bluuebunny/crossref_metadata_2025 huggingface dataset:
Microscale pressure fluctuations measured within the lower atmospheric boundary layer
Authors: Elliott J. A.
Published: March 2006

Eulerian measurements of microscale fluctuations in static pressure are used, in conjunction with measurements of air velocity, to describe some of the properties of the static pressure fluctuations that occur within the turbulent flow of the lower atmospheric boundary layer. Using an instrument developed to measure the static pressure at a point within the boundary layer, data were collected at heights ranging from the surface up to about 6 m. The results are presented as power spectra, cross-spectra, coherence and phase. For all observations over a flat boundary the root-mean-square pressure produced by the boundary-layer turbulence is about 2.6 times the mean stress. The pressure spectra are found to have a, well-defined shape which does not change with height above the surface; at the higher frequencies the spectra show a power-law behaviour with a mean slope of −1·7. A number of observations with two pressure sensors are used to describe the structure and propagation velocity of individual pressure pulses.

A dominant feature of the pressure-velocity relationship is that the large-scale pressure fluctuations are approximately in phase with the downstream velocity fluctuations; at small scales there is a large phase difference (∼−135°). These phase differences are interpreted to be the result of interaction of the large pressure-producing scales with the earth's surface, the small scales being ‘free’ of the surface. Prom the simultaneous measurements of pressure and downstream velocity the effect of pressure forces on the energy flux out of the downstream velocity fluctuations was evaluated. Typical values are about 0-45 of the net energy source to the downstream component. By means of pressure and vertical velocity measurements an estimate of the pressure divergence term in the net energy budget of a boundary layer is made. It was found to be about 1/10 of the energy feeding term.
Equilibrium and relaxation in turbulent wakes
Authors: Narasimha R. , Prabhu A.
Published: March 2006

In order to study the memory of the larger eddies in turbulent shear flow, experiments have been conducted on plane turbulent wakes undergoing transition from an initial (carefully prepared) equilibrium state to a different final one, as a result of a nearly impulsive pressure gradient. It is shown that under the conditions of the experiments the equations of motion possess self-preserving solutions in the sense of Townsend (1956), but the observed behaviour of the wake is appreciably different when the pressure gradient is not very small, as the flow goes through a slow relaxation process before reaching final equilibrium. Measurements of the Reynolds stresse show that the approach to a new equilibrium state is exponential, with a relaxation length of the order of 103 momentum thicknesses. It is suggested that a flow satisfying the conditions required by a self-preservation analysis will exhibit equilibrium only if the relaxation length is small compared with a characteristic streamwise length scale of the flow.
Turbulent non-equlibrium wakes
Authors: Prabhu A. , Narasimha R.
Published: March 2006

We consider here the detailed application of a model Reynolds stress equation (Narasimha 1969) to plane turbulent wakes subjected to pressure gradients. The model, which is a transport equation for the stress exhibiting relaxation and diffusion, is found to be consistent with the observed response of a wake to a nearly impulsive pressure gradient (Narasimha & Prabhu 1971). It implies in particular that a wake can be in equilibrium only if the longitudinal strain rate is appreciably less than the wake shear.

We then describe a further series of experiments, undertaken to investigate the range of validity of the model. It is found that, with an appropriate convergence correction when necessary, the model provides excellent predictions of wake development under favourable, adverse and mixed pressure gradients. Furthermore, the behaviour of constant-pressure distorted wakes, as reported by Keffer (1965, 1967), is also explained very well by the model when account is taken of the effective flow convergence produced by the distortion. In all these calculations, only a simple version of the model is used, involving two non-dimensional constants both of which have been estimated from a single relaxation experiment.
The wall region in turbulent shear flow
Authors: Wallace James M. , Eckelmann Helmut , Brodkey Robert S.
Published: March 2006

Hot-film measurements in a fully developed channel flow have been made in an attempt to gain more insight into the process of Reynolds stress production. The background for this effort is the observation of a certain sequence of events (deceleration, ejection and sweep) in the wall region of turbulent flows by Corino (1965) and Corino & Brodkey (1969). The instantaneous product signal uv was classified according to the sign of its components u and v, and these classified portions were then averaged to obtain their contributions to the Reynolds stress $-\rho\overline{uv} $. The signal was classified into four categories; the two main ones were that with u negative and v positive, which can be associated with the ejection-type motion of Corino & Brodkey (1969), and that with u positive and v negative, associated with the sweep-type motion. It was found that over the wall region investigated, 3·5 [les ] y [les ] 100, these two types of motion give rise to a stress considerably greater than the total Reynolds stress. Two other types of motion, (i) u negative, v negative, corresponding to low-speed fluid deflected towards the wall, and (ii) u positive, v positive, corresponding to high-speed fluid reflected outwards from the wall, were found to account for the ‘excess’ stress produced by the first two categories, which give contributions of opposite sign.

