bluuebunny/crossref_metadata_2025 huggingface dataset:
A two-dimensional boundary layer encountering a three-dimensional hump
Authors: Smith F. T. , Sykes R. I. , Brighton P. W. M.
Published: April 2006

A shallow three-dimensional hump disturbs the two-dimensional incompressible boundary layer developed on an otherwise flat surface. The steady laminar flow is studied by means of a three-dimensional extension of triple-deck theory, so that there is the prospect of separation in the nonlinear motion. As a first step, however, a linearized analysis valid for certain shallow obstacles gives some insight into the flow properties. The most striking features then are the reversal of the secondary vortex motions and the emergence of a ‘corridor’ in the wake of the hump. The corridor stays of constant width downstream and within it the boundary-layer displacement and skin-friction perturbation are much greater than outside. Extending outside the corridor, there is a zone where the surface fluid is accelerated, in contrast with the deceleration near the centre of the corridor. The downstream decay (e.g. of displacement) here is much slower than in two-dimensional flows.
Variable-viscosity flows in heated and cooled channels
Authors: Ockendon H. , Ockendon J. R.
Published: April 2006

An asymptotic description is given of Newtonian fluid flow in a channel which is suddenly heated or cooled. The viscosity is assumed to be purely a function of temperature. The asymptotic approximation is that the downstream viscosity at the channel wall differs by an order of magnitude from that in the upstream flow. Although we make the drastic assumption that viscous dissipation is negligible, we can analyse flows where the viscosity depends either algebraically or exponentially on the temperature.
Variable-viscosity flows in channels with high heat generation
Authors: Pearson J. R. A.
Published: April 2006

This paper presents a similarity solution for plane channel flow of a very viscous fluid, whose viscosity is exponentially dependent upon temperature, when heat generation is very large. A dimensionless formulation of the problem involves two length scales (the depthhand lengthl, respectively, of the channel), one velocity scale (the mean velocityVof the fluid along the channel), the thermal conductivityk, thermal diffusivitykand viscosityVof the fluid, and the temperature coefficientbof the viscosity. From these, two important dimensionless groups arise, the Graetz number (Gz = Vh2/kl) and the Nahme–Griffith number (G= μV2b/k). In the case of steady flow withG−1[Lt ]Gz−1[Lt ] 1 a thin thermal boundary layer of thickness proportional toGz−½arises at each wall with an even thinner shear layer, detached from the wall and embedded in the thermal boundary layer, of thickness proportional toGz−½(lnG)−1, coinciding with the region of maximum temperature (lnG)/b. The similarity variable is (Pe½y/x½) wherePeis the Péclet number (Vh/k) andyandxare measured away from and along (either) boundary wall. The analogous unsteady uniform flow solution is also given.
Small perturbation expansions in unsteady aerofoil theory
Authors: Graham J. M. R. , Kullar I.
Published: April 2006

Perturbation expansions are derived to second order in a wavenumber parameter for the unsteady lift induced on an aerofoil by disturbances convected past it at subsonic speeds. The results are used to discuss other approximate methods which have been used to predict the unsteady forces and noise generated by an aerofoil in turbulent flow.
Experimental study of the stability of heated laminar boundary layers in water
Authors: Strazisar A. J. , Reshotko E. , Prahl J. M.
Published: April 2006

Linear sinusoidal disturbances are introduced into the boundary layer over a heated flat plate of uniform surface temperature using a vibrating ribbon. The experiment is performed in a low turbulence water tunnel with free-stream turbulence intensities of 0[sdot ]1–0[sdot ]2%. Measurements are made using temperature-compensated hot-film anemometry. Neutral-stability characteristics obtained for the unheated case agree favourably with previous results obtained both in water and in air. Neutral-stability and spatial disturbance-growth-rate characteristics measured for wall temperatures up to 8°F above the free-stream temperature verify trends established by parallel-flow solutions of the disturbance momentum and energy equations. Disturbance growth rates and the band of amplified disturbance frequencies both decrease as wall heating is increased. The experimentally observed increase in the minimum critical Reynolds number Recmin with increased wall heating agrees with the trend predicted by theory. However, effects of non-parallel flow act to reduce the measured values of Recmin by about 120 units compared with predicted parallel-flow values independent of the level of wall heating.
Computational and experimental investigations of two-dimensional nonlinear peristaltic flows
Authors: Brown Thomas D. , Hung Tin-Kan
Published: April 2006

