bluuebunny/crossref_metadata_2025 huggingface dataset:
On the criteria for reverse transition in a two-dimensional boundary layer flow
Authors: Narayanan M. A. Badri , Ramjee V.
Published: March 2006

Experiments on reverse transition were conducted in two-dimensional accelerated incompressible turbulent boundary layers. Mean velocity profiles, longitudinal velocity fluctuations$\tilde{u}^{\prime}(=(\overline{u^{\prime 2}})^{\frac{1}{2}})$and the wall-shearing stress (TW) were measured. The mean velocity profiles show that the wall region adjusts itself to laminar conditions earlier than the outer region. During the reverse transition process, increases in the shape parameter (H) are accompanied by a decrease in the skin friction coefficient (Cf). Profiles of turbulent intensity (u’2) exhibit near similarity in the turbulence decay region. The breakdown of the law of the wall is characterized by the parameter\[ \Delta_p (=\nu[dP/dx]/\rho U^{*3}) = - 0.02, \]whereU* is the friction velocity. Downstream of this region the decay of$\tilde{u}^{\prime}$fluctuations occurred when the momentum thickness Reynolds number (R) decreased roughly below 400.
Velocity gradients at the wall for flow around a cylinder at Reynolds numbers from 5 × 103 to 105
Authors: Son Jaime S. , Hanratty Thomas J.
Published: March 2006

Electrochemical techniques have been used to measure the velocity gradients at the surface of a cylinder for Reynolds numbers from 5 × 103 to 105. This is a companion study to that already reported by Dimopoulos & Hanratty (1968) for a Reynolds number range of 60–360. The use of a specially designed sandwich electrode enabled the direction of the velocity gradient as well as its magnitude to be measured. Of particular interest is the region of definite length after separation where the velocity gradient is negative, followed by an ill-defined region where the flow moves in the positive direction. Still farther downstream the direction of flow changes with time in an irregular fashion. The measured velocity gradients prior to separation are described satisfactorily by boundary-layer theory. The presence of a splitter plate in the rear of the cylinder eliminates periodic fluctuations in the wake and has a significant effect on the boundary layer prior to separation.
Numerical solution for the flow around a cylinder at Reynolds numbers of 40, 200 and 500
Authors: Son Jaime S. , Hanratty Thomas J.
Published: March 2006

Finite difference solutions for the time dependent equations of motion have been carried out in order to extend the range of available data on steady flow around a cylinder to larger Reynolds numbers. At the termination of the calculations forR= 40 and 200, the separation angle, the drag coefficient and the pressure and vorticity distributions around the surface of the cylinder were very close to their steady-state values. ForR= 500 the separation angle and drag coefficient were very close to their steady-state values but the pressure distribution and vorticity distribution at the rear of the cylinder were still changing slightly. The results atR= 500 were found to be quite different from those atR= 200 so it is not clear how closely we approximated the steady solution forR→ ∞. The forces on the cylinder due to viscous drag and due to pressure drag are found to be smaller for steady flow than for laboratory experiments where the wake is unsteady.
The diffraction accompanying the regular reflexion of a plane obliquely impinging shock wave from the walls of an obtuse wedge
Authors: Ter-Minassiants S. M.
Published: March 2006

The diffraction problem of a plane shock wave at the apex of an obtuse wedge treated by Lighthill (1950) is extended by assuming that the shock wave strikes the walls of the obtuse wedge at some finite oblique angle of incidence (not exceeding the critical angle). Transformations similar to that performed in the above-mentioned paper lead to a non-symmetrical boundary-value problem for an analytic function of a complex variable having a non-homogeneity in the form of a delta-function. It was found possible to extend, for the case considered, the method developed by Lighthill and construct the solution in almost as simple a form as given in the above-mentioned paper. The case of three-dimensional stationary flow is considered when the line of reflexion makes a finite angle with the edge of the wedge.
The three-dimensional detonation polar and an application to spinning detonation
Authors: Macpherson A. K.
Published: March 2006

Expressions are derived for a three-dimensional polar in the pressure ratio, deflexion angle space to represent conditions downstream of a detonation wave with given upstream conditions. An analysis of reflected waves is undertaken and the representation of three wave confluences in a three-dimensional hodograph space studied. These techniques are applied to experimental results available for spin detonation in gaseous mixtures of acetylene-oxygen-argon and carbon monoxide-oxygen. Assumptions made in earlier papers concerning local extinction of combustion at the confluence point are not necessary in this picture.
Lee waves in a stratified flow Part 3. Semi-elliptical obstacle
Authors: Huppert Herbert E. , Miles John W.
Published: March 2006

The stratified shear flow over a two-dimensional obstacle of semi-elliptical crosssection is considered. The shear flow is assumed to be inviscid with constant upstream values of the density gradient and dynamic pressure (Long's model). Two complete sets of lee-wave functions, each of which satisfies the condition of no upstream reflexion, are determined in elliptic co-ordinates for ε ≤ 1 and ε ≥ 1, where ε is the ratio of height to half-width of the obstacle. These functions are used to determine the lee-wave field produced by, and the consequent drag on, a semi-elliptical obstacle as functions of ε and the reduced frequency (reciprocal Froude number) within the range of stable flow. The reduced frequency at which static instability first occurs is calculated as a function of ε.
Lee waves in a stratified flow. Part 4. Perturbation approximations
Authors: Miles John W. , Huppert Herbert E.
Published: March 2006