The autocorrelations of the classified portions of uv were obtained to determine the relative time scales of these four types of motion. The positive stress producing motions (u < 0, v > 0 and u > 0, v < 0) were found to have significantly larger time scales than the negative stress producing motions (u < 0, v < 0 and u > 0, v > 0). It was further surmised that turbulent energy dissipation is associated with the Reynolds stress producing motions, since these result in localized shear regions in which the dissipation is several orders of magnitude greater than the average dissipation at the wall.
Wave propagation across the continental shelf
Authors: Miles John W.
Published: March 2006

Wave propagation across the continental shelf is studied by analogy with transmission-line theory. Fourier transformation along the contours of constant depth, which are assumed parallel to a straight coastline, yields a Sturm-Liouville equation for a prescribed depth profile h(x). The modal spectrum of the profile, which comprises a finite, discrete spectrum of trapped modes and a continuous spectrum of radiated modes, is established. The Green's function for a point source on the coastline is constructed by Fourier superposition over this spectrum. Detailed results are calculated for a two-step model (level shelf separated from level abyss by vertical cliff) and for a gradually sloping shelf that merges smoothly into a level abyss. The radiation impedance of a harbour is calculated, and the effects of the continental shelf on the resonant response of the harbour to a tsunami are discussed.
The stability of Poiseuille flow in a pipe of circular cross-section
Authors: Salwen Harold , Grosch Chester E.
Published: March 2006

The stability of Poiseuille flow in a pipe of circular cross-section to azimuthally varying as well as axisymmetric disturbances has been studied. The perturbation velocity and pressure were expanded in a complete set of orthonormal functions which satisfy the boundary conditions. Truncating the expansion yielded a matrix differential equation for the time dependence of the expansion coefficients. The stability characteristics were determined from the eigenvalues of the matrix, which were calculated numerically. Calculations were carried out for the azimuthal wavenumbersn= 0,…, 5, axial wavenumbers α between 0·1 and 10·0 and αR[les ] 50000,Rbeing the Reynolds number. Our results show that pipe flow is stable to infinitesimal disturbances for all values of α,Randnin these ranges.
Linear spatial stability of pipe Poiseuille flow
Authors: Garg V. K. , Rouleau W. T.
Published: March 2006

A theoretical study of the spatial stability of Poiseuille flow in a rigid pipe to infinitesimal disturbances is presented. Both axisymmetric and non-axisymmetric disturbances are considered. The coupled, linear, ordinary differential equations governing the propagation of a disturbance that has a constant frequency and is imposed at a specified location in the fluid are solved numerically for the complex eigenvalues, or wavenumbers, each of which defines a mode of propagation. A series solution for small values of the pipe radius is derived and step-by-step integration to the pipe wall is then performed. In order to ascertain the number of eigenvalues within a closed region, an eigenvalue search technique is used. Results are obtained for Reynolds numbers up to 10000. For these Reynolds numbers it is found that the pipe Poiseuille flow is spatially stable to all infinitesimal disturbances.
Theoretical investigation of the interfacial stability of inviscid fluids in motion, considering surface tension
Authors: Berghmans Jan
Published: March 2006

The present work is an analytical study of the stability of interfaces between fluids in motion, special attention being given to the role of surface tension without consideration of viscous effects. A variational approach based upon the principle of minimum free energy, which was first formulated for stagnant fluids, is applied to fluids in motion. This generalization is possible if viscous and inertia effects are unimportant as far as stability is concerned. One stability problem is studied in detail: a gas jet impinging on a free liquid. The analytical results obtained by this variational technique lie within the range of accuracy (15%) of the experimental results for this gas-jet problem. The method is very general and therefore can be applied to quite a number of interface stability problems.
Instability of unsteady flows or configurations. Part 2. Convective instability
Authors: Yih Chia-Shun , Li Chin-Hsiu
Published: March 2006

The formation of convective cells in a fluid between two horizontal rigid boundaries with time-periodic temperature distribution is studied by the use of the Floquet theory. Numerical results for the critical Rayleigh number are given for a Prandtl number of 0·73 (air) and for various values of the frequency and magnitude of the primary temperature oscillation. Some numerical results for a Prandtl number of 7·0 (water) are also given. The most striking feature of the results is that the disturbances (or convection cells) oscillate either synchronously or with half frequency.
Momentum transport by gravity waves in a perfectly conducting shear flow
Authors: Rudraiah N. , Venkatachalappa M.
Published: March 2006