An implicit finite-difference technique employing orthogonal curvilinear co-ordinates is used to solve the Navier–Stokes equations for peristaltic flows in which both the wall-wave curvature and the Reynolds number are finite (§2). The numerical solutions agree closely with experimental flow visualizations. The kinematic characteristics of both extensible and inextensible walls (§3) are found to have a distinct influence on the flow processes only near the wall. Without vorticity, peristaltic flow observed from a reference frame moving with the wave will be equivalent to steady potential flow through a stationary wavy channel of similar geometry (§4). Solutions for steady viscous flow (§5) are obtained from simulation of unsteady flow processes beginning from an initial condition of potential peristaltic flow. For nonlinear flows due to a single peristaltic wave of dilatation, the highest stresses and energy exchange rates (§6) occur along the wall and in two instantaneous stagnation regions in the bolus core. A series of computations for periodic wave trains reveals that increasing the Reynolds number from 2[sdot ]3 to 251 yields a modest augmentation in the ratio of flow rate to Reynolds number but induces a much greater increase in the shear stress (§7.1). The transport effectiveness is markedly reduced for pumping against a mild adverse pressure drop (§7.2). Increasing the wave amplitude will lead to the development of travelling vortices within the core region of the peristaltic flow (§7.3).
Rods falling near a vertical wall
Authors: Russel W. B. , Hinch E. J. , Leal L. G. , Tieffenbruck G.
Published: April 2006

As an inclined rod sediments in an unbounded viscous fluid it will drift horizontally but will not rotate. When it approaches a vertical wall, the rod rotates and so turns away from the wall. Illustrative experiments and a slender-body theory of this phenomenon are presented. In an incidental study the friction coefficients for an isolated rod are found by numerical solution of the slender-body integral equation. These friction coefficients are compared with the asymptotic results of Batchelor (1970) and the numerical results of Youngren ' Acrivos (1975), who did not make a slender-body approximation.
Differential equations for long-period gravity waves on fluid of rapidly varying depth
Authors: Hamilton James
Published: April 2006

The conventional long-wave equations for waves propagating over fluid of variable depth depend for their formal derivation on a Taylor series expansion of the velocity potential about the bottom. The expansion, however, is not possible if the depth is not an analytic function of the horizontal co-ordinates and it is a necessary condition for its rapid convergence that the depth is also slowly varying. We show that if in the case of two-dimensional motions the undisturbed fluid is first mapped conformally onto a uniform strip, before the Taylor expansion is made, the analytic condition is removed and the approximations implied in the lowest-order equations are much improved.

In the limit of infinitesimal waves of very long period, consideration of the form of the error suggests that by modifying the coefficients of the reformulated equation we may find an equation exact for arbitrary depth profiles. We are thus able to calculate the reflexion coefficients for long-period waves incident on a step change in depth and a half-depth barrier. The forms of the coefficients of the exact equation are not simple; however, for these particular cases, comparison with the coefficients of the reformulated long-wave equation suggests that in most cases the latter may be adequate. This opens up the possibility of beginning to study finite amplitude and frequency effects on regions of rapidly varying depth.
Heat thermal structure in the interfacial boundary layer measured in an open tank of water in turbulent free convection
Authors: Katsaros Kristina B. , Liu W. Timothy , Businger Joost A. , Tillman James E.
Published: April 2006

The thermal structure in the boundary layer and its relation to the heat flux from the cooling and evaporating surface of a deep tank of water are investigated. When a deep layer of water in contact with still air above loses heat to the air, the cooled water in a region just under the surface converges along lines and then plunges down in sheets. These sheets of falling water dissipate as they move into the body of the water, which is in turbulent motion. The vertical profiles of the horizontally averaged temperature and its standard deviation agree fairly closely with theoretical profiles based on time averages of the solution to the heat diffusion equation. The differences between observed and thus predicted profile shapes are consistent with the expected effects of the falling cold thermals and the warm return flow, which are neglected in the theories. The profiles of the standard deviation have large values up to the interface and lie between predictions based on boundary conditions of constant surface temperature and constant heat flux, in keeping with the experimental conditions.

The relation between the net heat flux and the temperature difference across the boundary layer is given in non-dimensional form by N = 0[sdot ]156R0[sdot ]33, which is in good agreement with the asymptotic similarity prediction N [vprop ] R1/3 but lower than theoretical calculations of the upper bound of N vs. R.
Wind-forced linear and nonlinear Kelvin waves along an irregular coastline
Authors: Clarke Allan J.
Published: April 2006

Using a normal and tangential co-ordinate approach, a perturbation theory is developed for wind-forced linear and nonlinear Kelvin waves propagating along an irregular coastline. The theory is valid for coastline curvatures which are non-dimensionally small, the curvature being non-dimensionalized with respect to the reciprocal of the boundary-layer trapping scale, i.e. the reciprocal of the radius of deformation. According to linear theory, the main effect of a coastline of small curvature is to cause a phase-speed change in the wave (from – c to – c(1 – ½k(s)), where k(s) is the non-dimensional curvature a distance s along the coast from the origin) and to make the offshore Ekman transport change more rapidly along the coast, the latter effect implying a more ‘wavelike’ ocean or lake response. Two discernible nonlinear effects were found to be an increase (decrease) in the linear-solution longshore gradients in regions of positive (negative) isopycnal displacement and a tendency for increased (decreased) isopyncal displacement at capes (bays).
Eulerian and Lagrangian renormalization in turbulence theory
Authors: Kraichnan Robert H.
Published: April 2006