A two-dimensional stratified flow over an obstacle in a half space is considered on the assumptions that the upstream dynamic pressure and density gradient are constant (Long's model). A general solution of the resulting boundary-value problem is established in terms of an assumed distribution of dipole sources. Asymptotic solutions for prescribed bodies are established for limiting values of the slenderness ratio ε (height/breadth) of the obstacle and the reduced frequency k (inverse Froude number based on the obstacle breadth) as follows: (i) ε → 0 withkfixed; (ii)k→ 0 with ε fixed; (iii)k→ ∞ withkεfixed. The approximation (i) is deveoped to both first (linearized theory) and second order in ε in terms of Fourier integrals. The approximation (ii), which constitutes a modification of Rayleigh-scattering theory, is obtained by the method of matched asymptotic expansions and depends essentially on thedipole form(which is proportional to the sum of the displaced and virtual masses) of the obstacle with respect to a uniform flow. A simple approximation to this dipole form is proposed and validated by a series of examples in an appendix. The approximation (iii) is obtained through the reduction of the original integral equation to a singular integral equation of Hilbert's type that is solved by the techniques of function theory. A composite approximation to the lee-wave field that is valid in each of the limits (i)-(iii) also is obtained. The approximation (iii) yields an estimate of the maximum value ofkεfor which completely stable lee-wave formation behind a slender obstacle is possible. The differential and total scattering cross-sections and the wave drag on the obstacle are related to the power spectrum of the dipole density. It is shown that the drag is invariant under a reversal of the flow in the limits (i) and (ii), but only for a symmetric obstacle in the limit (iii). The results are applied to a semi-ellipse, an asymmetric generalization thereof, the Witch of Agnesi (Queney's mountain), and a rectangle. The approximate results for the semi-ellipse are compared with the more accurate results obtain by Huppert & Miles (1969). It appears from this comparison that the approximate solutions should be adequate for any slender obstacle within the range ofkεfor which completely stable lee-wave formation is possible. The extension to obstacles in a channel of finite height is considered in an appendix.
On the wavelength of convective motions
Authors: Koschmieder E. L.
Published: March 2006

It has been found experimentally that under a lid of excellent heat conductivity the wavelength of convective motions on a uniformly heated plane increases with increasing supercritical Rayleigh numbers. Under an insulating lid, the wavelength at the critical Rayleigh number is larger than under a well conducting lid. When heating from below is applied rapidly the wavelength is less than in the corresponding stationary case.
Transition from laminar convection to thermal turbulence in a rotating fluid layer
Authors: Küppers G. , Lortz D.
Published: March 2006

The convective flow in an infinite horizontal fluid layer rotating rigidly about a normal axis is investigated for the special case of infinite Prandtl number and free boundary conditions. For slightly supercritical Rayleigh numbers the solutions of the non-linear steady-state equations are derived approximately by an amplitude expansion. A stability calculation shows that no stable steady-state convective flow exists if the Taylor number exceeds the critical value 2285.
Experiments on the generation of small water waves by wind
Authors: Plate E. J. , Chang P. C. , Hidy G. M.
Published: March 2006

The generation and growth of small water waves by a turbulent wind has been investigated in a laboratory channel. The evolution of these oscillations with fetch was traced from their inception with amplitudes in the micron range under conditions of steady air flow. The experiments revealed that the waves are generated at all air velocities in small bursts consisting of groups of waves of nearly constant frequency. After travelling for some distance downstream, these wavelets attain sufficient amplitude to become visible. For this condition, a wind speed critical to raise waves is well defined. After the first wavelets appear, two new stages of growth are identified at longer fetches if the air speed remains unchanged. In the first of these, the wave component associated with the spectral peak grows faster with fetch than any other part of the wave spectrum of the initial waves until its amplitude attains an upper limit consistent with Phillips's equilibrium range, which appears to be universal for wind waves on any body of water. If the air flow is not changed, then the frequency of this dominant wave remains constant with fetch up to equilibrium. This frequency tends to decrease, however, with increasing wind shear on the water. In the second stage of growth, only the energy of wave components with spectral densities lower than the equilibrium limit tend to increase with fetch so that the wave spectrum is maintained near equilibrium in the high-frequency range of the spectrum.