Alfvén-gravitational waves propagating in a Boussinesq, inviscid, adiabatic, perfectly conducting fluid in the presence of a uniform aligned magnetic field in which the mean horizontal velocityU(z)depends on heightzonly are considered. The governing wave equation has three singularities, at the Doppler-shifted frequencies Ωd= 0, ± ΩA, where ΩAis the Alfvén frequency. Hence the effect of the Lorentz force is to introduce two more critical levels, called hydromagnetic critical levels, in addition to the hydrodynamic critical level. To study the influence of magnetic field on the attenuation of waves two situations, one concerning waves far away from the critical levels (i.e. Ωd[Gt ] ΩA) and the other waves at moderate distances from the critical levels (i.e. Ωd> ΩA), are investigated. In the former case, if the hydrodynamic Richardson numberJHexceeds one quarter the waves are attenuated by a factor exp{−2π(JH−¼)½} as they pass through the hydromagnetic critical levels, at which Ωd= ± ΩA, and momentum is transferred to the mean flow there. Whereas in the case of waves at moderate distances from the critical levels the ratio of momentum fluxes on either side of the hydromagnetic critical levels differ by a factor exp {−2π(J−¼)½}, whereJ(> ¼) is the algebraic sum of hydrodynamic and hydromagnetic Richardson numbers. Thus the solutions to the hydromagnetic system approach asymptotically those of the hydrodynamic system sufficiently far on either side of the magnetic critical layers, though their behaviour in the vicinity of such levels is quite dissimilar. There is no attenuation and momentum transfer to the mean flow across the hydrodynamic critical level, at which Ωd= 0. The general theory is applied to a particular problem of flow over a sinusoidal corrugation. This is significant in considering the propagation of Alfvén-gravity waves, in the presence of a geomagnetic field, from troposphere to ionosphere.
The mechanics of an organized wave in turbulent shear flow. Part 2. Experimental results
Authors: Hussain A. K. M. F. , Reynolds W. C.
Published: March 2006

Results on the behaviour of controlled wave disturbances introduced artificially into turbulent channel flow are reported. Weak plane-wave disturbances are introduced by vibrating ribbons near each wall. The amplitude and relative phase of the streamwise component of the induced wave is educed from a hot-wire signal, allowing the wave speed, the attenuation characteristics and the wave shape to be traced downstream. These results form a basis for evaluation of closure models for the dynamical equations describing wave components in shear-flow turbulence.
Secondary flows in ducts of square cross-section
Authors: Launder B. E. , Ying W. M.
Published: March 2006

The paper presents the outcome of experimental research on turbulence-induced secondary flows in square-sectioned ducts. The main emphasis of the experiments has been on the measurement of the secondary flows in a duct with equally roughened surfaces. Here the secondary flow is a substantially larger proportion of the axial flow than is the case in smooth-walled ducts. With the secondary velocities normalized by the friction velocity, however, the resultant profiles for smooth and rough surfaces are the same, within the precision of the measurements.
Strong shock propagation through decreasing density
Authors: Freiwald D. A.
Published: March 2006

The acceleration of a shock wave in an ideal gas of decreasing density has previously been studied. The problem is reconsidered here with empirical inclusion of real-gas effects for strong shocks in hydrogen. Experimental results suggest that previous shock acceleration models are valid only for a limited range of the Knudsen number in finite geometries and that for large final-state Knudsen numbers a free-expansion model best describes the experimental results.
Three-dimensional wings in hypersonic flow
Authors: Hillier R.
Published: March 2006

Messiter's thin shock layer approximation for hypersonic wings is applied to several non-conical shapes. Two calculation methods are considered. One gives the exact solution for a particular three-dimensional geometry which possesses a conical planform and also a conical distribution of thickness superimposed upon a surface cambered in the chordwise direction. Agreement with experiment is good for all cases, including that where the wing is yawed. The other method is a more general approach whereby the solution is expressed as a correction to an already known conical flow. Such a technique is applicable to conical planforms with either attached or detached shocks but only to the non-conical planform for the region in the vicinity of the leading edge when the shock is attached.
On the response of a sphere to an acoustic pulse
Authors: Temkin Samuel
Published: March 2006

The motion of a rigid sphere responding to the passage of an acoustic pulse is considered by means of a simple approximate model which neglects the diffraction of the pulse front. The model is based on a solution of the equivalent inviscid problem and assumes that, initially, the flow field around the sphere corresponds to the steady incompressible flow of an inviscid fluid over a sphere at rest. For t > 0, the motion is studied by means of the unsteady Stokes equations. Results for the sphere's velocity, displacement and drag are obtained in closed form in terms of tabulated functions and compared with results obtained by using the Stokes drag. It is found that, when the ratio of gas density to sphere material density is finite, the initial response of the sphere differs considerably from that predicted by the use of the Stokes drag. However, when the ratio of gas density to sphere material density is infinitesimal, the differences disappear. These results may be of some importance in the study of shock-induced droplet collisions in aerosol clouds.
Upstream influence of a dipole in rotating flow
Authors: Miles John W.
Published: March 2006