Systematic renormalized perturbation expansions for turbulence and turbulent convection are constructed which are invariant at each order under random Galilean transformations. Two types of expansion are developed whose lowest truncations give, respectively, the Lagrangian-history direct-interaction approximation and the abridged Lagrangian-history direct-interaction approximation. These approximations previously were derived as heuristic modifications of the Eulerian direct-interaction approximation (Kraichnan 1965). The techniques used involve reversion of primitive perturbation expansions for the generalized velocity field u(x, t/s), defined as the velocity measured at time s in the fluid element which passes through x at time t. The new expansions are illustrated by application to a random linear oscillator, to passive-scalar convection by a random velocity and to the Lagrangian velocity covariance. The lowest term of the expansion for the passive scalar gives Taylor's (1921) exact result for dispersion of fluid elements, and higher terms describe the deviations of the particle-displacement distribution from Gaussian form. In all the applications the assumed underlying statistics are more general than Gaussian statistics, which appear as a special case.
Finite amplitude instability of plane Couette flow
Authors: Coffee Terence
Published: April 2006

The Orr–Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials and the generalized Rayleigh quotient iteration. Accurate results for large values of the parameters are obtained, and these further verify the belief that plane Couette flow is stable to infinitesimal disturbances. For finite disturbances, a formal expansion based on the method of Stuart and Watson as modified by Reynolds & Potter is used. This method shows a transition to instability for a large enough amplitude.
Effects of horizontally two-dimensional bodies on the mass transport near the sea bottom
Authors: Lamoure Jacques , Mei Chiang C.
Published: April 2006

Mass transport close to the sea bottom is investigated for simple harmonic waves around a body with a small horizontal dimension. For gravity waves it is shown that the mass transport very near the bottom points towards a convex corner, but near the top of the boundary layer its direction reverses. Possible implications for silting near a pile and a harbour entrance are discussed and some experimental evidence given. For tides, the Coriolis force introduces a spiralling variation within the boundary layer, and possible inferences for coastline modification are drawn.
Wall shear stress caused by small amplitude perturbations of turbulent boundary-layer flow: an experimental investigation
Authors: Ronneberger D. , Ahrens C. D.
Published: April 2006

The oscillation of the wall shear stress caused by imposing sound on a turbulent boundary-layer flow constitutes a boundary condition for the solution of the acoustic wave equation. The no-slip condition at the wall requires the excitation of a shear wave which is superimposed on the sound wave. The shear wave propagates into the turbulent medium. The wall impedance (shear stress/velocity) of streamwise polarized shear waves has been measured in two different ways, namely (a) by evaluating the phase velocity and the attenuation of a plane sound, wave which propagates in turbulent pipe flow, and (b) by evaluating the resonance frequency and the quality factor of a longitudinally vibrating glass pipe which carries turbulent flow. The results, which were obtained over a wide range of Strouhal numbers, exhibit very good agreement between the two measuring methods. The wall shear stress impedance is strongly affected by the turbulence. This indicates that the turbulent shear stress is modulated by the shear wave. At all measuring conditions, the propagation of the shear wave was confined essentially to the inner portion of the turbulent boundary layer. In principle, two different Strouhal numbers, based on inner and outer variables respectively, describe the dynamics of the Reynolds stress, even in the inner layer (Laufer & Badri Narayanan 1971). However, it turns out that the outer Strouhal number (based on the diameter and the centre-line velocity) has no noticeable effect on the wall shear stress impedance. The dependence of the impedance on the inner Strouhal number (based on the friction velocity and the viscosity) reveals that the shear wave is strongly reflected at the edge of the viscous sublayer. It is concluded that the stress-to-strain ratio at the edge of the viscous sublayer corresponds either to a viscoelastic medium or even to a medium with negative viscosity.
Numerical solution of conservation equations arising in linear wave theory: application to aeroacoustics
Authors: Candel SÉBastien M.
Published: April 2006

The propagation of waves in slightly inhomogeneous dispersive media is conveniently described by a geometrical or kinematic theory. In such frameworks the solution of the propagation problem is constructed by (a) deriving a dispersion relation and determining its characteristic lines and (b) solving an equation expressing the conservation of a field invariant like the wave action. This paper is concerned with the implementation of the last step under general field and boundary conditions. The method presented is based on the derivation of a variational system of differential equations for the geodesic elements of the wave front. The elementary cross-section of the wave front is obtained by integration and the principle of conservation of the field invariant directly yields the field amplitude. In addition, suitable jump conditions are derived for treating specular reflexions at solid boundaries. The method is illustrated by specific problems of interest in aeroacoustics.
Acoustic scattering by density gradients
Authors: Kempton A. J.
Published: April 2006