The origin of the first waves and the rate of their subsequent growth was examined in the light of possible generating mechanisms. There was no indication that they were produced by direct interaction of the water surface with the air turbulence. Neither could any significant feedback of the waves into the turbulence structure be detected. The growth of the waves was found to be in better agreement with theoretical predictions. Under the shearing action of the wind, the first waves were found to grow exponentially. The growth rates agreed with the estimates from the viscous shearing mechanism of Miles (1962a) to a fractional error of 61% or less. A slight improvement was obtained with the viscous theory of Drake (1967) in which Miles’ model is extended to include the effect of the drift current induced by the wind in the water. Since the magnitude of the water currents observed in the tunnel is very small, this improvement is not significant.
Response of gravity water waves to wind excitation
Authors: Bole James B. , Hsu En Yun
Published: March 2006

The primary objective of this work was to study the response of gravity water waves to wind excitation and, in particular, the applicability of the Miles inviscid shear-flow theory of gravity wave growth, by conducting experiments in a laboratory wind-wave channel under conditions approximating the assumptions of the mathematical model. Mechanically generated wave profiles subjected to wind action were measured with capacitance wire sensors and wave energy was calculated at seven stations spaced at 10ft. intervals along the channel test section. Waves varied in length from about 2·5 to 6·5 ft. and maximum wind speeds ranged from 12 to 44 ft./sec. Vertical mean air velocity profiles were taken at six stations in the channel, fitted near the air-water interface with semi-logarithmic profiles, and used in a stepwise computation of theoretical wave growth. The results show that the measured wave energy growth is exponential but considerably larger than the growth predictions of Miles's theory. Derived experimental values of the phase-shifted pressure component β are greater than theoretical values by a factor varying from 1 to 10, with a mean of about 3. Wind mean velocity profiles appear to be closely logarithmic near the air-water interface. Wind-generated ripples superposed on mechanically generated waves created a rough water surface with standard deviation larger, in all cases, than the respective critical-layer thickness.
Pathological oscillations of a rotating fluid
Authors: Stewartson K. , Rickard J. A.
Published: March 2006

A theoretical study is made of the free periods of oscillation of an incompressible inviscid fluid, bounded by two rigid concentric spheres of radii a, b (a > b), and rotating with angular velocity Ω about a common diameter. An attempt is made to use the Longuet-Higgins solution of the Laplace tidal equation as the first term of an expansion in powers of the parameter ε = (a − b)/(a + b), of the solution to the full equations governing oscillations in a spherical shell. This leads to a singularity in the second-order terms at the two critical circles where the characteristic cones of the governing equation touch the shell boundaries.

A boundary-layer type of argument is used to examine the apparent non-uniformity in the neighbourhood of these critical circles, and it is found that, in order to remove the singularity in the pressure, an integrable singularity in the velocity components must be introduced on the characteristic cone which touches the inner spherical boundary. Further integrable singularities are introduced by repeated reflexion at the shell boundaries, and so, even outside the critical region the velocity terms contain what may reasonably be described as a pathological term, generally of order ε½ compared to that found by Longuet-Higgins, periodic with wavelength O(εa) in the radial and latitudinal directions.

Some consequences of this result are discussed.
Instabilities of a buoyancy-driven system
Authors: Gill A. E. , Davey A.
Published: March 2006

A buoyancy-driven system can be unstable due to two different mechanisms—one mechanical and the other involving buoyancy forces. The mechanical instability is of the type normally studied in connexion with the Orr-Sommerfeld equation. The buoyancy-driven instability is rather different and is related to the ‘Coriolis’-driven instability of rotating fluids. In this paper, the stability of a buoyancy-driven system, recently called a ‘buoyancy layer’, is examined for the whole range of Prandtl numbers, s. The buoyancy-driven instability becomes increasingly important as the Prandtl number is increased and so particular interest is attached to the limit in which the Prandtl number tends to infinity. In this limit, the system is neutrally stable to first order, but second-order effects render the flow unstable at a Reynolds number of order σ-½. Consequences of the results for the stability of convection in a vertical slot are examined.
An exact solution for a diffusive flow in a porous medium
Authors: List E. J.
Published: March 2006

It is shown that Yih's exact solution for the non-diffusive flow of a non-homogeneous fluid into a sink in a confined porous medium is equivalent to a class of diffusive flows with isopycnic lateral boundaries.
Cavities formed on liquid surfaces by impinging gaseous jets
Authors: Cheslak Frank R. , Nicholls J. Arthur , Sichel Martin
Published: March 2006

Experimental tests of an axisymmetric jet of air impinging on both water and wet cement were performed and analyzed. Since the cavities formed on the water were unsteady and irregular, cavities were formed on wet fast-setting cement and allowed to set with the jet impinging. In this way, detailed measurements of the solidified cavity shape were made and shown to agree well with theory. This correlation of the data with the theory indicates that little gas was entrained in the liquid and that the influence of liquid viscosity and surface tension was small for the experimental conditions tested. A simplified analysis is also presented for an incompressible axisymmetric gas jet impinging normally on a liquid surface. The analysis was effected by combining the following physical conditions and assumptions: (i) the stagnation pressure corresponding to the centreline conditions of the jet at the bottom of the cavity is equal to the hydrostatic pressure, wherein an empirical turbulent jet decay law is used to predict the variation of stagnation pressure with distance from the nozzle; (ii) the force on the liquid is equal to the total change in normal momentum, which is equal to the weight of the displaced liquid; (iii) the shape of the cavity is a paraboloid.
Heat transfer and transition to turbulence in the shock-induced boundary layer on a semi-infinite flat plate
Authors: Davies W. R. , Bernstein L.
Published: March 2006

The results of experiments designed to investigate the shock-induced boundary layer on a semi-infinite flat plate are described.

