bluuebunny/crossref_metadata_2025 huggingface dataset:
Two-dimensional inflated buildings in a cross wind
Authors: Newman B. G. , Goland D.
Published: April 2006

Model experiments have been done on two-dimensional inflated buildings in thick boundary layers that simulate either an onshore wind, or flow over sparsely wooded country. A theory has been developed which replaces the boundary layer by an inviscid flow of uniform vorticity. The replacement flow matches both the velocity and the velocity gradient of the wind at the maximum height of the building. The tension in the membrane is quite well predicted by the theory, but the external pressure is in general too low owing to the presence of separation bubbles at the leading and trailing edges.
Non-uniform discharges of contaminants in shear flows
Authors: Smith Ronald
Published: April 2006

For a non-uniform discharge of contaminant in a shear flow the initial advection velocity and the amount of shear across the contaminant cloud depend upon the discharge shape across the flow. Here i t is shown how the continuing influence of the discharge non-uniformity can be incorporated into a delay-diffusion description of the dispersion process (Smith 198 1). An important improvement over the variable coefficient diffusion equation derived by Gill 85 Sankarasubramanian (1971) is that the solutions have the physically correct superposition property.
Free-surface flow past oscillating singularities at resonant frequency
Authors: Dagan G. , Miloh T.
Published: April 2006

This paper analyses the problem of a flow past an oscillating body moving with constant velocity, below and parallel to a free surface. Special attention is given to frequencies of oscillation in the neighbourhood of the critical frequency ωc= 0.25 g/U, where the classical linearized solution yields infinitely large wave amplitude. As a result both the lift and drag forces acting on the oscillating body at the resonant frequency are singular. It is demonstrated in the paper how this resonance is elimi- nated by considering higher-order free-surface effects, in particular the interaction between the first- and third-order terms. The resulting generalized solution yields finite wave amplitudes at the resonant frequency which are O(ε½) and O(εlogε) for 2 and 3 dimensions respectively. Here 6 is a measure of the singularity strength. It is also shown that inclusion of third-order terms causes a shift in the wavenumber and group velocity which eliminates the singularity in the lift and drag expressions at the resonant frequency. These results are illustrated by computing the lift and drag experienced by a submerged oscillating horizontal doublet in a uniform flow.
Discrete-vortex simulation of a turbulent separation bubble
Authors: Kiya Masaru , Sasaki Kyuro , Arie Mikio
Published: April 2006

The discrete-vortex model is applied to simulate the separation bubble over a two- dimensional blunt flat plate with finite thickness and right-angled corners, which is aligned parallel to a uniform approaching stream. This flow situation is chosen because, unlike most previous applications of the model, the separation bubble is supposed to be strongly affected by a nearby solid surface. The major objective of this paper is to examine to what extent the discrete-vortex model is effective for such a flow. A simple procedure is employed to represent the effect of viscosity near the solid surface; in particular, the no-slip condition on the solid surface. A reduction in the circulation of elemental vortices is introduced as a function of their ages in order to represent the three-dimensional deformation of vortex filaments, An experiment was also performed for comparison purposes.

The calculation yielded reasonable predictions of the time-mean and r.m.s. values of the velocity and the surface-pressure fluctuations, together with correlations between their fluctuating components, over most of the separation bubble. The interrelation between instantaneous spatial variations of the surface-pressure and velocity fluctuations were also obtained. A comparison between the calculated and measured results suggests that, in the real flow, the three-dimensional deformation of vortex filaments will become more and more dominant as the reattachment point is approached.
On flow between counter-rotating cylinders
Authors: Jones C. A.
Published: April 2006

Axisymmetric flows between counter-rotating cylinders of varying radius ratio are examined. The stability of these flows to non-axisymmetric disturbances is considered, and the results of these calculations are compared with experiments.
Wind-induced growth of water waves
Authors: Mitsuyasu H. , Honda T.
Published: April 2006

Spatial growth of mechanically generated water waves under the action of wind has been measured in a laboratory wind-wave flume both for pure water and for water containing a surfactant (sodium lauryl sulphate, concentration 2.6 × 10−2%). I n the latter case, no wind waves develop on the surface of the mechanically generated waves as well as on the still water surface for wind speeds up to U10≈ 15 m/s, where U10 is the wind velocity at the height Z = 10 m. Therefore we can study the wind-induced growth of monochromatic waves without the effects of co-existing short wind waves. The mechanically generated waves grew exponentially under the action of the wind, with fetch in both cases. The measured growth rate β for the pure water can be fitted by β/f = 0.34(U*/C)2 0.1 [lsime ] U*/C [lsime ] 1.0, where f is the frequency of the waves, C is the corresponding phase velocity, and U, is the friction velocity obtained from vertical wind profiles. The effect of the wave steepness H/L on the dimensionless growth rate β/f is not clear, but seems to be small. For water containing the surfactant, the measured growth rate is smaller than that for pure water, but the friction velocity of the wind is also small, and the above relation between β/f and U*/C holds approximately if the measured friction velocity U* is used for the relation.
Rarefaction shock wave near the critical liquid–vapour point
Authors: Borisov A. A. , Borisov Al. A. , Kutateladze S. S. , Nakoryakov V. E.
Published: April 2006

