible. This idea is explored by developing a theoretical model and by making a laboratory experiment, but difficulties are encountered in estimating the size of the parameters which characterize the natural phenomenon.
On the nonlinear evolution of three-dimensional disturbances in plane Poiseuille flow
Authors: Davey A. , Hocking L. M. , Stewartson K.
Published: March 2006

The equations governing the nonlinear development of a centred three-dimensional disturbance to plane parallel flow at slightly supercritical Reynolds numbers are obtained, In contrast to the corresponding equation for two-dimensional disturbances, two slowly varying functions are needed to describe the development: the amplitude function and a function related to the secular pressure gradient produced by the disturbance. These two functions satisfy a pair of coupled partial differential equations. The equations derived in Hocking, Stewartson & Stuart (1972) are shown to be incorrect, Some of the properties of the governing equations are discussed briefly.
Conical flow near singular rays
Authors: Zahalak G. I. , Myers M. K.
Published: March 2006

The steady flow of an ideal gas past a conical body is investigated by the method of matched asymptotic expansions, with particular emphasis on the flow near the singular ray occurring in linearized theory. The first-order problem governing the flow in this region is formulated, leading to the equation of Kuo, and an approximate solution is obtained in the case of compressive flow behind the main front. This solution is compared with the results of previous investigations with a view to assessing the applicability of the Lighthill-Whitham theories.
Onset of cellular convection in a salinity gradient due to a lateral temperature gradient
Authors: Chen C. F.
Published: March 2006

We consider the two-dimensional problem of a linearly stratified salt solution contained between two infinite vertical plates. The fluid and the plates are initially at the same temperature. At t = 0, one of the plates is given a step increase in temperature, while the other is maintained at the initial temperature. A time-dependent basic flow is thus generated. The stability of such a time-dependent flow is analysed using an initial value problem approach to the linear stability equations. The method consists of initially distributing small random disturbances of given vertical wavelength throughout the fluid. The disturbances may be in the vorticity, temperature or salinity. The linearized field equations are integrated numerically. The growth or decay of the kinetic energy of the perturbation delineates unstable and stable states. Results have been obtained for a wide range of gap widths. The critical wavelength and the critical Rayleigh number compare favourably with those obtained previously in both physical and numerical experiments.
Two-dimensional effects in double-diffusive convection
Authors: Turner J. S. , Chen C. F.
Published: March 2006

The limitations of existing one-dimensional experiments on double-diffusive convection are discussed, and a variety of new two-dimensional phenomena are described. We have used the sugar-salt system and shadowgraph photography to make exploratory studies of motions which can arise in a fluid with two smooth, opposing, vertical concentration gradients, with and without horizontal gradients. Many different effects have been observed, the most important of which are the following, (a) In the ‘finger’ case, local disturbances can propagate rapidly as wave motions, which cause a simultaneous breakdown to convection over large horizontal distances. (b) Layers formed in the’ diffusive’ sense overturn locally to produce fingers, but propagate more slowly, as convective rather than wave motions, (c) A series of layers, separated by diffusive interfaces, can become unstable, in the sense that successive layers merge in time as their densities become equal, (d) The presence of horizontally separated sources of water of similar density but differentT,Scharacteristics can lead to the development of strong vertical gradients and extensive quasi-horizontal layering.

Most of our results are qualitative, but it is hoped that they will stimulate further quantitive work on each of the new processes described. It is already clear that much more needs to be done before the mechanism of formation of layers observed in the ocean can be regarded as properly understood.
Hydromechanics of low-Reynolds-number flow. Part 1. Rotation of axisymmetric prolate bodies
Authors: Chwang Allen T. , Wu T. Yao-Tsu
Published: March 2006

The present series of studies is concerned with low-Reynolds-number flow in general; the main objective is to develop an effective method of solution for arbitrary body shapes. In this first part, consideration is given to the viscous flow generated by pure rotation of an axisymmetric body having an arbitrary prolate form, the inertia forces being assumed to have a negligible effect on the flow. The method of solution explored here is based on a spatial distribution of singular torques, called rotlehs, by which the rotational motion of a given body can be represented.

