bluuebunny/crossref_metadata_2025 huggingface dataset:
Nonlinear cellular motions in Poiseuille channel flow
Authors: Zahn J.-P. , Toomre Juri , Spiegel E. A. , Gough D. O.
Published: March 2006

We expand the equations describing plane Poiseuille flow in Fourier series in the co-ordinates in the plane parallel to the bounding walls. There results an infinite system of equations for the amplitudes, which are functions of time and of the cross-stream co-ordinate. This system is drastically truncated and the resulting set of equations is solved accurately by a finite difference method. Three truncations are considered: (I) a single mode with dependence only on the downstream co-ordinate and time, (II) the mode of (I) plus its first harmonic, (III) a single three-dimensional mode. For all three cases, for a variety of initial conditions, the solutions evolve to a steady state as seen in a particular moving frame of reference. No runaways are encountered.
Radiation properties of the semi-infinite vortex sheet: the initial-value problem
Authors: Crighton D. G. , Leppington F. G.
Published: March 2006

The interaction between an acoustic source, an unstable shear layer and a large inhomogeneous solid surface is studied, using an idealized model in which a vortex sheet is generated by uniform subsonic flow on one side of a semi-infinite plate, and subjected to line-source irradiation. Both the steady-state (time-harmonic) and initial-value (impulsive source) situations are examined. In particular, the time-harmonic field which can develop in a causal manner from a quiescent initial state is examined, and a specific criterion is given by which one may obtain the correct causal harmonic solution without explicit consideration of an initial-value problem. The satisfaction of this criterion demands not only the presence in the harmonic problem of the Helmholtz instability of an infinite vortex sheet (Jones & Morgan 1972), but additionally the presence of an edge-scatttered instability which in real time consists of a singular line plus a tail. The harmonic solution is discussed in some detail, and the consequences of omitting the unstable solutions and thereby violating causality are shown greatly to affect the diffracted field in some circumstances. The general features of the initial-value problem are also dealt with, the various waves being classified and their arrival times at any point being given in simple form. The paper ends with some speculations as to the applicability of these phenomena to the description of the process of ‘parametric amplification’, by which sound generated within a duct can be greatly amplified in the far field by triggering unstable modes on the shear layer shed from the duct.
Experimental investigation of rarefied gas flow in different channels
Authors: Porodnov B. T. , Suetin P. E. , Borisov S. F. , Akinshin V. D.
Published: March 2006

An experimental investigation of flows of a large number of inert and polyatomic gases in various channels, a non-ideal orifice, flat slits with different surface roughnesses and wall materials, capillary packets with molten walls and a capillary sieve, has been made.

The unsteady flow method and a highly sensitive capacitance micromanometer were used (the sensitivity being ∼ 3 × 10−4N/m2Hz). Measurements were made in a range of Knudsen numbers 5 × 104–10−3at ∼ 293 °K, and some measurements for flow through a non-ideal orifice were carried out at 77.2°K.

It was found that, both in the viscous slip-flow and free-molecule regimes for the channels with molten walls, the experimental conductivities were higher (by ∼ 15%) than theoretical ones calculated assuming diffuse molecular scattering by the walls. We have also observed that the channel conductivity essentially depends on the channel surface roughness and on the kind of gas. The larger the roughness height, the lower the conductivity. From the experimental data the tangential momentum accommodation coefficients were calculated.
Natural convection of viscoelastic fluids in a vertical slot
Authors: Gözüm Dogan , Arpaci V. S.
Published: March 2006

Linear stability theory is applied to the natural convection of slightly, elastic, viscous fluids in an infinitely long vertical slot. Travelling, as well as stationary, disturbances are considered. It is found that the elasticity (i) slightly stabilizes the stationary disturbances while strongly destabilizing the travelling disturbances, (ii) strongly increases the wave speed while slightly decreasing the wavenumber and (iii) reduces the transition Prandtl number, which separates the stationary cells from the travelling waves, from its value of 12.7 for Newtonian fluids.

Experiments are carried out with a viscoelastic fluid prepared by mixing Separan AP30 with water, giving a Prandtl number of about 30. This fluid is shown to produce wave instability at a Grashof number between 3900 and 4300. Under the same conditions, a Newtonian fluid is shown to remain stable to both stationary and travelling disturbances.
Drag due to the motion of a Newtonian fluid through a sparse random array of small fixed rigid objects
Authors: Howells I. D.
Published: March 2006