Those for the laminar boundary layer are shown to be in agreement with a theory due to Lam & Crocco (1958) which describes two distinct domains, one near the shock where the flow is quasi-steady in a shock-fixed co-ordinate system and an unsteady region in which the flow characteristics approach the familiar steady state asymptotically. Experimental results are also presented for the non-laminar boundary layer. In particular the transition to turbulence in this unsteady boundary layer is discussed in some detail.

‘Establishment times’ for steady boundary layers are given for both laminar and turbulent flows, and their relevance to the testing times available in shock tubes is discussed. The measured heat transfer rates are compared with existing theories.
The analogy between streamline curvature and buoyancy in turbulent shear flow
Authors: Bradshaw P.
Published: March 2006

A formal algebraic analogy is drawn between meteorological parameters, such as the Richardson number, and the parameters describing the effect of rotation or streamline curvature on a turbulent flow. The analogy between thephenomenais a good first approximation. Semi-quantitative use of the analogy to apply meteorological data to curved shear layers shows that the effects of curvature on the apparent mixing length are appreciable if the shear-layer thickness exceeds roughly 1/300 of the radius of curvature; larger effects may occur in compressible flow. Application of the Monin-Oboukhov formula considerably improves the agreement between prediction and experiment in boundary layers on curved surfaces.
Some aspects of time-dependent motion of a stratified rotating fluid
Authors: Walin GÖUsta
Published: March 2006

Time-dependent motion of a rotating stratified fluid is analyzed within the quasigeostrophic approximation. A few examples of mechanically driven flow are analyzed. It is found that the motion is characterized by the ratio B of the stability frequency and the Coriolis parameter. Thus the ratio of the horizontal and vertical characteristic scale is in general O(B). In particular the decay process caused by a horizontal boundary will penetrate a distance B−1L into the fluid, L denoting the horizontal scale of the motion.
On the high Reynolds number flow over a wavy boundary
Authors: Davis Russ E.
Published: March 2006

The nature of a shear flow over a wavy boundary of small amplitude is investigated. It is found that if the viscosity is small, the nature of the flow is highly dependent on the wave amplitude. If the wave amplitude is truly infinitesimal, the flow is described by the Orr-Sommerfeld equation and in the neighbourhood of the critical layer viscous stresses are important even in the limit of vanishing viscosity. However, if the wave is sufficiently large, viscous stresses may be neglected even in the critical layer. An approximate solution of the inviscid equations of motion is obtained to describe the flow over a small but finite wave in the limit of infinite Reynolds number.
The onset of cellular convection in a fluid layer with time-dependent density gradients
Authors: Blair L. M. , Quinn J. A.
Published: March 2006

Onset times for convection induced by buoyancy forces have been measured. Results on three aqueous systems are summarized in terms of a critical value for a time-dependent Rayleigh number. Because of the presence of minute traces of unavoidable surface-active contaminants, a ‘free’ water surface behaved as if it were inflexible and laterally rigid so far as determining first convective motion was concerned. The form of the onset motion was observed with schlieren photography for both top and side view. The pattern at onset was frequently in the form of plunging rings. Surface effects were demonstrated with an organic liquid layer in which onset times were measured for convection driven by surface tension gradients as well as by buoyancy forces. The data are compared with some recent predictions of linear stability analyses.
Mixing shocks in two-phase flow
Authors: Witte Jan H.
Published: March 2006

In gas-liquid flows a certain sudden change of the flow structure may occur, which can be described as a transition from ‘jet flow’ to ‘froth flow’ accompanied by energy dissipation and pressure build-up. Upstream of this phenomenon the gas is the continuous phase; downstream the liquid is the continuous phase. The phenomenon, which has been called ‘mixing shock’, shows some similarity and also some differences with the plane shock wave in gasdynamics. In the first part of this paper the mixing shock is treated as a one-dimensional macroscopic process. With the aid of the laws of conservation of mass, momentum and energy, expressions are obtained for the pressure and entropy change across the mixing process. In addition the stability of the mixing shock in a cylindrical flow channel is treated. Next, a theory that explains the gas entrainment mechanism in the mixing shock is proposed. As an experimental tool a water-air ejector with the water as a driving medium was used. The experiments confirm the macroscopic and the microscopic theory. In the last section of this paper theoretical and experimental evidence is combined to construct a model of the processes that play a role in the shock.
The stability of plane Couette flow with viscosity stratification
Authors: Craik Alex D. D.
Published: March 2006

The stability of plane Couette flow is examined for liquids in which the viscosity varies with depth. Under suitable conditions, the flow may be stable or unstable at small Reynolds numbers for disturbances with wavelengths long compared with the liquid depth.