Exact solutions are determined in closed form for a number of body shapes, including the dumbbell profile, elongated rods and some prolate forms. In the special case of prolate spheroids, the present exact solution agrees with that of Jeffery (1922), this being one of very few cases where previous exact solutions are available for comparison. The velocity field and the total torque are derived, and their salient features discussed for several representative and limiting cases. The moment coefficient CM = M/(8πμω0ab2) (M being the torque of an axisymmetric body of length 2a and maximum radius b rotating at angular velocity ω0 about its axis in a fluid of viscosity μ) of various body shapes so far investigated is found to lie between $\frac{2}{3}$ and 1, usually very near unity for not extremely slender bodies.

For slender bodies, an asymptotic relationship is found between the nose curvature and the rotlet strength near the end of its axial distribution. It is also found that the theory, when applied to slender bodies, remains valid at higher Reynolds numbers than was originally intended, so long as they are small compared with the (large) aspect ratio of the body, before the inertia effects become significant.
Turbulent/non-turbulent decisions in an intermittent flow
Authors: Hedley Thomas B. , Keffer James F.
Published: March 2006

The purpose of this study is to generalize the experimental method for deciding when a fluid motion can be considered turbulent. The rationale advanced for processing a transducer signal, which indicates the intermittent nature of a turbulent field, is given a probabilistic outlook. In addition an improved detector function is introduced which uses information from longitudinal and lateral fluctuation components.
Some turbulent/non-turbulent properties of the outer intermittent region of a boundary layer
Authors: Hedleyt Thomas B. , Keffer James F.
Published: March 2006

A detailed study of the intermittency in the outer region of a flat-plate turbulent boundary layer has been carried out using digital sampling and processing techniques. Conditional averages are used to generate mean and fluctuating components for the turbulent and non-turbulent zones of fluid. More particularly, point averages of these variables, taken with reference to the instantaneous position of the turbulent/non-turbulent interface, have been made to show the distribution of various quantities through the turbulent front. The results indicate that significant differences exist at leading and trailing edges of the turbulent bursts and a more complete picture of the motion of an average large eddy is deduced.
Use of a pseudo-turbulent signal to calibrate an intermittency measuring circuit
Authors: Antonia R. A. , Atkinson J. D.
Published: March 2006

Measurements of the intermittency factor γ and in particular the crossing frequencyfγof the turbulent/non-turbulent interface in the outer regions of various turbulent shear flows depend strongly on the settings of the intermittency meter used. Two methods of calibrating an intermittency meter of conventional design are described. In the first, turbulent and non-turbulent signals are simulated and switched at random times using an analog computer. Particular attention is given to the spectra of the switching and turbulent signals but the non-turbulent signal is assumed to have the same spectrum as the turbulent signal. In the second method, the same switching process is applied to two real signals, obtained in the fully turbulent and irretational flow regions associated with a turbulent jet with a co-flowing external air stream. A rather simple calibration procedure derived using the results of both methods is applied to the measurements of γ andfγin the same jet. It is suggested that the simulation process adopted here could be useful in inferring properties of intermittent turbulent flows.
Non-equilibrium dissociating nitrogen flow over a wedge
Authors: Kewley D. J. , Hornung H. G.
Published: March 2006

Experimental results for dissociating nitrogen flow over a wedge, obtained in a free-piston shock tunnel, are described. Interferograms of the flow show clearly the curvature of the shock wave and the rise in fringe shift after the shock associated with the dissociation. It is shown that the shock curvature a t the tip of the wedge can be used to calculate the initial dissociation rate and that it is a more sensitive indication of the rate than can be obtained from fringe shift measurements under the prevailing experimental conditions. Because the free-stream dissociation fraction can be adjusted in the shock tunnel, the dependence on atomic nitrogen concentration of the dissociation rate can be determined by the shock curvature method. A detailed calculation of the flow field by an inverse method, starting from the measured shock shape, shows good agreement with experiments.
Evolution of a moderately short turbulent boundary layer in a severe pressure gradient
Authors: Deissler R. G.
Published: March 2006

The early and intermediate development of a highly accelerated (or decelerated) turbulent boundary layer is analysed. For sufficiently large accelerations (or pressure gradients) and for total normal strains which are not excessive, the equation for the Reynolds shear stress simplifies to give a stress that remains approximately constant as it is convected along streamlines. The theoretical results for the evolution of the mean velocity in favourable and adverse pressure gradients agree well with experiment for the cases considered. A calculation which includes mass injection at the wall is also given.
On density effects and large structure in turbulent mixing layers
Authors: Brown Garry L. , Roshko Anatol
Published: March 2006