The averaged equations of slow flow in random arrays of fixed spheres are developed as a hierarchy of integro-differential equations, and an iteration procedure is described for obtaining the mean drag in the case of small volume concentration c. The leading approximation is that given by Brinkman's model of flow past a single fixed sphere, in which the effects of all other spheres are treated as a Darcy resistance. The higher approximations take account of the modification to the mean flow, particularly in the near field, due to the localized nature of the actual resistance. Thus the second approximation finds the change due to a second sphere, and averages over all its possible positions. The result for the mean drag confirms Childress’ terms in clogc and c (apart from an arithmetical correction to the latter), but indicates that for practical values of c numerical evaluation of integrals is needed, rather than expansion in powers of c and log c. The last section of the paper develops the corresponding results for flow through random arrays of fixed parallel circular cylinders.
Wakes behind two-dimensional surface obstacles in turbulent boundary layers
Authors: Counihan J. , Hunt J. C. R. , Jackson P. S.
Published: March 2006

By making simple assumptions, an analytical theory is deduced for the mean velocity behind a two-dimensional obstacle (of heighth) placed on a rigid plane over which flows a turbulent boundary layer (of thickness δ). It is assumed thath[Gt ] δ, and that the wake can be divided into three regions. The velocity deficit −uis greatest in the two regions in which the change in shear stress is important, a wall region (W) close to the wall and a mixing region (M) spreading from the top of the obstacle. Above these is the external region (E) in which the velocity field is an inviscid perturbation on the incident boundary-layer velocity, which is taken to have a power-law profileU(y) =U∞(y−y1)n/δn, wheren[Gt ] 1. In (M), assuming that an eddy viscosity (=KhU(h)) can be defined for the perturbed flow in terms of the incident boundary-layer flow and that the velocity is self-preserving, it is found thatu(x,y) has the form$\frac{u}{U(h)} = \frac{ C }{Kh^2U^2(h)} \frac{f(n)}{x/h},\;\;\;\; {\rm where}\;\;\;\; \eta = (y/h)/[Kx/h]^{1/(n+2)}$, and the constant which defines the strength of the wake is$C = \int^\infty_0 y^U(y)(u-u_E)dy$, whereu=uE(x, y) asy→ 0 in region (E).

In region (W),u(y) is proportional to Iny.By considering a large control surface enclosing the obstacle it is shown that the constant of the wake flow is not simply related to the drag of the obstacle, but is equal to the sum of the couple on the obstacle and an integral of the pressure field on the surface near the body.

New wind-tunnel measurements of mean and turbulent velocities and Reynolds stresses in the wake behind a two-dimensional rectangular block on a roughened surface are presented. The turbulent boundary layer is artificially developed by well-established methods (Counihan 1969) in such a way that δ = 8h. These measurements are compared with the theory, with other wind-tunnel measurements and also with full-scale measurements of the wind behind windbreaks.

It is found that the theory describes the distribution of mean velocity reasonably well, in particular the (x/h)−1decay law is well confirmed. The theory gives the correct self-preserving form for the distribution of Reynolds stress and the maximum increase of the mean-square turbulent velocity is found to decay downstream approximately as$ (\frac{x}{h})^{- \frac{3}{2}} $in accordance with the theory. The theory also suggests that the velocity deficit is affected by the roughness of the terrain (as measured by the roughness lengthy0) in proportion to In (h/y0), and there seems to be some experimental support for this hypothesis.
Convective temperature oscillations in molten gallium
Authors: Hurle D. T. J. , Jakeman E. , Johnson C. P.
Published: March 2006

An experimental study of the occurrence of temperature oscillations in molten gallium contained in a rectangular boat and heated from the side is reported. The dependence of the critical temperature difference across the boat for which oscillations set in upon the boat dimensions and upon the strength of a transverse magnetic field is described. The dependence of the frequency of oscillation on these parameters is also reported together with measurements of the variation of the phase of the oscillations over the top surface of the melt. The results are discussed in relation to the theory in the companion paper by Gill (1974).
An experimental investigation of high Reynolds number steady streaming generated by oscillating cylinders
Authors: Bertelsen Arnold F.
Published: March 2006

The steady streaming generated in the boundary layer on a cylinder performing simple harmonic motion in a viscous incompressible fluid which is otherwise at rest is investigated in the case where the Reynolds numberRsassociated with this streaming is large. Comparison is made between experimental results obtained here and the theories of Riley (1965) and Stuart (1966). This comparison shows good agreement between the theories and the experiment close to the cylinder, but away from the cylinder significant discrepancies are observed. Possible reasons for these discrepancies are discussed.
Free convection in low-temperature gaseous helium
Authors: Threlfall D. C.
Published: March 2006

Free convection has been studied in gaseous helium at low temperatures in a cylindrical vessel of aspect ratio (diameterlheight) 2·5. Compared with measurements in fluids at room temperature the present arrangement has the advantages of small size, a short time constant and improved accuracy. As the Rayleigh number was varied from 60 to 2 × 109, the Nusselt number rose from 1 to 69, obeying the relationNu= 0·173Ra0·2800±0·0005over the upper four decades ofRa.The critical Rayleigh number was 1630, but the conditions of the experiment did not allow reliable measurements at such low values ofRa.The very high sensitivity within a given experiment showed the presence of several ‘discrete transitions’, which were often step like and not merely a change of gradient as reported by other workers. The largest of these, atRa= 3 · 105, involved a drop in heat flux of some 6% and was somewhat hysteretic. The temperature fluctuations increased markedly as the step was crossed.
Fine-structure turbulence in the wall region of a turbulent boundary layer
Authors: Ueda H. , Hinze J. O.
Published: March 2006

Measurements have been made concerning the fine structure of the turbulence in the part adjacent to the wall of the wall region of a plane turbulent boundary layer. The objective was to gain further information concerning the larger-scale disturbance mechanism which is mainly responsible for the generation of turbulence. Hot-wire anemomet.ry was used and information on the fine structure was obtained by differentiating and filtering the hot-wire signal.