The existence of a rarefaction shock wave or negative shock wave in a substance whose unperturbed state is close to the thermodynamic critical liquid–vapour point has been demonstrated experimentally. Its evolution and propagation velocity in a shock tube with Freon-13 as the test substance are described. It is shown that the steepness of the wave front does not diminish as the wave evolves. An equation is derived that describes the evolution of long-wave perturbations near the critical point.
On perturbation methods in nonlinear stability theory
Authors: Herbert Thorwald
Published: April 2006

This paper reconsiders formal expansion methods for the analysis of the nonlinear properties of a modal disturbance. A survey is given of the various types of expansions based on different assumptions, and their range and shortcomings are discussed. By introducing a well-defined amplitude, Watson's expansion in a time-dependent amplitude is developed into a rational method for uniquely determining Landau constants of arbitrary order. Complementary to the common orthogonality condition for points at the neutral curve, an alternative definition of the Landau constants is given for points in the unstable domain. The method is not restricted to small amplification rates but is invalid in the stable domain. The method of Reynolds and Potter for a direct attack on equilibrium states is extended into a class of rational methods. The methods in this class agree to within a rearrangement of the infinite expansion series but differ in their respective range of validity.
Instantaneous pressure fields at a corner associated with vortex impingement
Authors: Tang Y.-P. , Rockwell D.
Published: April 2006

The impingement of concentrations of vorticity upon a corner is studied using simultaneous flow visualization and correlation of pressure fluctuations, revealing the relations between the instantaneous pressure fields along the top and front faces of the corner and the instantaneous distortion of the incident vortex.

By varying the transverse offset of the corner relative to the incident vortex, several distinct and consistent patterns of incident vortex–corner interaction are evident. The corresponding form and phasing of the instantaneous pressure fields are strongly dependent upon the nature of the vortex–corner interaction, though the maximum amplitude on the top and front faces is always of the same order. For certain interactions, there is separation of flow from the edge of the corner, as well as from the front face of the corner, leading to secondary-vortex formation and corresponding peaks in the local pressure fields.

By integrating the instantaneous pressure fields along the top and front faces of the corner, the phasing between the respective forces is shown to exhibit varying degrees of dipole-like behaviour, depending upon the character of the incident vortex–corner interaction. Amplitudes of the corresponding moments of the pressure fields are remarkably insensitive to this interaction.
Double-diffusive convection caused by coupled molecular diffusion
Authors: Mcdougall Trevor J.
Published: April 2006

Double-diffusive convection is studied for the case where a large coupled diffusion (or cross-diffusion) effect is present. The Soret effect is a familiar example of this cross-diffusion where the flux of the solute depends not only on its own spatial gradient but also on the in situ temperature gradient. The linear stability analysis of double-diffusive convection has been extended to include the two cross-diffusion flux terms and it has been shown that, with a sufficiently large coupled diffusion effect, fingers can form even when the concentrations of both components make the fluid's density gradient statically stable. The conditions under which the diffusive instability can occur are compared with those for the formation of fingers and it is shown that these two types of double-diffusive convection cannot occur together in any particular set of linear property gradients. We then consider finite-amplitude, steady, infinitely long fingers and show that a sufficiently large cross-diffusion effect can again allow fingers to exist when the concentrations of both solutes increase with depth. It is also shown that the diffusion of properties from an initially sharp interface may set up vertical gradients that are favourable for the formation of fingers.
Oscillatory Hele-Shaw convection
Authors: Frick H. , MÜLler U.
Published: April 2006

Time-dependent convection motions in the form of rolls in a thin vertical fluid layer (Hele-Shaw cell) heated from below are investigated numerically. Perpendicular to the convection-roll axis the fluid is bounded by parallel adiabatic rigid sidewalls. Stress-free top, bottom and end boundaries are assumed. The horizontal extension of the convection rolls is described by the wavenumber α. Solutions for the time-dependent behaviour of the convective motion are presented for a range of wavenumbers between α = ½π and 2π. The onset of the oscillation is shifted to higher Rayleigh numbers with increasing wavenumber. The oscillatory Hele-Shaw convection is caused by an instability of the thermal boundary layer, as is evident from the plotted temperature field and streamlines. From the variation of the Nusselt number with time it is found that the oscillatory motion starts with a sinusoidal time dependence and passes into a periodic state with several frequencies as the Rayleigh number is increased. Quantitative and qualitative agreement with previous experimental and numerical results is found.
Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface
Authors: Preisser F. , Schwabe D. , Scharmann A.
Published: April 2006

In liquid columns (Prandtl number 8·9) with free cylindrical surface heated from above, strong thermocapillary convection (TC) has been observed. Stationary thermocapillary convection exists in the form of a single axially symmetric roll bound to the free surface. For aspect ratios l/a < 1 the radial extension of the roll equals the zone length. The stream velocities and the temperature distribution were measured.