In this paper we solve some model problems by the method of matched expansions and deduce some features of Green's function using the reciprocal theorem to demonstrate that scattering by density gradients can enhance the radiation efficiency of quadrupoles to that of dipoles. If a fluid is subjected to body forces close to and on both sides of a density interface, then the source system degenerates to a quadrupole only if the components of the forces perpendicular to the interface are equal in magnitude and opposite in direction and, additionally, the components of the forces per unit fluid density parallel to the interface are equal but opposite. In other cases dipole rather than quadrupole radiation efficiency is achieved. But we also show that, despite published assertions to the contrary, the radiation efficiency is not enhanced further and there is no monopole contribution to the radiated sound.
Laminar flow in a square duct of strong curvature
Authors: Humphrey J. A. C. , Taylor A. M. K. , Whitelaw J. H.
Published: April 2006

Calculated values of the three velocity components and measured values of the longitudinal component are reported for the flow of water in a 90° bend of 40 x 40mm cross-section; the bend had a mean radius of 92mm and was located downstream of a 1[sdot ]8m and upstream of a 1[sdot ]2m straight section. The experiments were carried out at a Reynolds number, based on the hydraulic diameter and bulk velocity, of 790 (corresponding to a Dean number of 368). Flow visualization was used to identify qualitatively the characteristics of the flow and laser-Doppler anemometry to quantify the velocity field. The results confirm and quantify that the location of maximum velocity moves from the centre of the duct towards the outer wall and, in the 90° plane, is located around 85% of the duct width from the inner wall. Secondary velocities up to 65% of the bulk longitudinal velocity were calculated and small regions of recirculation, close to the outer corners of the duct and in the upstream region, were also observed.

The calculated results were obtained by solving the Navier–Stokes equations in cylindrical co-ordinates. They are shown to exhibit the same trends as the experiments and to be in reasonable quantitative agreement even though the number of node points used to discretize the flow for the finite-difference solution of the differential equations was limited by available computer time and storage. The region of recirculation observed experimentally is confirmed by the calculations. The magnitude of the various terms in the equations is examined to determine the extent to which the details of the flow can be represented by reduced forms of the Navier–Stokes equations. The implications of the use of so-called ‘partially parabolic’ equations and of potential- and rotational-flow analysis of an ideal fluid are quantified.
On the dispersion of small particles suspended in an isotropic turbulent fluid
Authors: Reeks M. W.
Published: April 2006

A solution to the dispersion of small particles suspended in a turbulent fluid is presented, based on the approximation proposed by Phythian for the dispersion of fluid points in an incompressible random fluid. Motion is considered in a frame moving with the mean velocity of the fluid, the forces acting on the particle being taken as gravity and a fluid drag assumed linear in the particle velocity relative to that of the fluid. The probability distribution of the fluid velocity field in this frame is taken as Gaussian, homogeneous, isotropic, stationary and of zero mean. It is shown that, in the absence of gravity, the long-time particle diffusion coefficient is in general greater than that of the fluid, approaching with increasing particle relaxation time a value consistent with the particle being in an Eulerian frame of reference. The effect of gravity is consistent with Yudine's effect of crossing trajectories, reducing unequally the particle diffusion in directions normal to and parallel to the direction of the gravitational field. To characterize the effect of flow and gravity on particle diffusion it has been found useful to use a Froude number defined in terms of the turbulent intensity rather than the mean velocity. Depending upon the value of this number, it is found that the particle integral time scale may initially decrease with increasing particle relaxation time though it eventually rises and approaches the particle relaxation time. It is finally shown how this analysis may be extended to include the extra forces generated by the fluid and particle accelerations.
Microscale temperature and velocity spectra in the atmospheric boundary layer
Authors: Williams R. M. , Paulson C. A.
Published: April 2006

High-frequency fluctuations in temperature and velocity were measured at a height of 2 m above a harvested, nearly level field of rye grass. Conditions were both stably and unstably stratified. Reynolds numbers ranged from 370000 to 740000. Measurements of velocity were made with a hot-wire anemometer and measurements of temperature with a platinum resistance element which had a diameter of 0[sdot ]5 μm and a length of 1 mm. Thirteen runs ranging in length from 78 to 238 s were analysed.

Spectra of velocity fluctuations are consistent with previously reported universal forms. Spectra of temperature, however, exhibit an increase in slope with increasing wavenumber as the maximum in the one-dimensional dissipation spectrum is approached. The peak of the one-dimensional dissipation spectrum for temperature fluctuations occurs at a higher wavenumber than that of simultaneous spectra of the dissipation of velocity fluctuations. It is suggested that the change in slope of the temperature spectra and the dissimilarity between temperature and velocity spectra may be due to spatial dissimilarity in the dissipation of temperature and velocity fluctuations. The temperature spectra are compared with a theoretical prediction for fluids with large Prandtl number, due to Batchelor (1959). Even though air has a Prandtl number of 0[sdot ]7, the observations are in qualitative agreement with predictions of the theory. The non-dimensional wavenumber at which the increase in slope occurs is about 0[sdot ]02, in good agreement with observations in the ocean reported by Grantet al. (1968).