A mechanism which may be stabilizing or destabilizing is found to derive from the role of diffusion in the neighbourhood of a ‘critical layer’, where the liquid velocity equals the phase velocity of a wave-like disturbance. This mechanism, which requires a viscosity gradient, is quite distinct from that found by Yih (1967) for the case of a viscosity discontinuity. An example is considered, for which these two mechanisms may be of comparable importance.
On some problems of similarity flow of fluid with a free surface
Authors: Dobrovol'skaya Z. N.
Published: March 2006

The paper presents the method of solving a class of two-dimensional problems of the similarity flow of an incompressible fluid with a free surface. The fluid is assumed to be non-viscous and weightless. We consider two-dimensional irrotational similarity flows with dimensionless hydrodynamic characteristics depending only on the ratiosx/v0t, y/v0t, wherex, yare Cartesian co-ordinates,tis time andv0is a constant of the velocity dimension.

The proposed method is based upon using the function introduced by Wagner (1932) and can be applied to the problems where the flow region is bounded by free surfaces and uniformly moving (or fixed) rectilinear impermeable boundaries. Introduction of Wagner's function makes it possible to reduce each of the problems under consideration to a non-linear singular integral equation for the real function.

The method is illustrated by solving the classical problem of the uniform symmetrical entry of a wedge into a half-plane of a fluid.
Experiments on the instability of stratified shear flows: immiscible fluids
Authors: Thorpe S. A.
Published: March 2006

When a long rectangular tube containing two immiscible fluids is slightly tilted away from the horizontal, a uniformly accelerating flow is produced with shear at the interface. The presence of shear leads to instability, which is characterized by the spontaneous and rapid growth of almost stationary waves if the fluid depths are equal and the density difference small. The conditions for the onset of Kelvin-Helmholtz instability, taking account of the accelerating flow and the presence of a velocity transition region at the interface, are investigated theoretically and comparison made with observations. The time at which instability occurs is quite well predicted by this theory, but the wavelength of the unstable waves is rather greater than predicted in the accelerating flow. The difference between the predictions and observations may be the result of finite amplitude effects or of the development of Tollmien-Schlichting instability before Kelvin-Helmholtz.
Surface tension driven oscillatory instability in a rotating fluid layer
Authors: McConaghy G. A. , Finlayson B. A.
Published: March 2006

Oscillatory convective instability is shown to occur in a rotating fluid layer when convection is caused by surface-tension gradients at a free surface. The asymptotic equations, valid when the Taylor number approaches infinity, are solved analytically, and the critical Marangoni number is evaluated numerically. Fluids with Prandtl numbers above 0·201 will exhibit only stationary instability. Fluids with smaller Prandtl numbers will exhibit oscillatory instability with the critical Marangoni number varying as M0T½ where M0 depends on the Prandtl number and T is the Taylor number.
On the two-dimensional viscous counterpart of the one-dimensional sonic throat
Authors: Weinbaum Sheldon , Garvine Richard W.
Published: March 2006

An analysis of the full, compressible, non-adiabatic boundary-layer equations is presented to describe the so-called ‘throat’ formed when a two-dimensional viscous layer, interacting with a supersonic inviscid outer stream, is accelerated or decelerated through sonic velocity defined in some mean sense. The basic analysis differs from previous momentum integral theories in that the dynamics of the viscous layer is described by the exact local expressions for the streamwise gradients of the flow variables that obtain from the boundary-layer conservation equations, rather than on streamwise derivatives of integral properties of these equations. The theory is then used to develop an extensive analogy with the classical analysis of the throat in the inviscid quasi one-dimensional streamtube. The theory shows that a single integral constraint exists at the throat, which relates the velocity and temperature profiles in the viscous layer to the motion of the inviscid outer flow. One consequence of this constraint is that, for a one-parameter family of profile shapes, the solution can be started at the throat station by specifying only a single variable, the free stream Reynolds number based on the physical thickness of the viscous layer at the throat station. For the hypersonic near wake, this simplification permits one to obtain an approximate solution for the downstream flow without first solving the detailed motion in the base recirculation region. The paper ends with a discussion of the numerical results for the Stewartson family of wake-like profiles.
On two-dimensional laminar wakes and jets
Authors: Chen Karl K.
Published: March 2006

The flow fields in two-dimensional, isoenergetic, viscous free mixing with constant β and with initial velocity profiles deviating slightly from those given by wakelike solutions of the Falkner-Skan equation for that β are considered. The similar solutions of the Falkner-Skan equation are investigated in more detail than in the past, e.g. we show that as β → −1 the flows approach the pure jet with the surrounding fluid at rest, and that there are new branch solutions for β < −1. We have investigated the spatial stability of these flows; it is found that for β > − 0·5 the only spatially stable solutions are the trivial ones f′(η) ≡ 1, but for −1 < β < − 0·5 there are non-trivial, jet-like solutions which are spatially stable. As to the new branch solutions for β < − 1, all are spatially unstable.
On hydromagnetic waves in a stratified rotating incompressible fluid
Authors: Hide R.
Published: March 2006