McIntyre (1972) has demonstrated that transient nonlinear self-interactions among the lee waves downstream of an obstacle in an axisymmetric, inviscid, rotating flow yield a columnar disturbance that moves upstream of the obstacle. This disturbance is calculated for a dipole, the moment of which increases slowly from 0 to a3, in a tube of radius R as a function of δ = a/R and K = 2ΩR/U (Ω and U being angular and axial velocities in basic flow). The asymptotic limit δ ↓ 0 with k ≡ K δ fixed, which is relevant for typical laboratory configurations and for the abstraction of unbounded flow, yields: (a) an upstream velocity with an axial peak of u0 = 0·011k5 δ U and a first zero at a radius of 2·8U/Ω; (b) an upstream energy flux of roughly $- \frac{3}{2}\pi\rho U^2 R^2 u_0$; (c) an upstream impulse flux of 0·20D (D = wave drag on dipole). The results (a) and (b), albeit based on the hypothesis of small disturbances, suggest that nonlinear self-interactions among the lee waves could be responsible for upstream blocking. The results (a) and (c) imply that, although upstream influence is absent from an unbounded (δ = 0) flow in the sense that the axial velocity vanishes like δ, it is present in the sense that approximately one-fifth of the impulse flux associated with the wave drag appears in the upstream flow.
A temperature adjustment process in a Boussinesq fluid via a buoyancy-induced meridional circulation
Authors: Sakurai Takeo , Matsuda Takuya
Published: March 2006

The existence of a new time scale t = σ-¼(L2/kN)½, where σ, k, L and N are the Prandtl number, the thermometric conductivity, a typical length and the Brunt-Väisälä frequency, respectively, is clarified for a temperature adjustment process of a Boussinesq fluid in a circular cylinder.
Microscale pressure fluctuations near waves being generated by the wind
Authors: Elliott J. A.
Published: March 2006

Measurements of static pressure and wave height are used to describe the waveinduced pressure field above generating sea waves. A large hump in the pressure spectra is observed at the wave frequencies. The amplitude of this hump increases and the rate of its vertical decay decreases as the mean wind speed increases. The phase difference between the pressure and the waves during active generation is about 135°, pressure lagging the waves, and does not change vertically for measurements at heights greater than the wave crests. In the present data, active wave generation appears to occur only when the wind at a height of 5 metres is greater than or about equal to twice the phase speed of the waves.
Motion due to a moving internal heat source
Authors: Douglas H. A. , Mason P. J. , Hinch E. J.
Published: March 2006

An experimental study has been made of the flow produced by an internal heat source as it moves around a fixed annulus of fluid. The mean surface flow relative to the annulus is found to be in the opposite direction to the movement of the heat source. The variation in its magnitude with changes in the external parameters is investigated. Thermocouple measurements and streak photography are used to examine the interior temperature and flow structure.
Large-scale instabilities of turbulent wakes
Authors: Reynolds W. C.
Published: March 2006

The equations describing the statistical features of small amplitude waves in a turbulent shear flow are derived from the Navier-Stokes equations. Closure is achieved through a postulated constitutive equation for the alteration of the statistical properties of the turbulence by the organized wave. The theory is applied in an examination of the stability of a hypothetical wake consisting of small-scale turbulence enclosed within a steady uncontorted superlayer. A set of superlayer jump conditions is derived from fundamental considerations, and these are of more general interest. For this hypothetical flow the analysis predicts largescale instabilities and superlayer contortions reminiscent of large-eddy structures observed in real flows. These instabilities therefore offer an explanation of the presence of large-scale organized motions in turbulent free shear flows.
Errors in static pressure measurements due to protruding pressure taps
Authors: Zogg H. , Thomann H.
Published: March 2006

Errors in static pressure measurements caused by taps which protrude beyond the wall and disturb the boundary layer locally are investigated experimentally. The resulting error is presented as a function of the wall shearing stress, the protrusion height and the probe diameter in a representation similar to the calibration curve of Preston tubes. If suitably plotted, the present results can be made to fit this calibration curve to within the experimental accuracy, in spite of the differences between the geometries being compared.
A similarity solution for viscous internal waves
Authors: Thomas N. H. , Stevenson T. N.
Published: March 2006

A similarity solution is presented which describes the internal waves generated by a simple-harmonic localized disturbance in a stably stratified viscous fluid. Some experimental results support the theoretical predictions for the waves in a linearly stratified salt solution.
Bounds for heat transport in a porous layer
Authors: Busse F. H. , Joseph D. D.
Published: March 2006

Bounds on the heat transport in a porous layer are derived using the variational method of Howard (1963) and Busse (1969b). The relatively simple structure of the variational problem in the case of porous convection allows one to formulate the theory more simply and to investigate some of the mathematical questions posed by the earlier work. A precise characterization of the solution with N wavenumbers is given. The variational problem is solved exactly among functions with a single overall wavenumber and this solution is in good agreement with a nonlinear perturbation solution of the governing equations and with experiments. An N-wavenumber solution is constructed for large Nusselt numbers by boundary-layer methods. The asymptotic solution is compared with a numerical solution of the problem for N = 2. The comparison supports the boundary-layer assumptions introduced in the asymptotic analysis.
Conjugate-flow theory for heterogeneous compressible fluids, with application to non-uniform suspensions of gas bubbles in liquids
Authors: Benjamin T. Brooke
Published: March 2006

Conjugate flows have been defined generally as flows uniform in the direction of streaming that separately satisfy the relevant hydrodynamical equations, so allowing a transition from one flow to its conjugate to be consistent with mass and energy conservation. In previous studies of various examples, certain general principles have been found to apply to conjugate flows: in particular, one in a pair of such flows is subcritical (subsonic) and the other supercritical (supersonic), the former having greater flow force (i.e. momentum flux plus pressure force). In this paper these principles are confirmed in another field of application, for which the theory of conjugate flows takes a novel course.