The distributions of the Kolmogorov microscale and of the flatness and skewness factors of the axial fluctuating velocity u and its first and second derivative determined at two Reynolds numbers suggest the existence of Reynolds number similarity. In the region y+ < 15 the flatness and skewness factors of u increase with decreasing y+. At approximately y+ = 15 the flatness factor shows a minimum value, while the skewness factor becomes zero. This location agrees with that where the turbulence intensity u′ has a maximum value. In the outer part of the wall region (y+ > 100) the flatness and skewness factors approach values obtained in shear-free turbulence at the same turbulence Reynolds number.

The fine structure of the turbulence is strongly associated with and dominated by the random, larger-scale, intermittent inrush-ejection cycle. In the viscous sublayer both the fine structure, and the large-scale mechanism of the turbulence are influenced mainly by the inrush phase, while further out in the wall region (y+ > 40) they are influenced by both inrush and ejection. As a result, in the viscous sublayer the average burst periods of the high frequency turbulence components and their flatness factors (of ∂u/∂t and of ∂2u/∂t2) attain values twice those in the outer part.

The change in the mechanism of the fine structure with distance from the wall is clearly demonstrated by the spectra of non-negative variables, i.e. (∂u/∂t)2 and (∂2u/∂t2)2. The spectra agree with each other and decrease with increasing frequency, following a power law as predicted by Gurvich & Yaglom (1967). The power law applies to almost the whole frequency range, when the highest, viscous, frequency range is excluded. However, the exponent is different for the viscous sublayer and the outer part of the wall region. In the buffer layer the spectra have two distinct power-law regions. In the lower frequency range the exponent is the same as that for the viscous sublayer, while in the higher frequency range it is the same as that for the outer part of the wall region.
A thermal boundary layer in a reversing flow
Authors: Pedley T. J.
Published: March 2006

Conventional boundary-layer theory cannot be applied when the fluid velocity outside the layer changes direction, and the leading edge of a finite body changes ends. In this paper an approximate method for examining the details of the boundary layer during a single flow reversal (occurring at t = 0) is described. It is based on the expectation that (a) long before reversal (t < -t1), there will be a quasi-steady boundary layer appropriate to flow in one direction; (b) long after reversal (t > t2) there will be a quasi-steady boundary layer appropriate to flow in the opposite direction, and (c) in between there will be a period of pure diffusion. The method is applied to a simple heat-transfer problem, in which a fluid of thermal diffusivity D flows with uniform velocity U = At over the plane y = 0; the strip 0 < x < L of the plane is maintained at temperature T1, while the restof the plane and the fluid far away have temperature T0. The approximate solution is compared with an exact solution of the boundary-layer equation, and is shown to give an accurate prediction of the heat transfer as a function of time. The boundary-layer approximation itself breaks down in regions of length O(D2/3A−1/3) near the ends of the heated strip, as usual; it also breaks down in the neighbourhood of the point x = 1/2At2, t > 0, at which the influence of the new leading edge is first felt after flow reversal. In a solution of the full equation, this region is examined in detail, and boundary-layer theory is shown to be sufficiently accurate for the calculation of heat transfer.
The vortex-street structure of ‘turbulent’ jets. Part 1
Authors: Lau J. C. , Fisher M. J.
Published: March 2006

It was suggested by Lau, Fisher & Puchs (1972) that the basic structure of a ‘turbulent’ round jet might consist, essentially, of an axial array of fairly evenly spaced vortices moving downstream in the mixing region of the jet. The present experimental study is an attempt to establish this hypothesis on a sound footing. The problem which was posed was first to find proof of the existence of a fairly regular pattern in the mixing region, and second to extract detailed information on the component parts of this pattern to identify the nature of the structure.

Hot-wire signals in the mixing layer are known to possess a predominance of spikes. In the region closer to the high velocity side of the layer, these spikes tend to be downward ones whilst in the opposite region, they are upward. These spikes have been attributed to the entrainment mechanism in the mixing layer and had been thought to be random. A closer study of time-history curves of these hotwire signals suggests that they might not be as random as would appear at first glance. A probability analysis was conducted of the time intervals between the successive downward spikes in the u′ signals, and it was found that indeed the highest probability occurred when the time interval corresponded to a frequency equal to the vortex passing frequency.