The influence of buoyant forces due to horizontal temperature gradients in the experiments was also studied. Buoyant forces become obvious for a contaminated free surface and in bulk regions far from the cylinder surface.

The thermocapillary convection shows a transition to time-dependent oscillatory motion when a critical Marangoni number Mac is exceeded. A unique Mac = 7 × 103 has been found for zones with lengths l < 3·5 mm. The oscillatory state of thermocapillary convection has experimentally been proved to be a distortion of the laminar state in form of a wave travelling in the azimuthal direction. A unique non-dimensional wavenumber ≈ 2·2 (near Mac) of the distortion has been found. The non-dimensional frequency of the temperature oscillations is independent of zone size if the aspect ratio is held constant. However, the non-dimensional frequency of temperature oscillations increases linearly with the aspect ratio of the zone. This result is interpreted as a dependence of the phase velocity of the running disturbance on the aspect ratio.
Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities
Authors: Smith Marc K. , Davis Stephen H.
Published: April 2006

A planar liquid layer is bounded below by a rigid plate and above by an interface with a passive gas. A steady shear flow is set up by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. This dynamic state is susceptible to two types of thermal-convective instabilities: (i) stationary longitudinal rolls, which involve the classical Marangoni instability studied by Pearson; and (ii) unsteady hydrothermal waves, which involve a new mechanism of instability deriving its energy from the horizontal temperature gradients. Thermal stability characteristics for liquid layers with and without return-flow profiles are presented as functions of the Prandtl number of the liquid and the Biot number of the interface. Comparisons are made with available experimental observations.
Dispersal by randomly varying currents
Authors: Csanady G. T.
Published: April 2006

The long-term oceanic dispersal of persistent contaminants is approached as a problem in turbulent diffusion, with tidal, wind-driven, and other variable currents relegated to turbulence. The mean advection velocity in this problem is typically small compared with the r.m.s. fluctuation. Therefore, close to a continuous concentrated source, puffs of contaminant of all ages are present and have significant effects. Old puffs, i.e. those released a long time previously, give rise to a background concentration field. Young puffs affect the local contaminant concentration p.d.f. according to the probability of their presence, quantified by the visitation frequency.

The behaviour of young puffs is governed by variable advection and may be described approximately in terms of probability distributions obtainable from current-meter data. The visitation frequency can be calculated from the distribution of escape probability density, a Lagrangian equivalent of flux. A long-term effect of variable advection is the distribution of the contaminant over an ‘extended’ source, which serves as a starting point for the random walk of old puffs. The conventional approach of using the diffusion equation to describe this random walk is therefore valid as a description of the near-source background concentration field, provided that the extended source is used in place of the physical source.

A sample calculation for a typical open coastal case shows that the background concentration plume becomes wide compared with source dimensions, of order KH/U, with KH horizontal (eddy and shear) diffusivity, U mean advection velocity. The near-source value of the background concentration is correspondingly low, of order m/hKn, with m the mass-release rate and h the water depth. Visitation frequencies calculated with the aid of current statistics drop rapidly with distance from the source, especially in the cross-shore direction. The typical cross-shore diameter of the extended source region is a few kilometres.
A resonant test-field model of gravity waves
Authors: West Bruce J.
Published: April 2006

In this paper we propose an ‘irreversible’ resonant test-field (RTF) model to describe the statistical fluctuations of gravity waves on deep water driven by a turbulent wind field. The non-resonant interactions in the gravity-wave Hamiltonian are replaced by a Markov process in the equation of motion for the resonantly interacting gravity waves, i.e. Hamilton's equations are replaced by a Langevin equation for the RTF waves. The RTF models the irreversible energy-transfer process by a Fokker-Planck equation for the phase-space probability density, the exact steady-state solution of which is determined to be non-Gaussian. An H-theorem for the RTF predicts the monotonic approach to the asymptotic steady state near which the transport properties of the field are studied. The steady-state energy-spectral density is calculated (in some approximation) to be k−4.
Practical use of Hamilton's principle
Authors: Salmon Rick
Published: April 2006

Hamilton's principle of mechanics has special advantages as the beginning point for approximations. First, it is extremely succinct. Secondly, it easily accommodates moving disconnecting fluid boundaries. Thirdly, approximations – however strong – that maintain the symmetries of the Hamiltonian will automatically preserve the corresponding conservation laws. For example, Hamilton's principle allows useful analytical and numerical approximations to the equations governing the motion of a homogeneous rotating fluid with free boundaries.
The effect of Brownian diffusion on shear-induced coagulation of colloidal dispersions
Authors: Feke D. L. , Schowalter W. R.
Published: April 2006