The theoretical model defined in § 2 consists of a straight duct of arbitrary cross-section filled with a perfect fluid whose constitutive properties vary with cross-sectional position, and whose primary, prescribed flow is axial with a velocity distribution that may be non-uniform. In § 3 the possibility of a conjugate flow in the same duct is investigated, and its principal properties relative to those of the primary flow are deduced from certain simple inequalities between integrals over the cross-section. A Lagrangian description of the conjugate flow is essential, but the properties in question are established without the necessity of determining this flow explicitly. At the end of § 3, a modification of the model is discussed accounting for dissipative, flow-force conserving transitions (shocks). The application of the theory to flows of non-uniform suspensions of gas bubbles is considered in § 4.
Experiments on the flow past spheres at very high Reynolds numbers
Authors: Achenbach Elmar
Published: March 2006

The present work is concerned with the flow past spheres in the Reynolds number range 5 × 104 [les ] Re [les ] 6 × 106. Results are reported for the case of a smooth surface. The total drag, the local static pressure and the local skin friction distribution were measured at a turbulence level of about 0·45%. The present results are compared with other available data as far as possible. Information is obtained from the local flow parameters on the positions of boundary-layer transition from laminar to turbulent flow and of boundary-layer separation. Finally the dependence of friction forces on Reynolds number is pointed out.
Convection in boxes: experiments
Authors: Stork K. , Möller U.
Published: March 2006

Convective motions in rectangular boxes with one side horizontal have been studied. The critical Rayleigh numbers were determined. In most cases cell patterns with rolls parallel to the shorter side wall of the rectangular box were observed. The results have been compared with the known theoretical results of Davis (1967). In general, good agreement has been found.
An electrochemical study of flow instability on a rotating disk
Authors: Chin Der-Tau , Litt Mitchell
Published: March 2006

Data for the fluctuating mass-transfer coefficient to point electrodes on the surface of a rotating disk are presented for transition and turbulent flow, along with analysis of the energy spectrum. The results corroborate previous evidence of standing vortices on the surface in the transition region. It is shown that the electrochemical method gives a more sensitive probe of flow instabilities than has been possible previously; the transition region is found to be wider than has been previously thought to be and lies between roughlyRe= 1·7 × 105and 3·5 × 105, whereRe=r2ω/vis the Reynolds number, ω being the angular velocity of the disk (in rad/s) andvthe kinematic viscosity. As the Reynolds number is increased, the stationary vortices in the transition region propagate primarily with a frequency matching that of the disk speed. After a peak energy has been reached atRe= 2·6 × 105, the vortices break down into a fully developed turbulent flow.
On the vertical transport due to fingers in double diffusive convection
Authors: Lambert R. B. , Demenkow J. W.
Published: March 2006

Salt fingering across a density interface produced by sugar and salt is investigated experimentally for varying values of initial concentrations and for times sufficiently long to observe the régimes of growth, equilibrium and final decay. Simultaneous measurements of sugar and salt concentrations and interface geometry are made. Calculations based on Stern's collective instability model allow explicit evaluation of the coefficients of the $\frac{4}{3}$-law for the sugar flux in the form suggested by Stern & Turner (1969) for the equilibrium régime. The results are verified by the experimental data. Predictions of the finger wavelengths from this model are in general agreement with the results of previous authors, while the flux-law coefficient is an order of magnitude smaller. It is concluded that the collective instability mechanism is an adequate physical description of the salt-finger mechanism.
The stability of a helical vortex filament
Authors: Widnall Sheila E.
Published: March 2006

The stability of a helical vortex filament of finite core and infinite extent to small sinusoidal displacements of its centre-line is considered. The influence of the entire perturbed filament on the self-induced motion of each element is taken into account. The effect of the details of the vorticity distribution within the finite vortex core on the self-induced motion due to the bending of its axis is calculated using the results obtained previously by Widnall, Bliss & Zalay (1970). In this previous work, an application of the method of matched asymptotic expansions resulted in a general solution for the self-induced motion resulting from the bending of a slender vortex filament with an arbitrary distribution of vorticity and axial velocity within the core.