Plane turbulent mixing between two streams of different gases (especially nitrogen and helium) was studied in a novel apparatus. Spark shadow pictures showed that, for all ratios of densities in the two streams, the mixing layer is dominated by large coherent structures. High-speed movies showed that these convect at nearly constant speed, and increase their size and spacing discontinuously by amalgamation with neighbouring ones. The pictures and measurements of density fluctuations suggest that turbulent mixing and entrainment is a process of entanglement on the scale of the large structures; some statistical properties of the latter are used to obtain an estimate of entrainment rates. Large changes of the density ratio across the mixing layer were found to have a relatively small effect on the spreading angle; it is concluded that the strong effects, which are observed when one stream is supersonic, are due to compressibility effects, not density effects, as has been generally supposed.
Stokes flow about a sphere attached to a slender body
Authors: Mestre N. J. De , Katz D. F.
Published: March 2006

Stokes flow is analysed for a combination body, consisting of a sphere attached to a slender body, translating along its axis in an infinite and otherwise un-disturbed fluid. The cross-section of the after-body, or tail, is circular; the radius, while not necessarily constant, is small compared with the radius of the spherical head. The tail is represented by a distribution of Stokeslets of strength per unit length F(z), located and directed along its axis. The interactive effect of head-tail attachment is manifested by the presence of image singularities located within the sphere. The image system for a single tail Stokeslet must be such that the no-slip condition is satisfied on the surface of the sphere. It is shown that this system consists of a Stokeslet, a Stokes doublet (stresslet only) and a source doublet located a t the image point. The strength F(z) is obtained by applying the no-slip condition to the combination body. The solution follows the lines of traditional slender-body theory, an expansion being performed in ascending powers of the reciprocal of the logarithm of the aspect ratio. The integral force parameters and F(z) are obtained to second order. The interactive effect is assessed, and the results are discussed in the context of a sedimenting micro-organism, such as a spermatozoon. The drag on the combination body is shown to be less by around 10% than the sum of the drags on an isolated sphere and tail. This drag, for a sperm-shaped body, is divided approximately equally between head and tail.
On the rapid rotation of a massive sphere in a monatomic gas
Authors: Foster M. R.
Published: March 2006

We consider the rapid rotation, in the sense of large Reynolds number ε−1, of a gravitating solid sphere in a monatomic gas. The flow is characterized by a thin boundary layer on the sphere and a thin, swirling, buoyant, radial jet in the equatorial plane. When the Prandtl number σ is of order unity, the boundary layer and jet are to first order uncoupled from the outer flow. For sufficiently small Prandtl number (which may be interpreted as approximating an optically thick radiating gas), the outer flowisboundary-layer driven. The parameter boundary between these two dissimilar steady states is σ =O(ε⅙).
On the propulsion of micro-organisms near solid boundaries
Authors: Katz David F.
Published: March 2006

In this paper an infinite waving sheet is used to model a micro-organism swimming either parallel to a single plane wall, or along a channel formed by two such walls. The sheet surface, which undergoes small amplitude waves, can represent either a single flagellum or the envelope of the tips of numerous cilia. Two different solutions of the equations of motion are presented, depending upon whether or not the wave amplitude is small compared with the separation distances between the sheet and walls. It is found that the velocity of propulsion is bounded by the velocity of wave propagation by the sheet. Both the propulsive velocity and rate of working by the sheet increase as the separation distances decrease. However, it is demonstrated that suitable alterations in wave speed or wave shape can fix the rate of working while still causing increases in propulsive velocity. Reductions in propagated wave speed, i.e. beat frequency, are particularly effective in this regard.
The stability of a thermally radiating stratified shear layer, including self-absorption
Authors: Dudis Joseph J.
Published: March 2006