A time-domain averaging (or eduction) technique was used to try to identify the nature of the flow structure using the spikes to trigger the eduction process. On the basis of these results it would seem that the suggestion of a vortex street is well founded. Furthermore, it appears that, as the individual vortices in the street move downstream, they are continuously transporting fluid masses across the mixing layer, and it is this effect which is producing the Reynolds stresses in the mixing layer, and causing the spikes in the u’ signals in this region.
Mixing across an interface due to turbulence generated by an oscillating grid
Authors: Thompson S. M. , Turner J. S.
Published: March 2006

Many experimenters have used oscillating grids to produce turbulence for various laboratory purposes, especially in studies of mixing, but there have been few direct measurements of the properties of the turbulence itself. In the present paper we report experiments which attempt to relate the turbulent velocity and length scales to the external parameters, the frequency and amplitude, for three forms of grid oscillated in a tank of water. Turbulent velocities have been measured in the absence of a mean flow by using a hot film moved through the fluid to provide its own mean velocity. The output is stored and analysed in a small computer, which rapidly evaluates velocity and length scale statistics from an ensemble of records. The spatial variation of these quantities with distance from the stirrer is of special interest. It agrees with results suggested by an inertial-decay theory, and with previous measurements made by Bouvard & Dumas (1967) using a different form of stirrer. A particular purpose of the work has been to ‘calibrate’ the entrainment experiments of Turner (1968), by providing absolute scales of velocity and length in the fluid near a mixing interface, for the same grid as was used in the earlier experiments. Evidence is presented which suggests that other forms of grid may not be calibrated simply by extrapolating these results.
Wave forces on vertical axisymmetric bodies
Authors: Black Jared L.
Published: March 2006

An integral-equation formulation is used to calculate wave forces on bodies having a vertical axis of symmetry. The development enables one to calculate the forces without completely determining the local pressure field, thus offering a considerable reduction of computational effort. Numerical results are presented for a hemisphere at the water surface and vertical circular cylinders.
Helmholtz resonance of harbours
Authors: Miles John W. , Lee Y. K.
Published: March 2006

The resonant response of a harbour H of depth scale d and area A to excitation of frequency ω through a mouth M of width a is calculated in the joint limit a2/Aω2A/gd↓0. The results are relevant to the tsunami response of narrow-mouthed harbours. 16 is assumed that an adequate approximation to the radiation impedance of the external domain is available (Miles 1972). The boundary-value problem for H is reduced to the solution of ∇. (h∇ϕ) = −1/A, where h is the relative depth, the normal derivative of ϕ is prescribed in M and vanishes elsewhere on the boundary of H, and the spatial mean of ϕ must vanish. The kinetic energy in H is proportional to an inertial parameter M that is a quadratic functional of ϕ. It is demonstrated that decreasing/increasing h increases/decreases M. Explicit lower bounds to M are developed for both uniform and variable depth. The results are extended to coupled basins (inner and outer harbours). Several examples are considered, including a model of Long Beach Harbor, for which the calculated resonant frequency of the dominant mode is within 1% of the measured value. The effects of entry-separation and bottom-friction losses are considered; the latter are typically negligible, whereas the former may be comparable with, or dominate, radiation losses.
Rectangular resonators on infinite and semi-infinite channels
Authors: Buchwald V. T. , Williams N. V.
Published: March 2006

The surface elevations in a strip 0 <y<band in a rectangle -d<y< 0, |x| <aare expressed as a Fourier integral and Fourier series respectively. Using a Galerkin technique to match boundary conditions, the solution to the general problem of the response of a rectangular resonator to inviscid shallow-water waves in infinite and semi-infinite channels is obtained.

Theoretical results are compared with laboratory experiments of James (1970, 1971a, b). Agreement is generally very good, except that the inviscid and linear theory does not predict the observed large energy losses in the resonator at resonance.

The theory is also applied to a geometry corresponding to the Gulf of Carpentaria, and the calculated response of the Gulf to semi-diurnal tides gives a zero response at Kuramba, in agreement with observations. The full response of the Gulf is calculated in subsequent work (Williams 1974) which takes the effects of the earth's rotation into account.
The Kelvin-Helmholtz instability of the gas-liquid interface of a sonic gas jet submerged in a liquid
Authors: Chawla T. C.
Published: March 2006