The results of the stability calculations presented in this paper show that the helical vortex filament has three modes of instability: a very short-wave instability which probably exists on all curved filaments, a long-wave mode which is also found to be unstable by the local-induction model and a mutual-inductance mode which appears as the pitch of the helix decreases and the neighbouring turns of the filament begin to interact strongly. Increasing the vortex core size is found to reduce the amplification rate of the long-wave instability, to increase the amplification rate of the mutual-inductance instability and to decrease the wavenumber of the short-wave instability.
The solution of sharp-cone boundary-layer equations in the plane of symmetry
Authors: Murdock John W.
Published: March 2006

A detailed study has been made of the solutions to cone boundary-layer equations in the symmetry plane in order to increase understanding of the mathematical nature and physical meaning of these solutions. A typical set of symmetry-plane solutions is presented. Included in this set are various solution branches not previously published. A double-valued solution curve is found which has not been studied prior to this time except at one trivial point. The extension of an existing solution branch through a removable singular point has also been accomplished. The solutions presented are categorized according to whether they are dependent on or independent of the boundary layer outside the symmetry plane. The region in which no solutions to the usual symmetry-plane equations exist is examined. Solutions in which the usual boundary-layer model predicts that conservation of mass is not satisfied at the symmetry plane are discussed. Non-analytical behaviour at the symmetry plane is also investigated. In both of these cases a boundary region exists at the symmetry plane.
Experiments on Taylor columns in rotating stratified fluids
Authors: Davies Peter A.
Published: March 2006

Experiments have been conducted to determine the effect of density stratification upon certain characteristic features of so-called Taylor columns. The interior structure of the homogeneous Taylor column is first of all described and compared with flow patterns obtained when the fluid is stratified. Qualitative features of the horizontal and vertical motion (in particular, the attenuation with height of the distortion created by the obstacle) are then described for values of the stratification parameter S (defined as S = N/2 Ω, whereN and Ω are the Brunt-Väisälä and rotation frequencies respectively) in the range 0 [les ] S [les ] 0·24. The effect of density stratification upon, specifically, the length of the column is then described. A working definition for the existence of a Taylor column in a given experimental situation is formulated, enabling the strength of the column to be quantified at a particular height above the obstacle. Using this method the column length is measured as a function of S in the range 0 [les ] S [les ] 0·24. It is shown that even very slight stratification is sufficient to produce noticeable modification of all aspects of the flow. In particular, the column length is considerably reduced by weak stratification.
Measurements of a laminar wake in a confined stratified fluid
Authors: Laws P. , Stevenson T. N.
Published: March 2006

Two-dimensional upstream and downstream wakes are produced by extremely slowly moving cylinders in a tank containing a linearly stratified salt solution. The upstream and downstream wakes appear to be of comparable strength, consistent with the symmetry predicted by theories that take account of density diffusion as well as viscosity. This contrasts with the quasi-non-diffusive régime recently studied experimentally by Browand & Winant (1972). The present velocity profiles are essentially similar to those predicted by diffusion theories, althought the magnitudes of the velocities appear to be greatly attenuated by the proximity of the upstream and downstream walls.
Supersonic laminar boundary layer near the plane of symmetry of a cone at incidence
Authors: Roux Bernard
Published: March 2006

Supersonic laminar boundary-layer equations near the plane of symmetry of a cone at incidence are treated by the similarity method. Numerical integration of differential equations governing such a flow is performed, taking into consideration the temperature dependence of the Prandtl numberPrand viscosity μ throughout the boundary layer. On the leeward side, a detailed consideration of the solutions shows the existence of two solutions up to a critical incidence beyond which it appears that no solution may be found. Calculations carried out for a set of values of the external flow Mach number show up a significant effect of this parameter on the behaviour of the boundary layer.
The structure and stability of vortex rings
Authors: Maxworthy T.
Published: March 2006

A series of observations on experimentally produced vortex rings is described. The flow field, ring velocity and growth rate were observed using dye and hydrogen-bubble techniques. It was found that stable rings are formed and grow in such a way that most of their vorticity is distributed throughout a fluid volume which is larger than and moving with the visible dye core.

As the vorticity diffuses out of this moving body of fluid into the outer irrotational fluid, it has two effects. It causes some of the fluid, with newly acquired vorticity, to be entrained into the interior of the bubble, while the rest is left behind and accounts for the appearance of ring vorticity in a wake. It was found that the velocity of translationUof these stable rings varies ast−1, at high Reynolds number, wheretis the time measured from the start of the motion at a virtual origin at downstream infinity. A simple theoretical model is presented which explains all of these features of the observed stable flow. Rings of even higher Reynolds number become unstable and shed significantly more vorticity into the wake. Under some circumstances a new more stable vortex emerges from this shedding process and continues with less vorticity than before. Eventually, the ring motion ceases as all of its vorticity is deposited into the wake and is spread by viscous diffusion. Observations of the interaction between two nearly identical rings travelling a common path showed that, contrary to popular belief, rings do not pass back and forth through one another, but that the rearward one becomes entrained into the forward one. Only when the rearward ring has a much higher velocity than its partner can it emerge from the joining process and leave a slower-moving ring behind.
On some exact solutions in magnetohydrodynamics with astrophysical applications
Authors: Sozou C.
Published: March 2006

Some exact solutions of the steady magnetohydrodynamic equations for a perfectly conducting inviscid self-gravitating incompressible fluid are discussed. It is shown that there exist solutions for which the free surface of the liquid is that of a planetary ellipsoid and rotates with constant angular velocity about its axis. The stability of the equilibrium configuration is not investigated.
Numerical studies of the stability of inviscid stratified shear flows
Authors: Hazel Philip
Published: March 2006

