bluuebunny/crossref_metadata_2025 huggingface dataset:
Effect of ohmic dissipation on internal Alfvén-gravity waves in a conducting shear flow
Authors: Rudraiah N. , Venkatachalappa M.
Published: March 2006

Internal Alfvén-gravity waves of small amplitude propagating in a Boussinesq, inviscid, adiabatic, finitely conducting fluid in the presence of a uniform transverse magnetic field in which the mean horizontal velocityU(z) depends on heightzonly are considered. We find that the governing wave equation is singular only at the Doppler-shifted frequency Ωd= 0 and not at the magnetic singularities Ωd= ± ΩA, where ΩAis the Alfvén frequency. Hence the effect of ohmic dissipation is to prevent the resulting wave equation from having magnetic singularities. Asymptotic solutions of the wave equation, which is a fourth-order differential equation, are obtained. They show the presence of the magnetic Stokes points Ωd= ± ΩA. The interpretation of upward and downward propagation of waves is also discussed.

To study the combined effect of electrical conductivity and the magnetic field on waves at the critical level, we have used the group-velocity approach and found that the waves are transmitted across the magnetic Stokes points but are completely absorbed at the hydrodynamic critical level Ωd= 0. The general expression for the momentum flux is mathematically complicated but will be simplified under the assumption\[ \frac{\partial^2h}{\partial x^2}+\frac{\partial^2h}{\partial y^2}\gg \frac{\partial^2h}{\partial z^2}, \]wherehis the perturbation magnetic field. In this approximation we find that the momentum flux is not conserved and the waves are completely absorbed at Ωd= 0.

The general theory is applied to a particular problem of flow over a sinusoidal corrugation and asymptotic solutions are obtained by applying the Laplace transformation and using the method of steepest descent.
The mean electromotive force generated by turbulence in the limit of perfect conductivity
Authors: Moffatt H. K.
Published: March 2006

When homogeneous turbulence acts upon a non-uniform magnetic field B0(x, t), a mean electromotive force [Escr ](x, t) is in general established owing to the correlation between the velocity field and the fluctuating magnetic field that is generated. The relation between [Escr ] and B0 is linear, and it is generally believed that, when the scale of inhomogeneity of B0 is sufficiently large, it can be expressed as a series involving successively higher spatial derivatives of B0:
\[
{\cal E}_i = \alpha_{il} B_{0l}+\beta_{ilm}\partial B_{0l}/\partial x_m+\ldots,
\]
where the tensors αil, βilm,… are determined (in principle) by the statistical properties of the turbulence and the magnetic diffusivity Λ of the fluid. These tensors are of crucial importance in turbulent dynamo theory. In this paper the question of their asymptotic form in the limit Λ → 0 is considered. By putting Λ = 0 and assuming that the field is non-random at an initial instant t = 0, the developing form of the tensors αl(t) and βm(t) is determined. The expressions involve time integrals of Lagrangian correlation functions associated with the velocity field, which are comparable in structure with the eddy diffusion tensor in the analogous turbulent diffusion problem (Taylor 1921). Some doubts are expressed concerning the convergence of the time integrals as t → ∞, and it is concluded that a satisfactory treatment of the problem will require the inclusion of weak diffusion effects (as recognized by Parker 1955).
On the behaviour of small disturbances in plane Couette flow. Part 3. The phenomenon of mode-pairing
Authors: Gallagher A. P.
Published: March 2006

In two earlier papers (Gallagher & Mercer 1962, 1964) the results for the first four eigenvalues of the problem of the stability of plane Couette flow were given. The first twelve eigenvalues have been calculated by the same method and the results show that the manner in which the eigenvalues join to form complex pairs depends on α, the wavenumber of the disturbance. They also would appear to indicate that mode-crossing always occurs.
The solution of viscous incompressible jet and free-surface flows using finite-element methods
Authors: Nickell R. E. , Tanner R. I. , Caswell B.
Published: March 2006

We discuss the creation of a finite-element program suitable for solving incompressible, viscous free-surface problems in steady axisymmetric or plane flows. For convenience in extending program capability to non-Newtonian flow, non-zero Reynolds numbers, and transient flow, a Galerkin formulation of the governing equations is chosen, rather than an extremum principle. The resulting program is used to solve the Newtonian die-swell problem for creeping jets free of surface tension constraints. We conclude that a Newtonian jet expands about 13%, in substantial agreement with experiments made with both small finite Reynolds numbers and small ratios of surface tension to viscous forces. The solutions to the related ‘stick-slip’ problem and the tube inlet problem, both of which also contain stress singularities, are also given.
Wall pressure spectra calculations for equilibrium boundary layers
Authors: Panton Ronald L. , Linebarger John H.
Published: March 2006