The effect of a small amount of Brownian diffusion on shear-induced coagulation of spherical particles has been calculated. This has been accomplished by considering the binary collision process between a test sphere and identical spheres interacting with the test sphere through induced-dipole attraction, electrostatic repulsion and hydrodynamically induced forces. The effect of diffusion is found by means of an expansion in inverse Péclet number. Specific calculations were performed for uniaxial extension and for laminar shear flow. It is found that Brownian diffusion, the effect of which is nonlinearly coupled with flow type and strength, can act to increase or decrease the coagulation rate.
Propagation of obliquely incident water waves over a trench
Authors: Kirby James T. , Dalrymple Robert A.
Published: April 2006

The diffraction of obliquely incident surface waves by an asymmetric trench is investigated using linearized potential theory. A numerical solution is constructed by matching particular solutions for each subregion of constant depth along vertical boundaries; the resulting matrix equation is solved numerically. Several cases where the trench-parallel wavenumber component in the incident-wave region exceeds the wavenumber for freely propagating waves in the trench are investigated and are found to result in large reductions in wave transmission; however, reflection is not total owing to the finiteness of the obstacle.

Results for one case are compared with data obtained from a small-scale wave-tank experiment. An approximate solution based on plane-wave modes is derived and compared with the numerical solution and, in the long-wave limit, with a previous analytic solution.
A digital technique for the simultaneous measurement of streamwise and lateral velocities in turbulent flows
Authors: Kawall J. G. , Shokr M. , Keffer J. F.
Published: April 2006

A novel, digital, hot-wire anemometer technique for the simultaneous measurement of the instantaneous streamwise and lateral velocity fields in high-intensity turbulent flows is discussed. It involves the use of a three-wire probe comprising two 45° slanted hot wires and a normal hot wire. A comprehensive and systematic examination of several factors that can affect the fidelity of the streamwise and lateral velocity waveforms is developed to assess the performance of the new technique as well as hot-wire systems generally. These factors are: (i) rectification, which stems from the inherent insensitivity of hot wires to the direction of the instantaneous (total) velocity vector in a turbulent flow; (ii) spanwise velocity fluctuations; (iii) axial cooling of hot wires; (iv) unpredictable variations in one of four hot-wire calibration parameters; (v) random hot-wire calibration errors; (vi) spanwise separation of the hot wires. Relevant hot-wire anemometer-response equations relating instantaneous anemometer output voltages to instantaneous flow velocities were established on the basis of extensive voltage-velocity calibration data pertaining to hot wires orientated with respect to the calibration flow velocity at various yaw and pitch angles ranging from 0° to 90°. Simulated Gaussian (streamwise, lateral and spanwise) velocity fields appropriate to flows with turbulence intensity levels varying between 5 and 80% and Reynolds shear-stress coefficients varying between 0.1 and 0.5 were generated by means of a digital computer, and the associated anemometer-voltage signals computed in accordance with the response equations subject to different combinations of the first four of the aforementioned factors. In order to take into account the effects of the last two factors, viz calibration errors and spanwise wire separation, uncorrelated Gaussian ‘noise’ fluctuations were superimposed on the above voltage signals. Estimates of the known (simulated) streamwise and lateral velocity signals were then determined by simultaneous solution of (a) the actual instantaneous response equations, (b) approximate versions of them, and (c) linearized versions of them. The results indicate that reasonably accurate estimates of velocity signals from a turbulent flow can be obtained by means of conventional hot-wire anemometer techniques – which assume that anemometer voltage fluctuations are linear functions of corresponding velocity fluctuations – only if the turbulent intensity level of the flow does not exceed about 20%. In marked contrast, the 3-wire anemometer technique introduced here can be used to measure streamwise and lateral velocity signals simultaneously with a high degree of accuracy for turbulence-intensity levels of up to 40%. In addition, this technique is capable of yielding high-fidelity streamwise velocity waveforms for levels in excess of 70%.
Diffusion in oscillatory pipe flow
Authors: Watson E. J.
Published: April 2006

The rate of mass transfer of a diffusing substance along a pipe is augmented by an oscillatory motion of the ambient fluid in the pipe. The increase of the flux is evaluated for the cases of a circular pipe and of a two-dimensional channel. Results are given for a general cross-section in the limiting cases of slow and fast oscillations of the flow.
The influence of surface tension on cavitating flow past a curved obstacle
Authors: Vanden-Broeck Jean-Marc
Published: April 2006