The infinitesimal stability of inviscid, parallel, stratified shear flows to two-dimensional disturbances is described by the Taylor-Goldstein equation. Instability can only occur when the Richardson number is less than 1/4 somewhere in the flow. We consider cases where the Richardson number is everywhere non- negative. The eigenvalue problem is expressed in terms of four parameters,Ja ‘typical’ Richardson number, α the (real) wavenumber andcthe complex phase speed of the disturbance. Two computer programs are developed to integrate the stability equation and to solve for eigenvalues: the first findscgiven α andJ, the second finds α andJwhenc≡ 0 (i.e. it computes the stationary neutral curve for the flow). This is sometimes,but not always, the stability boundary in the α,Jplane. The second program works only for cases where the velocity and density profiles are antisymmetric about the velocity inflexion point. By means of these two programs, several configurations of velocity and density have been investigated, both of the free-shear-layer type and the jet type. Calculations of temporal growth rates for particular profiles have been made.
On the noise of a nearly ideally expanded supersonic jet
Authors: Tam Christopher K. W.
Published: March 2006

A noise generation mechanism for a nearly ideally expanded supersonic jet is proposed. It is suggested that the dominant part of the noise of a supersonic jet is generated at two rather localized regions of the jet. These regions are located at distances quite far downstream of the nozzle exit. Large-scale instabilities of the jet flow are believed to be responsible for transferring the kinetic energy of the jet into noise radiation. An analysis based on a simple mathematical model reveals that two large-scale unstable waves are preferentially amplified in a supersonic jet. The rapid growth of these waves causes the oscillations of the jet to penetrate the mixing layer at two locations and to interact strongly with the ambient fluid there. This gives rise to intense noise radiation. Theoretical results based on the proposed noise generation mechanism are found to compare favourably with experimental measurements. A simple scaling formula is also derived.
The unsteady laminar boundary layer on a semi-infinite flat plate due to small fluctuations in the magnitude of the free-stream velocity
Authors: Ackerberg R. C. , Phillips J. H.
Published: March 2006

Asymptotic and numerical solutions of the unsteady boundary-layer equations are obtained for a main stream velocity given by equation (1.1). Far downstream the flow develops into a double boundary layer. The inside layer is a Stokes shear-wave motion, which oscillates with zero mean flow, while the outer layer is a modified Blasius motion, which convects the mean flow downstream. The numerical results indicate that most flow quantities approach their asymptotic values far downstream through damped oscillations. This behaviour is attributed to exponentially small oscillatory eigenfunctions, which account for different initial conditions upstream.
An experimental and theoretical study of internal waves generated by the collapse of a two-dimensional mixed region in a density gradient
Authors: Schooley A. H. , Hughes B. A.
Published: March 2006

Previously reported experiments with a self-propelled body submerged in a fluid with a stable vertical density gradient have demonstrated that the turbulently mixed wake first expands more or less uniformly and then collapses vertically while continuing to expand horizontally (Schooley & Stewart 1963). It was also shown that the vertical collapse of the wake generates internal waves. Essentially two-dimensional experiments have also been used to explore some of the build-up and decay characteristics of vertical wake collapse induced by a sub-merged burst of turbulent mixing (Wu 1969; Schooley 1968). The present paper reports new experimental measurements and a linear theoretical analysis of the internal wave field created in stratified water by a burst of submerged turbulent mixing. The forcing function has been obtained in integral form for an initial-value model of wake collapse in terms of a general Brunt-Väisälä frequency profile, using normal mode theory. Numerical results have been determined for the specialized case of a completely mixed circular wake in a constant Brunt-Väisälä profile. These results are compared to the experimental measurements.
Transition to turbulence in pipe flow for water and dilute solutions of polyethylene oxide
Authors: Paterson R. W. , Abernathy F. H.
Published: March 2006

An experimental study of the transition from laminar to turbulent flow in a long 0·248in. I.D. pipe is reported for both water and dilute water solutions of polyethylene oxide which exhibit turbulent flow drag reduction (the Toms phenomenon). The drag-reducing solutions, ranging in effectiveness from near zero to the maximum attainable, are observed to undergo transition in a similar way to the Newtonian solvent in that the solutions exhibit intermittency and the growth rates of the turbulent patches are essentially equal to those of the pure solvent. The growth rate of turbulent patches indicates that drag reduction is associated with the small-scale structure of the turbulence near the pipe wall while patch growth is associated with the larger-scale turbulence in the outer flow. For low-disturbance pipe inlet conditions the strong drag-reducing solutions are observed to undergo transition at lower Reynolds numbers than the pure solvent.
Surface waves in flowing water
Authors: Yih Chia-Shun
Published: March 2006