The dispersion relationship for plane hydromagnetic waves in a stratified rotating fluid (α) indicates that the well-known analogy between rotating fluids and stratified fluids in regard to their hydrodynamic behaviour does not extend to magnetohydrodynamic behaviour, and (b) lends credence to a certain conjecture made in a previous paper, namely that effects due to density stratification can be neglected when considering the dispersion relationship for free hydromagnetic oscillations of the Earth's core if the Brunt—Väisälä frequency is much less than twice the angular speed of the Earth's rotation.
On the gas dynamics of an intense explosion with an expanding contact surface
Authors: Cheng H. K. , Kirsch J. W.
Published: March 2006

The structure of a strong blast wave under the influence of an expanding inner contact surface is studied asymptotically in the Newtonian limit: $\epsilon \equiv (\gamma - 1)/2\gamma \ll 1, \epsilon \dot{y}^2_s \gg a^2_{\infty}$. The theory treats the interaction of a shock layer and an inner flow region (the entropy wake) and reduces the problem to an ordinary differential equation for the shock radius. The pressure–volume relation of Cheng et al. (1961) is recovered and extended to a higher order of ε.

It is shown that, depending on the rate of growth of the contact surface, the shock layer may ‘reattach’ to the surface at large time. In a number of cases, the reattachment is approached in an oscillatory manner which leads to a period of non-uniformity. The associated problem of multiple time scales (treated in sequels to this paper) is identified.
Reflexion of Kelvin waves at the open end of a rotating semi-infinite channel
Authors: Packham B. A.
Published: March 2006

The problem of the reflexion of tides in an enclosed sea such as the North Sea at a point at which it either enters the ocean or its width suddenly increases is considered by investigating the reflexion of a Kelvin wave at the open end of a rotating uniform semi-infinite channel.

It is shown that for a given channel, if the wave period is less than a pendulum day, then, according to the linearized theory of long waves in a rotating system, the reflexion coefficient increases with the angular velocity of rotation. It is also shown that there is a resonance effect for certain critical channel widths, namely, those at which extra modes within the channel become possible.
Non-linear wave propagation in a relaxing gas
Authors: Ockendon H. , Spence D. A.
Published: March 2006

We consider the propagation of waves of small finite amplitude ε in a gas whose internal energy is characterized by two temperaturesT(translational) andTi(internal) in the forme=CvfT+CvfTi, andTiis governed by a rate equationdTi/dt= (T−Ti)/τ. By means of approximations appropriate for a wave advancing into an undisturbed regionx> 0, we show that to order εδ, the equation satisfied by velocity takes the non-linear form\[ \bigg(\tau\frac{\partial}{\partial t}+1\bigg)\bigg\{\frac{\partial u}{\partial t}+\bigg(a_1+\frac{\gamma + 1}{2}u\bigg)\frac{\partial u}{\partial x}-{\textstyle\frac{1}{2}}\lambda\frac{\partial^2u}{\partial x^2}\bigg\}=(a_1-a_0)\frac{\partial u}{\partial x}, \]wherea1,a0are the frozen and equilibrium speeds of sound in the undisturbed region, δ = ½(1 − (a20/a21)), and λ is the diffusivity of sound due to viscosity and heat conduction (λ may be neglected except when discussing the fine structure of a discontinuity). Some numerical solutions of this model equation are given.

When ε is small compared with δ, it is also possible to construct a solution for the flow produced by a piston moving with a constant velocity by means of a sequence of matched asymptotic expansions. The limit reached for large times for either compressive or expansive pistons is the expected non-linear solution of the exact equations. For a certain range of advancing piston speeds, this is a fully dispersed wave with velocityUin the rangea0<Ua1the solution is discontinuous, and indeterminate in the absence of viscosity; a singular perturbation technique based on λ is then used to determine the structure of the wave head.
Electron beam density measurements in shock waves in argon
Authors: Schmidt B.
Published: March 2006

An electron beam technique was used to measure density profiles of strong shock waves in argon with high accuracy. The experimental results are compared with the results of theoretical models. Of the models that are available in enough detail for comparison, the best agreement with experiment is shown by the direct simulation Monte-Carlo method (Bird 1968), assuming an inverse 12th power molecular interaction force law. It is shown that the density maximum slope thickness is not sufficient for a detailed description of the shock wave structure.
Pneumatic transport
Authors: Owen P. R.
Published: March 2006

Certain aspects of the transport of solid particles by a turbulent airstream are discussed, namely: the conveyance of particles in a horizontal pipe, including those carrying an appreciable electrostatic charge; the mechanism of deposition onto a solid wall; and the behaviour of fine particles in a shear flow, such as that in a round jet.

Rough estimates of the effect of the particles on the gaseous turbulence are made, and a primitive physical explanation is offered of the observed velocitylag and pressure drop associated with the transport of particles in a horizontal pipe, under conditions where the influence of the particles’ weight is significant.

Attention is drawn to the difficult problem of dynamically scaling a two-phase flow, and to the different types of interaction between the phases which can occur in a pipe according to its size, the gas velocity through it, and the physical characteristics of the particles.