For the two runs for which the stratification was stable, the normalized spectra of the temperature derivative fall on average slightly below the mean of the spectra of the remaining runs in the range in which the slope is approximately one-third. Hence the Reynolds number may not have always been sufficiently high to satisfy completely the conditions for an inertial subrange.

Universal inertial-subrange constants were directly evaluated from one-dimensional dissipation spectra and found to be 0[sdot ]54 and 1[sdot ]00 for velocity and temperature, respectively. The constant for velocity is consistent with previously reported values, while the value for temperature differs from some of the previous direct estimates but is only 20% greater than the mean of the indirect estimates. This discrepancy may be explained by the neglect in the indirect estimates of the divergence terms in the conservation equation for the variance of temperature fluctuations. There is weak evidence that the one-dimensional constant, and hence the temperature spectra, may depend upon the turbulence Reynolds number, which varied from 1200 to 4300 in the observations reported.
Unsteady flow in a supersonic cascade with strong in-passage shocks
Authors: Goldstein M. E. , Braun Willis , Adamczyk J. J.
Published: April 2006

Linearized theory is used to study the unsteady flow in a supersonic cascade with in-passage shock waves. We use the Wiener–Hopf technique to obtain a closed-form analytical solution for the supersonic region. To obtain a solution for the rotational flow in the subsonic region we must solve an infinite set of linear algebraic equations. The analysis shows that it is possible to correlate quantitatively the oscillatory shock motion with the Kutta condition at the trailing edges of the blades. This feature allows us to account for the effect of shock motion on the stability of the cascade.

Unlike the theory for a completely supersonic flow, the present study predicts the occurrence of supersonic bending flutter. It therefore provides a possible explanation for the bending flutter that has recently been detected in aircraft-engine compressors at higher blade loadings.
The interaction of sound with a subsonic jet issuing from a semi-infinite cylindrical pipe
Authors: Munt R. M.
Published: April 2006

The transmission of sound out of a semi-infinite circular jet pipe in the presence of subsonic flow from the pipe is investigated. An unstable cylindrical vortex layer attached to the edge of the pipe is considered across which differences in mean subsonic flow, density and temperature are included. A solution satisfying the Kutta condition and causality is found which possesses an instability wave term that dominates within a region of approximately 45° to the downstream jet axis. It is shown that when an exterior flow is imposed the noise level increases upstream whilst the instability wave weakens downstream. The stable part of the solution is shown to agree very well with some recent experimental results.
A time-domain analysis of the large-scale flow structure in a circular jet. Part 1. Moderate Reynolds number
Authors: Bruun H. H.
Published: April 2006

This paper presents a new experimental time-domain technique for the evaluation of the large-scale structure in a turbulent flow. The technique is demonstrated by hot-wire anemometry for a circular jet flow at a moderate Reynolds number of 104, and the large-scale structure identified is compared successfully with smoke flow-visualization observations. The temporal and spatial relationships of the separate large-scale flow events have been derived, and this information enabled the evaluation of the nonlinear spatial development of the large-scale flow structure.
Pattern-recognized structures in bounded turbulent shear flows
Authors: Wallace James M. , Brodkey Robert S. , Eckelmann Helmut
Published: April 2006

It is now well established that coherent structures exist in turbulent shear flows. It should be possible to recognize these in the turbulence signals and to program a computer to extract and ensemble average the corresponding portions of the signals in order to obtain the characteristics of the structures. In this work only the u-signal patterns are recognized, using several simple criteria; simultaneously, however, the v or w signals as well as uv or uw are also processed. It is found that simple signal shapes describe the turbulence structures on the average. The u-signal pattern consists of a gradual deceleration from a local maximum followed by a strong acceleration. This pattern is found in over 65% of the total sample in the region of high Reynolds-stress production. The v signal is found to be approximately 180° out of phase with the u signal. These signal shapes can be easily associated with the coherent structures that have been observed visually. Their details have been enhanced by quadrant truncating. These results are compared with randomly generated signals processed by the same method.
An averaged-equation approach to particle interactions in a fluid suspension
Authors: Hinch E. J.
Published: April 2006

Earlier ideas are combined to produce a systematic approach both to forming the bulk equations of motion of a dilute suspension and to calculating the overall hydrodynamic interactions between the suspended particles. Equations governing averaged field quantities are derived by taking ensemble averages of the conservation laws and constitutive relations. The bulk equations thus produced contain a term in which the averaging is performed holding one particle fixed. If now the same prescription is applied to fields averaged with one particle fixed, equations are produced containing a term averaged with two particles fixed, and so on up an infinite hierarchy. The hierarchy can be truncated in an asymptotic analysis for small particle concentrations.