It is well known that the small perturbation equation governing steady or mildly unsteady potential flow in a sonic gas jet is nonlinear. However, for a sonic gas jet submerged in a liquid with a disturbance on the gas-liquid interface, it is shown that the transient motion of the gas dominates, and the nonlinear term due to accumulation of disturbances in the basic flow becomes negligible; the condition necessary for the applicability of the linearized governing equation is obtained. It is demonstrated that most gas-jet/liquid systems of physical interest satisfy this condition and that the margin with which this condition is satisfied improves as the wave velocity of the disturbance or, more particularly, as the stagnation pressure or density of the gas for a given gas-liquid system increases. The Kelvin-Helmholtz instability of the gas-liquid interface of a sonic gas jet submerged in a liquid is predominantly governed by the transfer of energy from the gas phase to the liquid layer, both through wave-drag and ‘lift’ components of the pressure perturbation; at and above the cut-off wavenumber, which only exists for very low viscosity liquids owing to the stabilizing effect of surface tension, the pressure perturbation becomes in phase with the wave amplitude. It is shown that for low viscosity liquids the phase angle between the pressure perturbation exerted by the gas phase on the liquid a t the gas-liquid interface and the wave amplitude, which is the measure of the relative effectiveness of the ‘lift’ and wave-drag components of the pressure perturbation, is a function of the density ratio (ratio of gas density a t throat conditions to liquid density). At low density ratios both of these components are operative; however, at high density ratios the wave-drag component becomes dominant. The analysis further shows that the cut-off wave- number and the wavenumber a t maximum instability decrease with increasing density ratio. For highly viscous liquids and liquids having finite viscosity the pressure perturbation is always out of phase with the wave amplitude, and no cut-off wavenumber exists, i.e. the gas-liquid interface is always unstable in spite of the stabilizing effect of viscosity and surface tension.
Fine-structure of energy spectra of velocity fluctuations in the transition region of a two-dimensional wake
Authors: Sato Hiroshi , Saito Hironosuke
Published: March 2006

Measurements of the fine-structure of the energy spectrum of the velocity fluctuations were made in the transition region of a two-dimensional wake. Line and continuous spectra were determined separately with a high-selectivity band-pass filter. The transition was initiated by an external sinusoidal sound. The sound-induced periodic fluctuation and the natural random fluctuation in the wake were added and a system of line and continuous spectra was formed. Higher harmonics of the periodic component were produced by the nonlinear interaction. As a result of the interaction between discrete and continuous components, a continuous spectrum was generated at low wavenumbers. A simple model for the interaction is proposed. The evolution of the spectrum is explained by three fundamental rules concerning the nonlinear interaction between spectral components: (i) the growth of a spectral component is suppressed by the presence of another strong component, (ii) mutual interaction is more effective when the amplitudes of interacting components are closer, and (iii) a stronger interaction takes place between components of closer wavenumbers. The randomization of the regular fluctuation is properly expressed as the growth of the ‘randomness factor’, the ratio of the energy of the random components to the total fluctuation energy.
Eulerian and Lagrangian time microscales in isotropic turbulence
Authors: Tennekes H.
Published: March 2006

In isotropic ‘box’ turbulence without a mean flow, the Lagrangian frequency spectrum extends to frequencies of order$(\epsilon/\nu)^{\frac{1}{2}}$(ε is the rate of dissipation of kinetic energy per unit mass and ν is the kinematic viscosity of the fluid). This leads to an estimate that makes the r.m.s. value ofdu/dtof order$(\epsilon^3/\nu)^{\frac{1}{4}}$. The Eulerian frequency spectrum, however, extends to higher frequencies than its Lagrangian counterpart; this is caused by spectral broadening associated with large-scale advection of dissipative eddies. As a consequence, the r.m.s. value of ∂u/∂tat a fixed observation point is (apart from a numerical factor)$R_{\lambda}^{\frac{1}{2}}$times as large as the r.m.s. value ofdu/dt(RΛ is the turbulence Reynolds number based on the Taylor microscale). The results of a theoretical analysis based on these premises agree with data obtained by Comte-Bellot, Shlien and Corrsin. The analysis also suggests that the Eulerian frequency spectrum has a$\omega^{-\frac{5}{3}} $behaviour in the inertial subrange, and that it is not governed by Kolmogorov similarity.
The generation of sound by aerodynamic sources in an inhomogeneous steady flow
Authors: Howe M. S.
Published: March 2006

This paper examines the effect of steady flow on the generation of sound by aerodynamic sources located in the neighbourhood of a scattering body. The analysis is facilitated by the use of a reverse-flow reciprocal theorem which is valid for a certain class of inhomogeneous flow problems. In the case of acoustic ‘bremsstrahlung’, in which sound is generated during the passage of asilentfluid inhomogeneity, such as an entropy spot, past an obstacle in the flow, an elegant discussion of the interaction can be given in terms of arenormalizedGreen's function. Here the effect of the obstacle is equivalent to a local distortion of the geometry of the three-dimensional space occupied by the medium, the extent of which governs the properties of the acoustic radiation. This is illustrated by means of a detailed analysis of the sound generated during the unsteady convection of a source of constant strength through a neck in a duct.
On the viscous flow about the trailing edge of a rapidly oscillating plate
Authors: Brown S. N. , Daniels P. G.
Published: March 2006