The paper is an annotated version of a survey presented to the I.U.T.A.M. Symposium on ‘Flow of fluid-solid mixtures’ held in Cambridge during March 1969.
A theory of the propagation of internal gravity waves of finite amplitude
Authors: Rarity B. S. H.
Published: March 2006

A non-linear theory of internal gravity waves of finite amplitude is developed in terms of conservation equations averaged with respect to the phase. The theory overcomes the failure of linear ray theory in regions in which waves are trapped and establishes the conditions under which finite amplitude waves may propagate. It gives a geometrical representation of the degeneration of waves into quasi-turbulence and predicts the dependence of the energy density on its parameters.
On the spin-up of an electrically conducting fluid Part 1. The unsteady hydromagnetic Ekman-Hartmann boundary-layer problem
Authors: Benton Edward R. , Loper David E.
Published: March 2006

The prototype spin-up problem between infinite flat plates treated by Greenspan & Howard (1963) is extended to include the presence of an imposed axial magnetic field. The fluid is homogeneous, viscous, and electrically conducting. The resulting boundary initial-value problem is solved to first order in Rossby number by Laplace transform techniques. In spite of the linearization the complete hydromagnetic interaction is preserved: currents affect the flow and the flow simultaneously distorts the field. In part 1, we analyze the impulsively started time dependent approach to a final steady Ekman–Hartmann boundary layer on a single insulating flat plate. The transient is found to consist of two diffusively growing boundary layers, inertial oscillations, and a weak Alfvén wave front. In part 2, these one plate results are utilized in discussing spin-up between two infinite flat insulating plates. Two distinct and important hydromagnetic spin-up mechanisms are elucidated. In all cases, the spin-up time is found to be shorter than in the corresponding non-magnetic problem.
Cylindrical shock and detonation waves in magnetogasdynamics
Authors: Christer A. H. , Helliwell J. B.
Published: March 2006

Self-similar flow patterns are studied which arise when a cylindrically symmetric strong shock or detonation wave propagates outwards into a gas at rest in which the ambient density varies as the inverse square of the distance from the axis of symmetry along which flows a line current of either zero or finite constant strength. The electrical conductivity of the gas on either side of the wave is supposed perfect and the discontinuities discussed are either gasdynamic or magnetogas-dynamic in nature. It is shown that self-similar solutions exist for piston driven gasdynamic detonation and shock waves. Whilst no self-similar solutions may occur for magnetogasdynamic detonation waves, it is demonstrated that magnetogasdynamic shock waves do possess such solutions for which detailed flow patterns are presented.
Gravity waves over a non-uniform flow
Authors: Velthuizen H. G. M. , Wijngaarden L. Van
Published: March 2006

This paper is concerned with the propagation of small amplitude gravity waves over a flow with non-uniform velocity distribution. For such a flow Burns derived a relation for the velocity of propagation in terms of the velocity distribution of the mean flow. This result is derived here in another way and some of its implications are discussed. It is shown that one of these is hardly acceptable physically. Burns's result holds only when a real value of the propagation velocity is assumed; the mentioned difficulties vanish if complex values are allowed for, implying damping or growth of the waves. Viscous effects which are the cause of damping or growth are important in the wall layer near the bottom and also at the critical depth, which is present when the wave speed is between zero and the fluid velocity at the free surface.

In § 2 the basic equations for the present problem are given. In § 3 exchange of momentum and energy between wave and primary flow is discussed. This is analogous to what happens at the critical height in a wind flow over wind-driven gravity waves. In § 4 the viscous effects at the bottom are included in the analysis and the complex equation for the propagation velocity is derived. Finally in § 5 illustrations of the theory are given for long waves over running flow and for the flow along a ship advancing in a wavy sea. In these examples a negative curvature of the mean velocity profile is shown to have a stabilizing effect.
Sink flow turbulent boundary layers
Authors: Launder B. E. , Jones W. P.
Published: March 2006

The study of sink flow turbulent boundary layers is of particular relevance to the problem of laminarization. The reason lies in the fact that the acceleration parameter which principally determines when a turbulent boundary layer will begin to revert towards laminar is, in these flows, constant from station to station. The paper presents theoretical solutions to this class of boundary layer by making use of the Prandtl mixing-length formula to relate the turbulent shear stress to the mean velocity gradient. Near the wall the Van Driest recommendation for mixing length is adopted and the Van Driest function, A+, is chosen such that the skin friction coefficient does not exceed a certain maximum value.