A linear stability analysis is applied to a stably stratified, thermally radiating shear layer. The grey Milne–Eddington approximation is employed as a radiation model. In contrast to a previously reported optically thin analysis, no inviscid instability exists, in the limit of vanishing horizontal wavenumber, for this selfabsorbing model. The inviscid neutral-stability boundary (Richardson number us. dimensionless wavenumber) for the Milne–Eddington approximation converges to the optically thick limit as the optical depth of the shear layer is increased. As the optical depth of the shear layer is decreased, the inviscid Milne–Eddington neutral-stability boundary approaches the optically thin limit, although not uniformly in the wavenumber. For fixed mean velocity gradient and fluid properties, the inviscid critical Richardson number approaches infinity as the optical depth of the shear layer approaches zero. Viscous effects neutralize this radiative destabilization, and the critical Richardson number eventually returns to zero as the optical depth continues to decrease. A shearlayer thickness exists for which the viscous critical Richardson number is a maximum. For shear depths greater than this thickness, self-absorption effects increase the stability; and for shear depths less than this thickness, viscous effects increase the stability. Results of the analysis are applied to the atmospheres of Venus and the earth. A critical Richardson number somewhat above the non-radiating value of 3 (although below the previously reported optically thin value) is found for the lower troposphere of the earth. No substantial effect is found for the earth's lower stratosphere or for the 100 km level above Venus.
On optimum design in fluid mechanics
Authors: Pironneau O.
Published: March 2006

In this paper, the change in energy dissipation due to a small hump on a body in a uniform steady flow is calculated. The result is used in conjunction with the variational methods of optimal control to obtain the optimality conditions for four minimum-drag problems of fluid mechanics. These conditions imply that the unit-area profile of smallest drag has a front end shaped like a wedge of angle 90°.
Low Reynolds number flow over a plane symmetric sudden expansion
Authors: Durst F. , Melling A. , Whitelaw J. H.
Published: March 2006

Flow visualization and laser-anemometry measurements are reported in the flow downstream of a plane 3: 1 symmetric expansion in a duct with an aspect ratio of 9·2: 1 downstream of the expansion. The flow was found to be markedly dependent on Reynolds number, and strongly three-dimensional even well away from the channel corners except at the lowest measurable velocities. The measurements at a Reynolds number of 56 indicated that the separation regions behind each step were of equal length. Symmetric velocity profiles existed from the expansion to a fully developed, parabolic profile far downstream, although there were substantial three-dimensional effects in the vicinity of the separation regions. The velocity profiles were in good agreement with those obtained by solving the two-dimensional momentum equation. At a Reynolds number of 114, the two separation regions were of different lengths, leading to asymmetric velocity profiles; three dimensional effects were much more pronounced. At a Reynolds number of 252, a third separation zone was found on one wall, downstream of the smaller of the two separation zones adjacent to the steps. As at the lower Reynolds numbers, the flow was very stable. At higher Reynolds numbers the flow became less stable and periodicity became increasingly important in the main stream; this was accompanied by a highly disturbed fluid motion in the separation zones, as the flow tended towards turbulence.
A numerical study of turbulence transitions in convective flow
Authors: Daly Bart J.
Published: March 2006

A turbulence representation, consisting of a generalized set of transport equations for the Reynolds stress tensor and the turbulence energy decay rate, is applied to the study of convective heat transport between parallel plates at moderate Rayleigh numbers, 5 × 103 ≤ Ra ≤ 6·4 × 105. A series of heat flux transitions, in good agreement with those observed experimentally, is detect, ed in this study and found to correlate with changes in the turbulence structure. In the order of increasing Rayleigh number these structural changes correspond to: the transition from laminar to turbulent flow, the transition from low to locally high intensity turbulence, the transition to uniformly high intensity turbulence, and the transition from a buoyancy dominated turbulence to a shear dominated turbulence. An analysis is made of the effect of each of these transitions on the mechanism for heat transfer between the plates.
An experimental study of the flow of thin liquid sheets in hot atmospheres
Authors: Clark C. J. , Dombrowski N.
Published: March 2006

A study has been made of the flow and disintegration of thin liquid sheets in combustion gases up to temperatures of 950°C. It is found that below 300°C sheet breakdown occurs through the growth of antisymmetric Kelvin–Helmholtz waves. Above this temperature high frequency symmetric waves and localized disturbances are superimposed on the sheet and disintegration then occurs by the combined action of aerodynamic waves and perforations, the contribution of the latter predominating with increasing temperature. It is demonstrated that the new wave system is electrohydrodynamic in origin, the electric field being generated by the charged species present in the gas. The drop size is found to be critically dependent upon the nature of the disintegration process.
The formation of atmospheric fronts downstream in a deformation field
Authors: Hoskins Brian J.
Published: March 2006