The incompressible laminar flow in the neighbourhood of the trailing edge of an aerofoil undergoing sinusoidal oscillations of high frequency and low amplitude in a uniform stream is described in the limit as the Reynolds number R tends to infinity. The aerofoil is replaced by a flat plate on the assumption that leadingedge stall does not take place. It is shown that, for oscillations of non-dimensional frequency $O(R^{\frac{1}{4}})$ and amplitude $O(R^{\frac{9}{16}})$, a rational description of the flow at the trailing edge is based on a subdivision of the boundary layer above the plate into five distinct regions. Asymptotic analytic solutions are found in four of these, whilst in the fifth a linearized solution yields an estimate for the viscous correction to the circulation determined by the Kutta condition.
A method for determination and control of the frequency response of the constant-temperature hot-wire anemometer
Authors: Wood N. B.
Published: March 2006

The theory of the constant-temperature anemometer has been extended in order to obtain quantitative results for the frequency response. A simple electrical test against which to check the theory has been devised, and the validity of the anemometer equations is demonstrated. Important differences in design philo-sophies and modes of operation are indicated, and results are presented for a design in which high d.c. gain is employed in the servo amplifier. The square-wave response is briefly investigated, and it is concluded that commonly used criteria for determining the frequency response from it should be treated with caution.

To measure fluctuations with a hot-wire anemometer in flows containing both velocity and temperature perturbations, the hot wire must be operated at more than one temperature. Variation of the mean wire temperature causes, in general, a variation in the frequency response, as does variation of the mean flow conditions. It is shown that, by simultaneous variation of the gain of the servo amplifier in the anemometer, the frequency response may be held nearly constant over a useful range of both overheat and flow conditions.
Uniform asymptotic solutions for potential flow about a slender body of revolution
Authors: Geer James
Published: March 2006

The general problem of potential flow past a slender body of revolution is considered. The flow incident on the body is described by an arbitrary potential function and hence the results presented here extend those obtained by Handels-man & Keller (1967 α). The part of the potential due to the presence of the body is represented as a superposition of potentials due to point singularities (sources, dipoles and higher-order singularities) distributed along a segment of the axis of the body inside the body. The boundary condition on the body leads to a linear integral equation for the density of the singularities. The complete uniform asymptotic expansion of the solution of this equation, as well as the extent of the distribution, is obtained using the method of Handelsman & Keller. The special case of transverse incident flow is considered in detail. Complete expansions for the dipole moment of the distribution and the virtual mass of the body are obtained. Some general comments on the method of Handelsman & Keller are given, and may be useful to others wishing to use their method.
The distortion of turbulence by general uniform irrotational strain
Authors: Reynolds A. J. , Tucker H. J.
Published: March 2006

This paper describes the measured response of grid turbulence to three limiting types of uniform homogeneous strain: plane straining, axisymmetric elongation and axisymmetric flattening. Straining was achieved by allowing the turbulence to be convected through suitable distorting ducts; the maximum strain ratios were 5·8, 6·0 and 2·3, respectively. An attempt is made, using rapid-distortion theory, to specify an effective strain which accounts for the initial anisotropy of the grid turbulence; in the experiments, this effect was most important for the third species of strain. The maximum effective strain ratios were calculated as 4·05, 7·2 and 2·75, respectively. The rapid-distortion results are able to describe several features of the response of the turbulence with good accuracy: (i) the variation of total turbulence energy through the experimental ducts; (ii) the tendency of one component (that in the direction of the (larger) negative strain) to contain one-half of the turbulence energy after only moderate straining; and (iii) the changes in dimensionless structure parameters composed of ratios of component intensities. The first kind of prediction requires that the concurrent decay be specified in a simple way; (ii) and (iii) require that the initial anisotropy be taken into account. The predictions (iii) are generally less accurate than the others. The degree of success achieved by the rapid-distortion hypo-thesis is rather surprising, since the strain rates in the experiments were not as large as those for which the theory might have been expected to be valid. It is concluded that successful models of turbulence must provide a vorticity amplification essentially like that of rapid-distortion theory. However, the simple distorting flows considered here may not provide severe tests of more refined models, since many features of the response have already been accounted for.
Dissipative heating in convective flows
Authors: Hewitt J. M. , Mckenzie D. P. , Weiss N. O.
Published: March 2006

Dissipative heating is produced by irreversible processes, such as viscous or ohmic heating, in a convecting fluid; its importance depends on the ratio d/HT of the depth of the convecting region to the temperature scale height. Integrating the entropy equation for steady flow yields an upper bound to the total rate of dissipative heating in a convecting layer. For liquids there is a regime in which the ratio of dissipative heating to the convected heat flux is approximately equal to c(d/HT), where the constant c is independent of the Rayleigh number. This result is confirmed by numerical experiments using the Boussinesq approximation, which is valid only if d/HT is small. For deep layers the dissipative heating rate may be much greater than the convected heat flux. If the earth's magnetic field is maintained by a convectively driven dynamo, ohmic losses are limited to 5% of the convected flux emerging from the core. In the earth's mantle viscous heating may be important locally beneath ridges and behind island arcs.
Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence
Authors: Frisch U. , Pouquet A. , LÉOrat J. , Mazure A.
Published: March 2006