This approach to the mechanics of suspensions is illustrated by applying it to three problems which have already been well studied by different methods. The problems concern the first effects of hydrodynamic interactions on the bulk stress and sedimentation velocity of a free suspension, and on the permeability of a fixed bed. Earlier results are recovered in a new light. Multiparticle effects, which before have occurred as divergent sums, are seen to arise because the suspension described by the averaged equations assumes a viscosity and density different from the solvent, or in the case of the fixed bed because the suspension starts behaving as a porous medium instead of as a Newtonian solvent. A close connexion is thus revealed between the averaged-equation description of the interactions and a self-consistent-field model.
The motions of a floating slender torus
Authors: Newman J. N.
Published: April 2006

The motions of a floating torus oscillating in response to incident waves are analysed under the assumptions that the incident wavelength is comparable with the radius of the body section and small compared with the larger radius of the torus. This problem serves to illustrate certain features of the strip theory for ship motions, but the axisymmetric geometry and absence of body ends greatly simplify the analysis. Matched asymptotic expansions are used, with the inner solution close to the body section composed of suitable radiation and scattering problems for the two-dimensional circular cylinder. Resonant standing-wave modes in the internal basin have a singular effect upon the hydrodynamic forces acting on the body, and its response to incident waves.
On nonlinear interactions in a spectrum of inviscid gravity–capillary surface waves
Authors: Holliday Dennis
Published: April 2006

Using the Fourier components of the velocity potential at the surface in an iterative perturbation theory, the author derives expressions for the modal frequency shifts and modal decay rates in a spectrum of in viscid gravity–capillary surface waves. The expressions differ from those calculated by the perturbation methods of Hasselmann (1962) and Valenzuela & Laing (1972), which are based on expanding the velocity potential about the equilibrium fluid level z = 0. This difference is shown to be due to the failure of the z = 0 perturbation method to converge rapidly enough to produce lowest-order corrections that are smaller than unperturbed quantities. A physical explanation for this failure is given.
Cumulative nonlinear distortion of an acoustic wave propagating through non-uniform flow
Authors: Kurosaka M.
Published: April 2006

In this paper we examine how the unsteady flow field radiated from an oscillating body is altered from the result of acoustic theory as the direct consequence of disturbances propagating through the non-uniform flow produced by the presence of the body. Taking the specific example of an oscillating airfoil placed in supersonic flow and having the contour of a parabolic arc, we derive a closed-form representation for the unsteady flow field in terms of the confluent hypergeometric function. The analytical expression reveals explicitly that, though the body shape has a negligible effect in the near field, it inextricably affects the unsteady flow at a large distance, both in its amplitude and phase, and substantially modifies the results of acoustic theory. In addition, we display the relation of this solution to the ‘fundamental solution’ and the other salient physical features connected with disturbances propagating through non-uniform flow. The present results recover Whitham's rule in the limit of zero frequency of oscillation and also include, as another special case, the unsteady solution for a wedge obtained by Carrier and Van Dyke.
Aerodynamic sound in a relaxing medium
Authors: Liu J. T. C.
Published: April 2006

In this paper we formulate the aerodynamic sound problem for a relaxing medium in a rather general way, independent of the details of the relaxation process. The medium is characterized by an appropriate relaxation time τ0and by a frozen (af0) and an equilibrium (ae0) sound speed. The equation describing aerodynamic sound in such a medium is the familiar one describing acoustic waves in a non-equilibrium medium but subjected to aerodynamic sound sources expressed in terms of a frozen and an equilibrium form of the Lighthill stress tensor. The far-field result for both compact and non-compact sources in the frequency range ω [Gt ] τ0−1can be expressed as the ratio of far-field densities for the relaxing and non-relaxing propagation medium:\[ \frac{\rho}{\rho_L} = \exp\left[-\left(1-\frac{a^2_{e_0}}{a^2_{f_0}}\right)\frac{x}{2a_{f0}\tau_0}\right], \]wherexis the observation distance and the subscriptLstands for ‘Lighthill’. The result for the main radiated aerodynamic sound, which comes from sources in the range ω [Lt ] τ0−1, essentially propagates in a manner described by the lower-order equilibrium waves, the diffusive effects from the higher-order waves being small, and the result for compact sources is a restatement of Lighthill's result in terms of the equilibrium propagation speed with the source region identically in equilibrium. For non-compact sources the propagation is still given byae0but the source region is now understood to encompass relaxation effects, the details of which are left unspecified.
A numerical study of a converging cylindrical shock
Authors: Sod Gary A.
Published: April 2006

A numerical proceure is introduced to solve the one-dimensional equations of gasdynamics for a cylindrically or spherically symmetric flow. The method consists of a judicious combination of Glimm's method and operator splitting. The method is applied to the problem of a converging cylindrical shock.
The generation of Langmuir circulations by an instability mechanism
Authors: Craik A. D. D.
Published: April 2006

Equations governing the current system in the upper layers of oceans and lakes were derived by Craik & Leibovich (1976). These incorporate the dominant effects of both wind and waves. Solutions comprising the mean wind-driven current and a system of ‘Langmuir’ cells aligned parallel to the wind were found for cases in which the wave field consisted of just a pair of plane waves. However, it was not clear that such cellular motions would persist for the more realistic case of a continuous wave spectrum.