The problem of cavitating flow past a two-dimensional curved obstacle is considered. Surface tension is included in the dynamic boundary condition. A perturbation solution for small values of the surface tension is presented. It is found that the position of the separation points is uniquely determined by specifying the value of the Weber number and the contact angle at the separation points. In addition, for a given value of the Weber number there exists a particular position of the separation points for which the slope is continuous. This solution tends to the classical solution satisfying the Brillouin–Villat condition as the surface tension tends to zero. Graphs of the results for the cavitating flow past a circular cylinder are presented.
On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Reynolds numbers
Authors: Schewe Günter
Published: April 2006

Force measurements were conducted in a pressurized wind tunnel from subcritical up to transcritical Reynolds numbers 2.3 × 104[les ]Re[les ] 7.1 × 106without changing the experimental arrangement. The steady and unsteady forces were measured by means of a piezobalance, which features a high natural frequency, low interferences and a large dynamic range. In the critical Reynolds-number range, two discontinuous transitions were observed, which can be interpreted as bifurcations at two critical Reynolds numbers. In both cases, these transitions are accompanied by critical fluctuations, symmetry breaking (the occurrence of a steady lift) and hysteresis. In addition, both transitions were coupled with a drop of theCDvalue and a jump of the Strouhal number. Similar phenomena were observed in the upper transitional region between the super- and the transcritical Reynolds-number ranges. The transcritical range begins at aboutRe≈ 5 × 106, where a narrow-band spectrum is formed withSr(Re= 7.1 × 106) = 0.29.
Effects of rotation and shear on doubly diffusive instability
Authors: Worthem Sylvia , Mollo-Christensen E. , Ostapoff F.
Published: April 2006

A linear stability analysis of a doubly diffusive system, with rotation and shear, shows that overstable oscillations can occur in stratifications typical of the equatorial ocean, that internal waves encountering an equatorial current can exchange energy with the current, and that the wave-induced fluxes of salt and heat can lead to layer formation in the salinity, temperature and velocity fields.
On angles of separation in Stokes flows
Authors: O'Neill M. E.
Published: April 2006

A two-dimensional Stokes flow close to the line of contact of two touching cylinders or three-dimensional axisymmetric Stokes flow close to the point of contact of two touching bodies is shown in general to separate into infinite sets of eddies with angles of separation from the bodies which tend to 58.61° as the line or point of contact is approached. The flow near the vertex of a conical cusp is shown to be a system of nested toroidal vortices and the separation angles tend to 45.25° as the vertex is approached. Stokes flow between parallel planes or within a circular cylinder is shown in general to separate far from the generating disturbances with cellular eddy structure and separation angles which tend to 58.61° and 45.25° respectively. The mathematical equivalence of the various problems is established.
On the ability of drops or bubbles to stick to non-horizontal surfaces of solids
Authors: Dussan V. E. B. , Chow Robert Tao-Ping
Published: April 2006

It is common knowledge that relatively small drops or bubbles have a tendency to stick to the surfaces of solids. Two specific problems are investigated: the shape of the largest drop or bubble that can remain attached to an inclined solid surface; and the shape and speed at which it moves along the surface when these conditions are exceeded. The slope of the fluid-fluid interface relative to the surface of the solid is assumed to be small, making it possible to obtain results using analytic techniques. It is shown that from both a physical and mathematical point of view contact-angle hysteresis, i.e. the ability of the position of the contact line to remain fixed as long as the value of the contact angle θ lies within the interval θR [les ] θ [les ] θA, where θA [nequiv ] θR, emerges as the single most important characteristic of the system.
Structure of a turbulent separation bubble
Authors: Kiya Masaru , Sasaki Kyuro
Published: April 2006

Flow in the separation bubble formed along the sides of a blunt flat plate with right-angled corners has been studied in terms of extensive single- and two-point measurements of velocity and surface-pressure fluctuations. The cross-correlations between the surface-pressure and velocity fluctuations are found to be useful for the study of large-scale vortex structure in the bubble. Large-scale vortices are shed downstream from the separation bubble with a frequency of about 0.6U∞/xR, where U∞ is the approaching velocity and xR is the time-mean length of the bubble. On top of this regular vortex shedding, there exists a large-scale unsteadiness in the bubble. Vortices which are much larger than the regular vortices are shed with frequencies less than about 0.2U∞/xR. The large-scale unsteadiness is accompanied by enlargement and shrinkage of the bubble and also by a flapping motion of the shear layer near the separation line. The intermittent nature of the flow in the bubble is clarified in some detail. The distributions of the cross-correlations between the pressure and velocity fluctuations demonstrate the vortex structure in the reattaching zone. The longitudinal distance between the vortices is estimated to be (0.7–0.8) xR and their convection velocity is about 0.5U∞ near the reattachment line. The cross-correlations also suggest the existence of a longitudinal counter-rotating system in the bubble. The distance between the axes of the rotation is of the order of 0.6xR. Variations of timescales, lengthscales and phase velocities of the vortices are presented and discussed.
Measurement of streamwise vorticity fluctuations in a turbulent channel flow
Authors: Kastrinakis Elefterios G. , Eckelmann Helmut
Published: April 2006

In a fully developed turbulent channel flow, measurements of the streamwise vorticity fluctuations ωx have been made. A newly designed probe provides simultaneously in addition to the vorticity signal all three velocity signals. The new probe bears a likeness to the Kovasznay-type vorticity probe, but consists of four electrically independent hot wires, each mounted separately on a total of eight supporting prongs. A new calibration technique had to be developed for this probe.