Some of the consequences of the conservation of magnetic helicity$\int \rm{a.b}\it{d}^{\rm{3}}\rm{r\qquad (a\; =\; vector\; potential\; of\; magnetic\; field\; b)}$for incompressible three-dimensional turbulent MHD flows are investigated. Absolute equilibrium spectra for inviscid infinitely conducting flows truncated at lower and upper wavenumberskminandkmaxare obtained. When the total magnetic helicity approaches an upper limit given by the total energy (kinetic plus magnetic) divided bykmin, the spectra of magnetic energy and helicity are strongly peaked nearkmin; in addition, when the cross-correlations between the velocity and magnetic fields are small, the magnetic energy density nearkmingreatly exceeds the kinetic energy density. Several arguments are presented in favour of the existence of inverse cascades of magnetic helicity towards small wavenumbers leading to the generation of large-scale magnetic energy.
The ‘sliced-cylinder’ laboratory model of the wind-driven ocean circulation. Part 1. Steady forcing and topographic Rossby wave instability
Authors: Beardsley R. C. , Robbins K.
Published: March 2006

The nonlinear response of the ‘sliced-cylinder’ laboratory model for the wind-driven ocean circulation is re-examined here in part 1 for the case of strong steady forcing. Introduced by Pedlosky & Greenspan (1967), the model consists of a rapidly rotating right cylinder with a planar sloping bottom. The homogeneous contained fluid is driven by the slow rotation of the flat upper lid relative to the rest of the basin. Except in thin Ekman and Stewartson boundary layers on the solid surfaces of the basin, the horizontal flow in the interior and western boundary layer is constrained by the rapid rotation of the basin to be independent of depth. The model thus effectively simulates geophysical flows through the physical analogy between topographic vortex stretching in the laboratory model and the creation of relative vorticity in planetary flows by the β effect.

As the forcing is increased, the flow in both the sliced-cylinder laboratory and numerical models first exhibits downstream intensification in the western boundary layer. At greater forcing, separation of the western boundary current occurs with the development of stationary topographic Rossby waves in the western boundary-layer transition regions. The observed flow ultimately becomes unstable when a critical Ekman-layer Reynolds number is exceeded. We first review and compare the experimental and numerical descriptions of this low-frequency instability, then present a simple theoretical model which successfully explains this observed instability in terms of thelocalbreakdown of the finite-amplitude topographic Rossby waves embedded in the western boundary current transition region. The inviscid stability analysis of Lorenz (1972) is extended to include viscous effects, with the consequence that dissipative processes in the sliced-cylinder problem (i.e. lateral and bottom friction) are shown to inhibit the onset of the instability until the topographic Rossby wave slope exceeds a finite critical value.
The development of weak waves in the steady two-dimensional flow of a gas with vibrational relaxation past a thin wedge
Authors: Hornby R. P. , Johannesen N. H.
Published: March 2006

The method of characteristics is used to calculate the supersonic flow past a wedge of small angle with non-equilibrium effects. The wave decay and development distances are presented in a concise similarity form which permits accurate extrapolation to very weak waves. The numerical solutions are compared with shock-tube flows of CO2 and N2O.
The development of weak waves in the unsteady one-dimensional flow of a vibrationally relaxing gas ahead of an impulsively started piston
Authors: Dain C. G. , Hodgson J. P.
Published: March 2006

The method of characteristics is used to calculate the flow ahead of an impulsively started piston moving at constant velocity. Particular attention is paid to the development of weak shock waves which are either fully or partly dispersed at very large distances from the piston. It is found that the global features of the flows may be represented in similarity form, and the graphs obtained allow extrapolation to very weak waves.
Random waves and dynamo action
Authors: Soward A. M.
Published: March 2006

The propagation of waves in an inviscid, electrically conducting fluid is considered. The fluid rotates with angular velocity Ω* and is permeated by a magnetic field b* which varies on the length scale L = Ql, where Q = Ω*l2/λ (l is the length scale of the waves, λ is the magnetic diffusivity) is assumed large (Q [Gt ] 1). A linearized theory is readily justified in the limit of zero Rossby number R0 (= U0/Ω*l, where U0 is a typical fluid velocity) and for this case it is shown that the total wave energy of a wave train is conserved and transported at the group velocity except for that which is lost by ohmic dissipation. The analysis is extended to encompass the propagation of a sea of random waves.