An analytical study is made of simple models of steady fronts in the atmosphere in which the temperature field is subjected to deformation as the fluid moves downstream in a large-scale horizontal flow. One fundamental approximation is made and then a Lagrangian method, in which fluid particles are identified by conservation of entropy and potential vorticity, and by Bernoulli's theorem, enables the steady problem to be solved. Solutions for models of surface fronts and upper tropospheric fronts are compared with those obtained from a model in which there is no variation along the front and the frontogenesis proceeds in time. If the thermal wind is comparable with the basic wind, and the potential vorticity is not negligible in some sense, the frontogenesis is increased where the thermal wind opposes the basic flow but, decreased where it reinforces the flow.
Turbulent shear flow mixing and rapid chemical reactions: an analogy
Authors: Lin Chung-Hua , O'Brien Edward E.
Published: March 2006

Two-species, irreversible, very rapid reactions, with mild heat release, in a turbulent shear flow are shown to be analogous to the transport of two non-reacting species by the same shear field. Expressions for the probability density functions of the reacting species, the product species and the reaction-generated thermal field are obtained in terms of the joint probability density functions of the two nonreacting species. As an example we have constructed, from recent measurements of temperature statistics at a cross-section in a heated jet, the meanand fluctuating concentration fields of the reacting species and the mean concentration of the product.
The radiation and scattering of surface waves by vertical barriers
Authors: Porter D.
Published: March 2006

A train of small-amplitude surface waves is incident normally on an arbitrary arrangement of thin barriers lying in a vertical plane in deep water. Each barrier is allowed to make small rolling or swaying oscillations of the same frequency as that of the incident wave. The boundary-value problem for the consequent fluid motion, assumed two-dimensional, is solved exactly using a technique which enables the amplitudes of the scattered waves far from the barriers to be readily determined. Reference is made to the associated wave radiation problem and to the calculation of forces and moments on the barriers.
The structure of jets of water and polymer solution in air
Authors: Hoyt J. W. , Taylor J. J. , Runge C. D.
Published: March 2006

Jets of water and of poly(ethylene oxide) solutions discharging in air were photographed using a novel image-motion compensating camera. Spray droplet formation is inhibited by low concentration polymer solutions. The effect of the polymer is to reduce, dampen, or eliminate small-scale surface disturbances in the jet, while not reducing but even amplifying larger scale motions. The initial laminar zone present in the jet efflux with water is eliminated with trace quantities of polymer. When substantial quantities of polymer are present (200 p.p.m.), the jet breakup is accompanied by filament formation linking all the drops together.
Numerical and asymptotic solutions for the supersonic flow near the trailing edge of a flat plate at incidence
Authors: Daniels P. G.
Published: March 2006

The equations which govern the flow at high Reynolds number in the vicinity of the trailing edge of a finite flat plate at incidence to a uniform supersonic stream are solved numerically using a finite-difference procedure. The critical order of magnitude of the angle of incidence α* for the occurrence of separation on one side of the plate is α* = O(R−¼) (Brown & Stewartson 1970), where R is a representative Reynolds number for the flow, and results are computed for three such values of α* which characterize the possible behaviour of the flow above the plate. The final set of computations leads to a numerical value for the trailing-edge stall angle α*s, the angle of incidence which just causes the flow to separate at the trailing edge of the plate. Analytic solutions are available in the form of asymptotic expansions near the trailing edge in terms of the scaled variable of order R−⅜. A multi-layer-type of expansion which occurs in the case α* = αs* is presented in detail for comparison with the computed solution.
On magnetohydrodynamic flows generated by an electric current discharge
Authors: Sozou C.
Published: March 2006

Magnetohydrodynamic flows generated in a semi-infinite viscous incompressible conducting fluid by the discharge of an electric current J0 from a point on the infinite plane bounding the fluid develop singularities when J0 exceeds a certain critical value. In practical applications sometimes currents much in excess of the critical value of J0 may be passed between electrodes before singularities appear in the velocity field. In this paper we consider the flow field associated with some current distributions and attempt to provide an explanation for the discrepancy between theory and experiment.
Perturbed turbulent flow, eddy viscosity and the generation of turbulent stresses
Authors: Davis Russ E.
Published: March 2006