In addition to various statistical properties of the three velocity components, the distributions of vorticity fluctuations and of skewness and flatness factors are given up to wall distances as close as y+ = 19. A pronounced maximum of the streamwise vorticity fluctuations was found at y+ ≈ 20. Large values of the flatness factor characterize the outer flow region.
Determination of the constitutive equations for a magnetic fluid
Authors: Jansons Kalvis M.
Published: April 2006

The principal aim of this paper is to derive constitutive equations describing a magnetic fluid. The fluid is modelled as a dilute suspension of small spheroidal magnetic particles in a non-magnetic solute. The conditions for stability of fluid (against coagulation) are discussed and upper and lower bounds for particle sizes are determined. For a stationary fluid, the bulk magnetization is calculated with allowance for particle—particle interactions. The full stress tensor is determined for a flowing fluid that experiences an externally applied magnetic field. Both the flow and field may have arbitrary spatial and time dependences provided only that the lengthscale of spatial variations is large compared with particle dimensions, and that the timescale is long compared with the particle relaxation time due to Brownian motion. These results are applied to shear and pipe flows, where comparison with experiment is made, and to flow induced by rotating magnetic fields. Finally the damping of ultrasound having a characteristic period of the same order as the particle relaxation time is considered.
The long-time tail of the angular-velocity autocorrelation function for a rigid Brownian particle of arbitrary centrally symmetric shape
Authors: Hocquart R. , Hinch E. J.
Published: April 2006

The long-time t−5/2 behaviour of the angular-velocity autocorrelation function is determined by the diffusion of fluid motion to large distances, from where the particle appears a point singularity. From an examination of this flow, the coefficient of t−5/2 can be related to some effective aspect ratios which describe how the particle rotates in a simple shear flow.
The concentration-jump coefficient in a rarefied binary gas mixture
Authors: Shen C.
Published: April 2006

In this paper we consider the problem of the concentration jump of a vapour in the vicinity of a plane wall, which consists of the condensed phase of the vapour, in a rarefied gas mixture of that vapour (A) and another ‘inert’ gas (B). The general formulation of the problem of determining the concentration-jump coefficient CdA is given. In the Knudsen layer the simplest model of Boley-Yip theory is used to simplify the Boltzmann equations for the binary gas mixture. The numerical calculation of the concentration jump coefficient CdA for various values of evaporation coefficient αA is illustrated for the case of nB [Gt ] nA for which experimental data are available.
Interaction of rarefaction waves with area reductions in ducts
Authors: Gottlieb J. J. , Igra O.
Published: April 2006

The interaction of a rarefaction wave with a gradual monotonic area reduction of finite length in a duct, which produces transmitted and reflected rarefaction waves and other possible rarefaction and shock waves, was studied both analytically and numerically. A quasi-steady flow analysis which is analytical for an inviscid flow of a perfect gas was used first to determine the domains of and boundaries between four different wave patterns that occur at late times, after all local transient disturbances from the interaction process have subsided. These boundaries and the final constant strengths of the transmitted, reflected and other waves are shown as a function of both the incident rarefaction-wave strength and area-reduction ratio, for the case of diatomic gases and air with a specific-heat ratio of 7/5. The random-choice method was then used to solve numerically the conservation equations governing the one-dimensional non-stationary gas flow for many different combinations of rarefaction-wave strengths and area-reduction ratios. These numerical results show clearly how the transmitted, reflected and other waves develop and evolve with time, until they eventually attain constant strengths, in agreement with quasi-steady flow predictions for the asymptotic wave patterns. Note that in all of this work the gas in the area reduction is initially at rest.
Double-diffusive interleaving due to horizontal gradients
Authors: Holyer Judith Y.
Published: April 2006

In this paper we present a linear stability analysis for an unbounded, vertically stratified fluid which has compensating horizontal temperature and salinity gradients, so there is no horizontal density gradient. We obtain the most unstable perturbation for given linear horizontal and vertical gradients and calculate the growth rates, the vertical lengthscale of the intrusion and the slope of the intrusion to the horizontal. We show that the system is most unstable to two-dimensional disturbances and that, except for a small region in which the temperature stratification is unstable and the salinity stratification is stable, the most-unstable disturbance is non-oscillatory. We also obtain a solution to the fully nonlinear equations and calculate the fluxes of heat and salt. The nonlinear solution shows that alternating interfaces of salt-finger and diffusive interfaces will eventually appear on the intrusion when the vertical stratifications are both stable.
The resonant interaction of disturbances at laminar-turbulent transition in a boundary layer
Authors: Kachanov Yu. S. , Levchenko V. Ya.
Published: April 2006