A hydromagnetic dynamo model is considered in which the fluid is confined between two horizontal planes perpendicular to the rotation axis a distance L0(=O(L)) apart. Waves of given low frequency Ω*0 (= O(R0Q½Ω*)) and horizontal wavenumber l−1 but random orientation are excited at the lower boundary, where the kinetic energy density is 2πρU20. The waves are absorbed perfectly at the upper boundary, so that there is no reflexion. The linear wave energy equation remains valid in the double limit 1 [Gt ] R0Q½[Gt ]Q−½, for which it is shown that dynamo action is possible provided $\Delta = L_0U^2_0/l^3\omega_0^{*2} > 1 $. When dynamo action maintains a weak magnetic field (Δ −1 [Lt ] 1) which only slightly modifies the inertial waves analytic solutions are obtained. In the case of a strong magnetic field (Δ [Gt ] 1) for which Coriolis and Lorentz forces are comparable solutions are obtained numerically. The latter class includes the more realistic case (Δ → ∞) in which the upper boundary is absent.
Viscous flows past spherical gas bubbles
Authors: Brabston D. C. , Keller H. B.
Published: March 2006

Computations of the steady viscous flow past a fixed spherical gas bubble are reported for Reynolds numbers in the range 0·1 [les ]R[les ] 200. Good agreement with Moore's (1963) asymptotic theory for the drag coefficient is obtained forR[les ] 40 and with the well-known small-Rtheory forR[les ] ½. The method of series truncation is used to reduce the problem to a nonlinear two-point boundary-value problem, which is then solved by an accurate and efficient finite-difference procedure.
Source-sink flow in a gas centrifuge
Authors: Matsuda Takuya , Sakurai Takeo , Takeda Hidenori
Published: March 2006

We consider steady non-axisymmetric source-sink flow of a perfect gas in a rapidly rotating circular cylinder for the case in which the sources and the sinks are distributed on the top and bottom. We apply a linearized analysis to a small perturbation from the state of rigid-body rotation. We show that the radial pressure gradient plays an important role in the determination of the axisymmetric part of the flow field and that the effects of viscosity and thermal conductivity govern the overall configuration of the non-axisymmetric part. We also show that the transport of gas in the main inner flow is axial and that radial transport is confined to the horizontal boundary layers.
The effect of turbulence on the surface pressure field of a square prism
Authors: Lee B. E.
Published: March 2006

Measurements are presented of the mean and fluctuating pressure field acting on a two-dimensional square cylinder in uniform and turbulent flows. The addition of turbulence to the flow is shown to raise the base pressure and reduce the drag of the body. It is suggested that this is attributable to the manner in which the increased turbulence intensity thickens the shear layers, which causes them to be deflected by the downstream corners of the body and results in the downstream movement of the vortex formation region. The strength of the vortex shedding is shown to be reduced as the intensity of the incident turbulence is increased.
The slow motion of slender rod-like particles in a second-order fluid
Authors: Leal L. G.
Published: March 2006

The motion of a slender axisymmetric rod-like particle is investigated theoretically for translation through a quiescent second-order fluid and for rotation in a simple shear flow of the same material. The analysis consists of an asymptotic expansion about the limit of rheologically slow flow, coupled with an application of a generalized form of the reciprocal theorem of Lorentz to calculate the force and torque on the particle. It is shown that an arbitrarily oriented particle with fore-aft symmetry translates, to a first approximation, at the same rate as in an equivalent Newtonian fluid, but that the motion of particles with no fore-aft symmetry may be modified at the same level of approximation. In addition, it is found that freely translating particles with fore-aft symmetry exhibit a single stable orientation with the axis of revolution vertical. In simple shear flow at small and moderate shear rates, the non-Newtonian nature of the suspending fluid causes a drift through Jeffery orbits to the equilibrium orbit C = 0 in which the particle rotates about its axis of revolution. At larger shear rates, the particle aligns itself in the direction of flow and ceases to rotate. Comparison with the available experimental data indicates that the measured rate of orbit drift may be used to determine the second normal stress difference parameter of the second-order fluid model. Finally, in an appendix, some preliminary observations are reported of the motion of slender rod-like particles falling through a quiescent viscoelastic fluid.
The preparation of water for surface-clean fluid mechanics
Authors: Scott John C.
Published: March 2006

This paper describes the development of a new technique for removing surface-active contaminants from water so that it may be used for surface-clean experiments in fluid mechanics. The removal of contamination from concentrated aqueous solutions of non-surface-active materials is also possible, allowing considerable variation of density and viscosity in these experiments. Instead of using the conventional distillation processes necessary for most work involving surface chemical phenomena, surface-active substances are removed by adsorption onto a dense current of small nitrogen gas bubbles rising in a long vertical column of the water. The efficiency of the technique was found to increase to a great extent when common salt was dissolved in the water, up to concentrations around 40 g/l, and experiments are described which allow the identification of several physical processes which aid the operation of the method. The adequate performance of the cleaning technique in the removal both of an ionic surface-active material and also of Gentian Violet dye is demonstrated. The method should permit the design of surface-clean experiments using much larger volumes of water than are possible when the water has to be distilled using conventional surface chemical techniques. A simple apparatus for the measurement of surface tension is also described.