The predicted solutions, which are in good agreement with available experimental data, display a plausible shift from the turbulent towards the laminar solution as the acceleration parameter is increased.
Swirling flow in tubes of non-uniform cross-sections
Authors: Chow Chuen-Yen
Published: March 2006

A fluid swirling through an axisymmetrically deformed tube is considered, ignoring viscosity and compressibility. For a tube of radius R, having a longitudinal wall deformation of wave number k, the flow near the wall is blocked, if the Rossby number assumes one of the critical values (λ2n + k2R2)−½, where n is any positive integer, and λn is the nth zero of the Bessel function J1(λ). Rossby number is defined as W/2Rω, in which W and ω are the uniform axial and angular velocities in an undeformed tube. For a convergent-divergent nozzle, the critical Rossby numbers have the same form, with kR = 0. The flow exhibits radically different patterns when each critical Rossby number is crossed.
Roles of surface tension and Reynolds stresses on the finite amplitude stability of a parallel flow with a free surface
Authors: Lin S. P.
Published: March 2006

Subcritically stable motion of long gravity waves of finite amplitude in a liquid layer flowing down an inclined plane is shown to be impossible. However, super-critically stable wave régimes for such flows are found and curves of constant wave amplitude in such régimes are obtained. The mechanism of non-linear stability is investigated by considering the energy transfer between the mean flow and the disturbances. The results obtained show that the mechanism of stability in a parallel flow with a free surface is quite different from that in a parallel flow without a free surface.
A kinetic theory of steady condensation
Authors: Shankar P. N.
Published: March 2006

This paper pertains to the steady condensation on to, or evaporation from, a liquid droplet suspended in a mixture of its vapour and an inert gas. The treatment is from a kinetic theory viewpoint. The Maxwell moment method is used with Lees’ two stream Maxwellian representations for the distribution functions, to obtain a closed form result valid through the whole range from free molecule to continuum. In the diffusion control limit the formula reduces to approximate results obtained by Maxwell, Fuchs and others. In the limit where no inert gas is present the formula reduces to a result obtained earlier by the author. The formulae presented here for the mass and energy flux can now be used to calculate the growth rate of very small droplets, under a wide range of conditions.
An approach to turbulent flame theory
Authors: Williams F. A.
Published: March 2006

Is it possible to express the problem of calculating turbulent flame speeds as an eigenvalue problem that is analogous to the laminar flame speed problem? It is argued for grid turbulence that the answer is affirmative, and some benefits of pursuing such a calculation are exploited for the limiting case of a first-order reaction with vanishingly small heat release. The streamwise turbulent transport of reactant occupies a central role in the analysis. The equation governing the ensemble average of this quantity assumes different simplified forms in the limits of small-scale and large-scale turbulence. The criterion which is obtained for separating the small-scale and large-scale régimes differs from that of Damköhler and also from that of Kovasznay and Klimov. In the small-scale régime, turbulence produces a spatially varying diffusivity, the form of which can be ascertained only through an investigation of non-linear equations describing the statistical dynamics of production and decay of the velocity–concentration correlation. In the large-scale régime, which is of greater practical importance, the ensemble average of the streamwise turbulent reactant flux satisfies a linear ordinary differential equation whose solution for the growth and decay of the flux contains effects resembling wrinkling of the laminar flame, increasing of the effective diffusivity and augmentation of the effective reaction rate. An exact solution to the linear eigenvalue problem which arises in the large-scale limit reveals that turbulence enhances mean reactant consumption in the upstream portion of the flame and retards reactant consumption downstream. Formulas are given for the increase in flame speed and the increase in flame thickness that are produced by turbulence in the large-scale limit. Since the equations are relatively tractable in the large-scale limit, it is suggested that further study of these equations may yield improved descriptions of realistic turbulent flames.
Jet noise simulation on shallow water
Authors: Webster R. B.
Published: March 2006

A quantitative shallow water simulation technique for aerodynamic noise study is investigated. The technique is employed for the case of a free jet issuing from a nozzle with variable wall roughness.

The experimental results obtained are in remarkably good agreement with the theory. It is concluded that there is great potential for further work in even less well understood areas of aerodynamic noise research.
Diffraction of water waves by a submerged vertical plate
Authors: Evans D. V.
Published: March 2006

A thin vertical plate makes small, simple harmonic rolling oscillations beneath the surface of an incompressible, irrotational liquid. The plate is assumed to be so wide that the resulting equations may be regarded as two-dimensional. In addition, a train of plane waves of frequency equal to the frequency of oscillation of the plate, is normally incident on the plate. The resulting linearized boundary-value problem is solved in closed form for the velocity potential everywhere in the fluid and on the plate. Expressions are derived for the first- and second-order forces and moments on the plate, and for the wave amplitudes at a large distance either side of the plate. Numerical results are obtained for the case of the plate held fixed in an incident wave-train. It is shown how these results, in the special case when the plate intersects the free surface, agree, with one exception, with results obtained by Ursell (1947) and Haskind (1959) for this problem.
Experiments on liquid jet instability
Authors: Goedde E. F. , Yuen M. C.
Published: March 2006

The capillary instability of vertical liquid jets of different viscosities have been examined by imposing audio-frequency disturbances. Real time sequences of photographs allow a direct measurement of growth rates of disturbances of various wavelengths. Results show that in general non-linear effects dominate the growth processes. This is in agreement with Yuen's analysis. The growth rate of the difference between the neck and the swell, however, agrees well with the linearized analysis of Rayleigh and Chandrasekhar. The non-linear effect causes a liquid jet to disintegrate into drops with ligaments in between. The sizes of the ligaments decrease with increasing wave-number. The subsequent roll up of the ligament into droplet, the eventual coalescing of the droplet with the main drop and drop oscillation have also been studied.