The three-dimensional resonant interaction of a plane Tollmien-Schlichting wave, having a frequencyf1, with a pair of oblique waves having frequencies ½f1, was observed and studied experimentally. In the initial stages, the interaction proved to be a parametric resonance, resulting in the amplification of small random priming (background) oscillations of frequency ½f1, and of a packet of low-frequency oscillations. The resonant interaction of waves in a boundary layer was investigated also by introducing a priming oscillation with frequencyf’ = ½f1+ Δffor different values of the frequency detuning Δf. The importance of the discovered wave interaction in boundary-layer transition is demonstrated. Causes of realization of different types of laminar-flow breakdown are discussed.
Secondary flow and turbulence in a cone-and-plate device
Authors: Sdougos H. P. , Bussolari S. R. , Dewey C. F.
Published: April 2006

The flow between a shallow rotating cone and a stationary plate has been investigated using flow visualization, hot-film heat-transfer probes, and measurements of the torque required to rotate the cone against the retardation of the viscous fluid that fills the device. Theory appropriate to these experiments is also presented.

An expansion of the Navier–Stokes equations is performed for small values of the single parameter $\tilde{R} = r^2\omega\alpha^2/12\nu $. (Here r is the local radius, ω the angular velocity of the cone, α([Lt ] 1) is the angle between the cone and plate, and v is the fluid kinematic viscosity.) The measurements at low rotational speeds describe a simple linear velocity profile as predicted for the laminar flow of a Newtonian fluid. At larger rotational speeds, strong secondary flows are observed. There is agreement between the laminar theory and the measured streamline angles and shear stresses for values of $\tilde{R} < 0.5$. Turbulence is observed for $\tilde{R} \gtrsim 4$.
Hydrodynamics of small tubular pumps
Authors: Dijksman J. F.
Published: April 2006

Miniature tubular pumps are used to emit droplets from ink-jet matrix heads. This paper deals with the simulation of the behaviour of a viscous and compressible liquid in such pumps. The response of the liquid in the frequency and time domain is analysed.

An approximate method is given to determine the droplet speed and size.
On the detection of turbulence-generating events
Authors: Alfredsson P. Henrik , Johansson Arne V.
Published: April 2006

The structure of turbulence, especially in the near-wall region, was studied with the variable-interval time-averaging (VITA) technique and the uv-quadrant method. Both methods were applied to the same set of data, measured in a fully developed turbulent channel flow, to detect events associated with turbulence production. A close correspondence was found between VITA events and ejection type of events detected with the uv-quadrant method. Conditional averages of the fluctuating component of the streamwise velocity (u) and the component normal to the wall (v), as well as of the product uv, were constructed with both methods, and the cause for some of the apparent differences was investigated. In contrast to previous findings it was concluded that the uv-pattern obtained with the VITA technique has only one peak, and hence is quite similar to that obtained with the uv-quadrant method. It was shown that large peaks in the uv-signal (with u < 0, v > 0) imply large instantaneous outflow angles. For typical VITA events the outflow angle was often found to exceed 10°. Some events with large uv-peaks did not correspond to any strong activity in the u-component, but could be detected by applying the VITA technique to the v-signal.
Effect of gravity waves on turbulence decay in stratified fluids
Authors: Weinstock J.
Published: April 2006

A theoretical calculation is made of the decay of turbulence energy in the presence of coherent internal gravity waves of various intensities. The wave-turbulence interaction considered is energy production by wave shear. The production term (stress) is calculated by a second-order closure, with temperature fluctuations accounted for by buoyancy subrange theory. This formalism applies to large or small turbulence Froude number, both extremes of which are often encountered in experimental turbulence decay. The theoretical turbulence decay is shown to be a universal function of the wave shear (strain rate) and wave frequency provided that the energy is expressed in terms of the buoyancy wavenumberkB, and time is expressed in terms ofN, the Brunt-Väisälä frequency. With the amplitude of wave shear characterized by a gradient Richardson numberRi0, the turbulence decay is found to undergo a sudden transition from rapid decay to a much slower oscillating decay whenRi0is less than about 0.4. The transition time occurs at aboutt≈ 2πN−1. IfRi0exceeds 0.8 the rate of decay exceeds that of a neutral fluid. A transition in turbulence decay was observed in experiments by Dickey & Mellor (1980). It might explain the continued presence of turbulence in dynamically stable regions of oceans or atmosphere. The theory is compared in much detail with the Dickey & Mellor experiment. A briefer comparison is also made with other experiments, and with previous calculations of turbulence maintenance by steady mean shear. A simple explanation is proposed of why a transition is observed in a vertical grid experiment but not in horizontal grid experiments.
Jumps in layered miscible fluids
Authors: Wood I. R. , Simpson J. E.
Published: April 2006