The present paper shows that, in the latter case, infinitesimal spanwise periodic perturbations will grow on account of an instability mechanism. Mathematically, the instability is closely similar to the onset of thermal convection in horizontal fluid layers. Physically, the mechanism is governed by kinematical processes involving the mean (Eulerian) wind-driven current and the (Lagrangian) Stokes drift associated with the waves. The relationship of this mechanism to instability models of Garrett and Gammelsrød is clarified.
Doppler measurements of the effects of gravity waves on wind-generated ripples
Authors: Lee Peter H. Y.
Published: April 2006

The effects of gravity waves on wind-generated ripples are studied experimentally by means of Doppler spectra obtained through microwave Bragg backscattering. The measurements were made at 9·23 GHz with incidence angles of between 45° and 55°. It is found from the Doppler frequency shift that an increase in the speed of Bragg waves (ripples) of wavelength approximately 2 cm can be detected when a gravity wave is propagated into a pre-existing wind-wave field. The Doppler frequency shift corresponds, to first order, to the orbital speed of the gravity wave. Further studies, using a conditional sampling technique, reveal that the Bragg scatterers are localized on the gravity wave's crest. The mechanism leading to the ‘localization’ is as yet unidentified. Ratios of gravity wavelength to Bragg (ripple) wavelength ranging from 13 to 35 have been studied.
The interaction between capillary waves and a current and wave decay
Authors: Sorrell F. Y. , Sturm G. V.
Published: April 2006

Results of experiments on capillary-wave decay and energy transfer to mean currents are presented. The conditions investigated were those of a progressive wave train propagating on still water, on a constant current and on a spatially varying current. The waves were generated by either a mechanical or a pneumatic wave maker and the wave maker usually excited cross-wave motion. Thus the study also provides data on cross-wave generation and growth under these conditions. In particular these results indicate that the cross-waves obtain energy from a constant current as well as a spatially varying current. The progressive-wave energy was separated from that in the cross-waves by spatial averaging. When this is done the wave-current interaction and wave decay can be described by a first-order theory which includes viscous dissipation.
Novel Weissenberg effects
Authors: Beavers G. S. , Joseph D. D.
Published: April 2006

We have observed two novel manifestations of the Weissenberg effect in viscoelastic liquids which are set into motion by the rotation of a circular rod. In the first experiment we floated a layer of STP on water. The STP climbs up the rod into the air and down the rod into the water. The ‘down-climb’ is much larger than the ‘up-climb’, their ratio being roughly the square root of the density difference (STP-air)/ (water–STP). The magnification of the down-climb may be regarded asnormal-stress amplification. [dagger] The magnitudes of the up- and down-climbs are simultaneously in good agreement with the predictions of a theory of rod climbing when the angular frequency of the rod is small. In the second experiment, we set the rod into torsional oscillations. When the amplitude of the oscillation is small, the fluid climbs the rod; the climb is divided into an axisymmetric steady mean part and an oscillating part (Joseph 1976b; Beavers 1976). The mean axisymmetric climb dominates the total climb at low frequencies. At a higher critical speed the axisymmetric climbing bubble loses its stability to another time-periodic motion with the same period but with a ‘flower’ pattern displaying a certain integral number of petals.
Viscous flow in collapsible tubes of slowly varying elliptical cross-section
Authors: Wild Rosemary , Pedley T. J. , Riley D. S.
Published: April 2006

This paper is concerned with steady flow in collapsible tubes, such as veins, at fairly low Reynolds number. Lubrication theory is used to calculate the velocity and pressure distribution in an elliptical tube whose cross-sectional area and eccentricity vary slowly and in a given way with longitudinal distance x. The transverse velocity field and the effect of inertia on the primary velocity and pressure distributions are calculated to first order in the relevant small parameter. The results of these calculations are combined with a relationship between transmural pressure and the cross-sectional area at any x which is close to that measured in (large) veins, and are used to predict the pressure and flow in a collapsible tube when a given distribution of external pressure is applied. Different relationships between the tube perimeter and cross-sectional area are examined. The theory is applied to an experiment in which a segment of collapsible tube is supported between two rigid segments, and squeezed; predictions of the relationship between the pressure drop and flow rate are made for various experimental conditions. In particular, when the resistance of the downstream rigid segment is held constant, a range of flow rates is found in which the pressure drop falls as the flow rate is raised; this agrees with experiment.
Numerical computation of Taylor vortices
Authors: Majumdar A. K. , Spalding D. Brian
Published: April 2006

A finite-difference procedure for three-dimensional parabolic flows is used to predict the development of Taylor vortices in the flow between concentric rotating cylinders, resulting from the growth of small disturbances of a Couette flow. Predictions of such flows are presented in the developing and fully developed region. A precise calculation of the wavelength of the vortices has been possible by employing a periodic boundary condition on the pressure field. The predicted torque coefficient compares well with experimental data. The critical Taylor number has also been predicted with good accuracy.
Developing flow on a vertical wall
Authors: Ruschak K. J. , Scriven L. E.
Published: April 2006