Surface waves in flowing water and their stability are studied. With U(y) denoting the mean velocity and d the depth of water, the following results are obtained: (i) in the plane of the complex wave velocity, c = cr + ici, all eigenvalues c with a positive ci lie within a semicircle which has as its diameter the range of the velocity U(y) of the primary flow, y being the vertical co-ordinate. (ii) If U″(y) does not change sign and U is monotonic in the field of flow, singular neutral modes (for which c = U somewhere in the field of flow) are impossible and the flow is stable. (iii) If U is analytic and U″ vanishes at the point or points where U is equal to the same constant Uc and where U′ is not zero then at least one neutral mode exists with c = Uc, provided U(d) ≠ Uc. (iv) If U is monotonic and U″/(U—c) is finite and non-zero at the critical point (c real), where U″ vanishes, then the neutral mode mentioned in (iii) above is contiguous with unstable modes, (v) If U″ < 0 and U′ [ges ] 0 there are waves with c [les ] U(0), with a finite maximum wavenumber kc corresponding to c = U(0) and with c decreasing monotonically to a finite c0 for k = 0. (vi) If U″ < 0 and U′ [ges ] 0 waves of all wavenumbers can travel with c > U(d). The eigenvalue c for any k is bounded.
Cavity flows driven by buoyancy and shear
Authors: Torrance K. , Davis R. , Eike K. , Gill P. , Gutman D. , Hsui A. , Lyons S. , Zien H.
Published: March 2006

Fluid motion driven by the combined effects of a moving wall and natura convection is examined for rectangular cavities with heightlwidth ratios of ½, 1 and 2. The Reynolds number and Prandtl number are held fixed at Re = 100 and Pr = 1; the Grashof number is varied over the range of values Gr = 0, ±104, ±106. Flow and temperature fields obtained from numerical solutions of the Navier-Stokes equations reveal a marked influence of buoyancy for the larger aspect ratios when Gr = ±106 and the dominance of buoyancy for all aspect ratios when Gr = ± 106. Results are compared with earlier work where possible and some observations are offered on the convergence of the numerical solutions.
The stability of an incompressible two-dimensional wake
Authors: Mattingly G. E. , Criminale W. O.
Published: March 2006

The growth of small disturbances in a two-dimensional incompressible wake has been investigated theoretically and experimentally. The theoretical analysis is based upon inviscid stability theory wherein small disturbances are considered from both temporal and spatial reference frames. Through a combined stability analysis, in which small disturbances are permitted to amplify in both time and space, the relationship between the disturbance characteristics for the temporal and spatial reference frames is shown. In these analyses a quasi-uniform assumption is adopted to account for the continuously varying mean-velocity profiles that occur behind flat plates and thin airfoils. It is found that the most unstable disturbances in the wake produce transverse oscillations in the mean-velocity profile and correspond to growing waves that have a minimum group velocity.

Experimentally, the downstream development of the wake of a thin airfoil and the wave characteristics of naturally amplifying small disturbances are investigated in a water tank. The disturbances that develop are found to produce transverse oscillations of the mean-velocity profile in agreement with the theoretical prediction. From the comparison of the experimental results with the predictions for the characteristics of the most unstable waves via the temporal and spatial analyses, it is concluded that the stability analysis for the wake is to be considered solely from the more realistic spatial viewpoint. Undoubtedly, this conclusion is also applicable to other highly unstable flows such as jets and free shear layers.

In accordance with the disturbance vorticity distribution as determined from the spatial model, a description of the initial development of a vortex street is put forth that contrasts with the description given by Sato & Kuriki (1961).
Slow flow through stationary random beds and suspensions of spheres
Authors: Lundgren T. S.
Published: March 2006

Stokes flow through a random, moderately dense bed of spheres is treated by a generalization of Brinkman's (1947) method, which is applicable to both stationary beds and suspensions. For stationary beds, Darcy's law with a permeability result similar to Brinkman's is derived. For suspensions an effective viscosity μ/(1–2·60ψ) is found, where ψ is the volume fraction of spheres. Also, an expression for the settling velocity is derived.
High Reynolds number flow past a flat 'plate with strong blowing
Authors: Klemp J. B. , Acrivos A.
Published: March 2006

For the uniform flow past a semi-infinite flat plate subject to a blowing velocity profile equal to C(Uv/x),½ the conventional boundary-layer approximations break down as C approaches 0middot;6192. Here, we consider the structure of the flow for large Reynolds numbers R when C exceeds this critical value. It is shown that, for C > 0·6192, a region containing injected fluid O(R-1/3)) in thickness forms directly above the plate. To a first approximation the flow in this region is inviscid and the pressure a function of x only. This blowing region is separated from the free stream by a free shear boundary layer of thickness O(R-½). Thus the flow domain consists of three distinct regions which interact to yield a similarity solution valid for large values of Rx. This solution is then extended to higher order by expanding the stream function in each region in powers of (Rx)-1/3 and evaluating the first four terms in the resulting series using standard matching techniques. Finally, more general blowing profiles which also lead to boundary-layer ‘blow off’ are considered and an expression, valid far downstream of boundary-layer detachment, is derived for the position of the streamline separating the injected fluid from that of the free stream. For the case of uniform blowing the blowing region takes on the shape of a wedge, indicating that no solution can exist for the corresponding external flow if the plate is truly semi-infinite.