Experiments with hydraulic jumps in a layered flow with a small density difference at the interface are described. Two different configurations are examined, with shear between the fluids either upstream or downstream of the jump. It is shown that when the shear stress on all interfaces is small enough for there to be no mixing either the theory which assumes hydrostatic pressure on the face of the jump or that which assumes energy conservation in one of the layers describes the results. In the experiments for a jump in the lee of a towed obstacle this condition is always satisfied, but for a jump advancing into stationary layers it is only satisfied when the ratio of the height behind the jump to that in front is less than about 2. Beyond this limit there is mixing behind the first wave of the undular jump and the flow behaves like the head of a gravity current. The theory with energy conservation in one layer is extended to the case of a stationary jump, and for this case it is shown that for a given downstream control an approximate value of the fluid entrained can be computed.
Numerical computation of time-dependent Taylor-vortex flows in finite-length geometries
Authors: Neitzel G. P.
Published: April 2006

The time-dependent Navier-Stokes equations are integrated numerically for a finite-length concentric-cylinder geometry. The motion is initiated by an impulsive start of the inner cylinder from a state of rest. The transient development of a Taylor-vortex structure is discussed from the standpoint of the amplitude history, the onset time and vortex-front propagation; steady-state results are compared with previously published experimental results.
Over-reflection of internal-inertial waves from the mixed layer
Authors: Kamachi M. , Grimshaw R.
Published: April 2006

Near-inertial oscillations associated with downward energy propagation are commonly observed in the upper ocean. Stern (1977) has suggested that these observations may be internal-inertial waves over-reflected from the shear zone at the base of the mixed layer. In this paper we develop a criterion for over-reflection as a function of wavenumber and frequency for a class of shear flows in the mixed layer. By examining the vertical profile of the vertical wave action flux we demonstrate that the source of the over-reflection is the shear at the base of the mixed layer, which is maintained by the wind-induced turbulent Reynolds stress, here parametrized as a body force. The relationship between over-reflection and the wave-induced Lagrangian-mean flow is determined. We also determine a criterion for unstable waves, and show that these are contiguous in wavenumber-frequency space with points of resonant over-reflection. However, the growth rates of these unstable waves are quite small, and in practice unstable waves will be indistinguishable from waves generated by over-reflection.
On the propagation of waves exhibiting both positive and negative nonlinearity
Authors: Cramer M. S. , Kluwick A.
Published: April 2006

One-dimensional small-amplitude waves in which the local value of the fundamental derivative changes sign are examined. The undisturbed medium is taken to be a Navier–Stokes fluid which is at rest and uniform with a pressure and density such that the fundamental derivative is small. A weak shock theory is developed to treat inviscid motions, and the method of multiple scales is used to derive the nonlinear parabolic equation governing the evolution of weakly dissipative waves. The latter is used to compute the viscous shock structure. New phenomena of interest include shock waves having an entropy jump of the fourth order in the shock strength, shock waves having sonic conditions either upstream or downstream of the shock, and collisions between expansion and compression shocks. When the fundamental derivative of the undisturbed media is identically zero it is shown that the ultimate decay of a one-signed pulse is proportional to the negative 1/3-power of the propagation time.
Study of turbulent structure with hot wires smaller than the viscous length
Authors: Willmarth William W. , Sharma Lalit K.
Published: April 2006

The small-scale structure of the streamwise velocity fluctuations in the wall region of a turbulent boundary layer is examined in a new wind-tunnel facility using hot-wires smaller than any previously constructed (typical dimensions: l = 25 μm, d = 0.5 μm). In the boundary layer in which the measurements were made, the ratio of the hot-wire length to the viscous length is 0.3. The turbulent intensity measured with the small hot wires is larger than that measured with longer wires owing to the better spatial resolution of the small wires. The velocity fluctuations measured by the small hot wires are also analysed to determine the burst frequency at two Reynolds numbers and at various distances from the wall. The dimensionless burst frequency does not depend on the Reynolds number when scaled with wall parameters. However, it increases with Reynolds number when scaled with outer variables. Velocity fluctuations measured by two hot wires, less than two viscous lengths apart, are analysed to reveal the small-scale features present during a burst and in the absence of a burst. The main conclusions are: (1) intermittent small-scale shear layers occur most frequently when bursts are present, less frequently just after a burst, and even less frequently just before a burst; and (2) on occasion the velocity gradient of the small-scale shear layers is as large as the mean-velocity gradient at the wall.