Developing laminar flow in a liquid film issuing from a full slot and descending along a vertical wall is analysed for the limiting cases of low flow rate and high surface tension. Neither limiting case is approached uniformly and the singular perturbation method with matched asymptotic expansions is employed. The location of a free boundary, the curved meniscus, is unknown a priori, and the limiting meniscus profiles are obtained. An interesting viscous boundary layer is found at low flow rates.
A chemical reaction in a turbulent jet
Authors: Shea John R.
Published: April 2006

This experimental investigation determines the effect of the various parameters of a subsonic axisymmetric jet upon a fast chemical reaction between ozone contained dilutely in the primary jet and diluted nitric oxide being entrained from the ambient fluid. Radial profiles of ozone densities are determined from absorption measurements of a thin beam of ultraviolet light which is probed across the jet. Data have been obtained for five jet Reynolds numbers between 4000 and 32 000 to reflect variations in both gas density and nozzle velocity; the data confirm Reynolds number independence of reactant concentration profiles to within experimental accuracy. When the non-dimensional chemical reaction rate exceeds a determined value, the ozone profiles are observed to be independent of further increases in the reaction speed. The measured ozone concentration profiles are related directly to the molecular-scale mixing in the jet and to mixing intermittency in the mixing zone in particular.
A note on the slope of a density interface between two stably stratified fluids under wind
Authors: Wu Jin
Published: April 2006

Experiments were conducted with two layers of stably stratified fluid in a wind-wave tank. The slope of the density interface was measured and was related to the wind stress, the density difference between the two fluids and the depth of the interface.
Laboratory models of sea straits
Authors: Anati David A. , Assaf Gad , Thompson Rory O. R. Y.
Published: April 2006

Two basins maintained at different densities are connected by a relatively shallow strait. If the strait is short, the flow is such that the Froude number is unity. The thickness of the intermediate layer, between the outflow and the inflow, is controlled by the requirement that the Richardson number be critical; this thickness is always about one-fifth of the total depth, both in these experiments and in the Strait of Gibraltar. If the strait is long, the Froude number is less than unity in the interior but increases to unity at each end. A strait may be considered short when its length is less than a few hundred times the sill depth.
Steady flow in rapidly rotating variable-area rectangular ducts. Part 2. Small divergences
Authors: Calderon A. , Walker J. S.
Published: April 2006

This paper treats the steady inertialess flow of an incompressible viscous fluid through an infinite rectangular duct rotating rapidly about an axis (the y axis) perpendicular to its centre-line (the x axis). The prototype considered has parallel sides at z = ± 1 for all x, parallel top and bottom at y = ± a for x < 0 and straight diverging top and bottom at y = ± (a + bx) for x > 0. An earlier paper (Walker 1975) presented solutions for b = ±(1), for which the flow in the diverging part (x > 0) is carried by a thin, highvelocity sheet jet adjacent to the side at z = 1, the flow elsewhere in this part being essentially stagnant. The present paper considers the evolution of the flow as the divergence decreases from O(1) to zero, the flow being fully developed for b = 0. This evolution involves four intermediate stages depending upon the relationship between b and E, the (small) Ekman number. In each successive stage, the flow-carrying side layer in the diverging part becomes thicker, until in the fourth stage, it spans the duct, so that none of the fluid is stagnant.
The generation of sound by vorticity waves in swirling duct flows
Authors: Howe M. S. , Liu J. T. C.
Published: April 2006

Swirling flow in an axisymmetric duct can support vorticity waves propagating parallel to the axis of the duct. When the cross-sectional area of the duct changes a portion of the wave energy is scattered into secondary vorticity and sound waves. Thus the swirling flow in the jet pipe of an aeroengine provides a mechanism whereby disturbances produced by unsteady combustion or turbine blading can be propagated along the pipe and subsequently scattered into aerodynamic sound. In this paper a linearized model of this process is examined for low Mach number swirling flow in a duct of infinite extent. It is shown that the amplitude of the scattered acoustic pressure waves is proportional to the product of the characteristic swirl velocity and the perturbation velocity of the vorticity wave. The sound produced in this way may therefore be of more significance than that generated by vorticity fluctuations in the absence of swirl, for which the acoustic pressure is proportional to the square of the perturbation velocity. The results of the analysis are discussed in relation to the problem of excess jet noise.
An analytical solution for the profile and volume of a small drop or bubble symmetrical about a vertical axis
Authors: Chesters A. K.
Published: April 2006

A solution for the profile of a small drop or bubble symmetrical about a vertical axis and at rest in a second fluid is obtained as a first-order perturbation of a circle. At the end of the drop opposite the apex, the perturbation approach breaks down and a matching zero-gravity solution is used. The results agree with numerical solutions and indicate that the pendant-drop profile of maximum volume fitting a given small vertical tube intersects the exit plane at very nearly 90°. This enables the maximum volume to be determined accurately from a force balance.