The perturbation of a turbulent flow by an organized wavelike disturbance is examined using a dynamical, rather than phenomenological, approach. On the basis of the assumption that an infinitesimal perturbation results in a linear change in the statistics of the turbulence, and that the turbulence is either weak or that the turbulent perturbations are quasi-Gaussian, a method for predicting the perturbation turbulent Reynolds stresses is developed. The novel aspect of the analysis is that all averaging is delayed until the dynamical equations have been solved rather than attempting to find, apriori, equations for averaged quantities. When applied to long-wave perturbations the analysis indicates that the perturbation shear stress is of primary dynamical importance, and that this stress is determined by the principal component of mean shear through a relation which depends on the spectrum of the turbulent velocity component parallel to the gradient of the undisturbed mean velocity (the component perpendicular to the wall in a turbulent boundary layer). Theoretical arguments and observations are used to estimate the form of this spectrum in a constant stress shear layer. This results in a prediction of the constitutive law relating turbulent stress and the mean flow. The law is visco-elastic in nature, and is in agreement with the known constitutive relation for stress perturbations to a constant stress boundary layer; it resembles the eddy viscosity relation used successfully by others in describing perturbations in turbulent flows. The details of the constitutive law depend on how well the turbulence obeys Taylor's hypothesis that phase velocity equals mean flow velocity, and some insight into this question is given.
Finite-amplitude thermal convection in a spherical shell
Authors: Young Richard E.
Published: March 2006

The properties of finite-amplitude thermal convection for a Boussinesq fluid contained in a spherical shell are investigated. All nonlinear terms are retained in the equations, and both axisymmetric and non-axisymmetric solutions are studied. The velocity is expanded in terms of poloidal and toroidal vectors. Spherical surface harmonics resolve the horizontal structure of the flow, but finite differences are used in the vertical. With a few modifications, the transform method developed by Orszag (1970) is used to calculate the nonlinear terms, while Green's function techniques are applied to the poloidal equation and diffusion terms.

Axisymmetric solutions become unstable to non-axisymmetric perturbations at values of the Rayleigh number that depend on Prandtl number and shell thickness. However, even when stable, axisymmetric solutions are not a preferred solution to the full equations; steady non-axisymmetric solutions are obtained for the same parameter values. Initial conditions determine the characteristics of the finite-amplitude solutions, including, in the cases of non-axisymmetry, whether or not a steady state is achieved. Transitions in horizontal flow structure can occur, accompanied by a transition in functional dependence of heat flux on Rayleigh number. The dominant modes in the solutions are usually the modes most unstable to the onset of convection, but not always.
The inviscid nonlinear instability of parallel shear flows
Authors: Robinson J. L.
Published: March 2006

In this paper we assume the existence of a nonlinear boundary layer centred on the critical point, and explore its effect on the development of unstable parallel shear flows. A velocity matching condition derived in a qualitative discussion suggests a growth of harmonics which differs from that predicted by previous theories; however, the prediction is in excellent agreement with experimental data. A hyperbolic-tangent velocity profile, subjected to perturbations with wavenumbers and frequencies close to marginal values, is then chosen as a mathematical model of the nonlinear development, both temporal and spatial instability growth being considered.

A singularity in the analysis which has been treated in previous theories by the introduction of viscosity is dealt with in the present work by the introduction of a growth boundary layer. The asymptotics are non-uniform and the time-dependent solution does not resemble the steady viscous solutions, even as the growth rate tends to zero. The theory suggests that the instability will develop as a series of temporally growing spiral vortices, a description differing from that of a cat's-eye pattern predicted by existing theories, but in accord with experimental and field observations.
The stability of a trailing line vortex. Part 1. Inviscid theory
Authors: Lessen Martin , Singh Pawan Jit , Paillet Frederick
Published: March 2006

The inviscid stability of swirling flows with mean velocity profiles similar to that obtained by Batchelor (1964) for a trailing vortex from an aircraft is studied with respect to infinitesimal non-axisymmetric disturbances. The flow is characterized by a swirl parameterqinvolving the ratio of the magnitude of the maximum swirl velocity to that of the maximum axial velocity. It is found that, as the swirl is continuously increased from zero, the disturbances die out quickly for a small value ofqifn= 1 (nis the azimuthal wavenumber of the Fourier disturbance of type exp{i(αx+nϕ − αct)}); but for negative values ofn, the amplification rate increases and then decreases, falling to negative values atqslightly greater than 1·5 forn= −1. The maximum amplification rate increases for increasingly negativenup ton= −6 (the highest mode investigated), and corresponds toq≃ 0·85. The applicability of these results to attempts at destabilizing vortices is briefly discussed.
On the interaction of internal waves and surface gravity waves
Authors: Lewis John E. , Lake Bruce M. , Ko Denny R. S.
Published: March 2006

The perturbation of pre-existing surface gravity waves caused by the presence of an internal wave was studied both experimentally and analytically. An extensive series of experiments was performed, and quantitative results were obtained for the one-dimensional monochromatic interaction of internal waves and surface gravity waves. Internal wave-induced surface slope, amplitude and wavenumber modulations were measured for a wide range of interaction conditions. A complementary theoretical analysis, based on the conservation approach of Whitham (1962) and Longuet-Higgins & Stewart (1960,1961), was performed and a closed form solution obtained for the one-dimensional wave interaction. Both the theory and the experiment demonstrate that the effect increases with interaction distance. The maximum interaction effect is found to occur when the phase speed of the internal wave and the group velocity of the surface wave are matched. The phase of the internal wave at which maximum surface-wave modulation occurs is found to be a sensitive and continuous function of the relative wave speeds. The experimental data are in good agreement with the present theoretical analysis.
Unsteady viscous flow in a pipe of slowly varying cross-section
Authors: Hall P.
Published: March 2006

The steady streaming generated in a pipe of slowly varying cross-section when a purely oscillatory pressure difference is maintained between its ends is considered. It is assumed that the perturbation of the pipe wall in the r, θ plane is small compared with the characteristic thickness of the Stokes layer associated with the oscillatory motion of the fluid. The first-order steady streaming is evaluated for the cases when this characteristic thickness is large and small compared with a typical radius of the pipe. In both these limits it is found that the geometry of the pipe is crucial in determining the nature of the induced steady streaming. If the ends of the pipe have the same mean radius it is found that the steady streaming consists of regions of recirculation between the nodes of the pipe. Otherwise the steady streaming is of a larger order of magnitude and has a component which represents a net flow towards the wider end of the pipe.
Turbulent vortex rings
Authors: Maxworthy T.
Published: March 2006

We consider the motion of the mass of fluid ejected through a sharp-edged orifice by the motion of a piston. The vorticity formed by viscous forces within the separated flow at the sharp edge rolls up to form a concentrated vortex which, after a development period, consists of a core of very fine scale turbulence surrounded by a co-moving bubble of much larger scale turbulence. This bubble entrains outer fluid, mixes with it, and deposits the majority into a wake together with some small fraction of the total vorticity of the ring. Enough fluid is retained to account for the slow growth of the whole fluid mass. A theory which takes account of both the growth process and the loss of vorticity is proposed. By comparison with experimental measurements we have determined that the entrainment coefficient for turbulent vortex rings has a value equal to 0.011 ± 0.001, while their effective drag coefficient is 0.09 ± 0.01. These results seem to be independent of Reynolds number to within experimental accuracy.
Kelvin wave propagation along an irregular coastline
Authors: Mysak L. A. , Tang C. L.
Published: March 2006

We discuss the theory of Kelvin wave propagation along an infinitely long coast-line which is straight except for small deviations which are treated as a stationary random function of distance along the coast. An operator expansion technique is used to derive the dispersion relation for the coherent Kelvin wave field. For the subinertial case σ = ω/f < 1 (ω = wave frequency, f = Coriolis parameter), it is shown that the wave speed is always decreased by the coastal irregularities. Moreover, while the coherent wave amplitude is unaltered, the energy flux along the coast is decreased by the irregularities. For the case σ > 1, however, we show that in the direction of propagation the wave is attenuated (with the energy being scattered into the random Poincaré and Kelvin wave modes) and that the wave speed is again decreased. Applications of the theory are made to the California coast and North Siberian coast to determine the decrease in phase velocity due to small coastal irregularities. For the California coast the percentage decrease is only about 1%. For the Siberian coast, however, the percentage decrease is about 25% for the K1 tide, and a minimum of 25% for the M2 tide. The attenuation of a Kelvin wave, however, appears to be due to very large scale irregularities. An estimate of the actual attenuation rate is not possible, though, because of the relatively short extent of coastal contours available for spectral analysis.

Although attention in this paper has been focused on Kelvin wave propagation, the method developed could readily be used to study the behaviour of other classes of waves trapped against a randomly perturbed boundary.