Assuming information about the mean velocity and vertical turbulent velocity, it is possible to calculate the flow direction wavenumber spectrum of pressure fluctuations ϕ(k1 δ)/τ02δ. The law of the wall plus Cole's wake function represented the mean velocity profiles. A scale-anisotropic model of R22 was used and the component intensity û2 was assumed to vary across the boundary layer in constant proportionality to the Reynolds stress. Calculated zero-pressure-gradient spectra rise as k11.5 at low wavenumbers. Curves for various Reynolds numbers are closely similar, and diverge only slightly around the peak in the spectrum. A high wavenumber spectrum ϕk1v/u*. u*/τ02v is independent of Reynolds number. The calculations reveal an overlap region in which ϕ ∼ k1−1. Imposing an equilibrium pressure gradient increases the spectrum at the low and mid wavenumbers, but has no effect in the overlap region. The spectrum peak for II = 6 is a factor 102 higher than for the zero-pressure-gradient layer. It is proposed that the convective velocity Uc(k1) has an overlap region. The overlap law is found to be
\[
\frac{U_c}{u_{*}} = -\frac{1}{\kappa}\ln k_1\delta +\frac{1}{\kappa}\ln\frac{u_{*}\delta}{\nu}+A,
\]
where K and A are the same constants as in the mean velocity expression. Comparison with experiments shows very good agreement. A rough convective ‘wake’ function is formulated for the low-wavenumber range. Wavenumber spectra are converted to frequency spectra, and compared with experiments. Data from a zero pressure gradient and an adverse pressure gradient II = 3 show reasonable agreement with the calculations.
Unstable waves on an axisymmetric jet column
Authors: Mattingly G. E. , Chang C. C.
Published: March 2006

The growth of infinitesimal disturbances on an axisymmetric jet column is investigated theoretically and experimentally. The theoretical analysis is based upon inviscid stability theory, wherein axisymmetric, helical and double helical disturbances are considered from the spatial reference frame. In the jet flow field near the source, the mean velocity profile is observed to have a potential core and a thin, but finite, shear layer between the potential core and the quiescent ambient fluid. With downstream distance, the potential core diameter decreases and the shear-layer thickness increases. To incorporate these variations into the theory, a quasi-uniform assumption is adopted, whereby successive velocity profiles are analysed individually throughout the region in the jet flow where disturbances are observed to be small. The results of the theory indicate that initially, in the jet flow where the shear layer is thin and the potential core is larger, all disturbances considered are unstable. The dominant disturbance in the jet is an axisymmetric one. However, further downstream in the jet, where the half-breadth thickness of the shear layer is 55% of the potential core radius, a helical disturbance is found to dominate the axisymmetric and double helical modes. Nowhere in the jet flow field examined was the double helical disturbance found to be dominant. The cross-stream distributions of velocity and vorticity for the dominant disturbance modes are presented according to the spatial stability theory.

The downstream development of the jet column and the characteristics of the disturbances amplifying on it were also studied in a water tank. No artificial stimulation of any particular disturbance was used. The experimental results show good agreement with the results of the theory in the region where the disturbances are small. However, conclusive confirmation of the switch in the hierarchy of dominant disturbances was not found. Half of the time the disturbance observed experimentally exhibits an axisymmetric character and the other half a helical one. This apparently is due to the similar spatial amplification rates experienced by both of these disturbance modes. It is concluded that this switching of dominant modes is, in large part, responsible for (i) the well-known natural drifting of disturbance characteristics in jet flows, and (ii) the wide variety of observations made in previous jet experiments.
Diffusion-flame structure for a two-step chain reaction
Authors: Bush William B. , Fendell Francis E.
Published: March 2006

The low-speed combustion of initially unmixed gaseous reactants under an irreversible two-step chain reaction is examined. Both equilibrium burning, in which two spatially separated flames of zero thickness arise, and near-equilibrium burning, in which two spatially separated flames of small but finite thickness arise, are studied by limit-process expansion techniques. Two time-dependent flows are examined: the first is (one-dimensional) transient mixing flow; and the second is (two-dimensional) transient counterflow. The latter flow, in which there is an impressed finite strain parallel to the flame, such that the flame itself is longitudinally stretched, is discussed as elucidating the characteristics of combustion in non-equilibrium turbulent shear flow.
Large amplitude convection in porous media
Authors: Straus Joe M.
Published: March 2006

The properties of convective flow driven by an adverse temperature gradient in a fluid-filled porous medium are investigated. The Galerkin technique is used to treat the steady-state two-dimensional problem for Rayleigh numbers as large as ten times the critical value. The flow is found to look very much like ordinary Bénard convection, but the Nusselt number depends much more strongly on the Rayleigh number than in Bénard convection. The stability of the finite amplitude two-dimensional solutions is treated. At a given value of the Rayleigh number, stable two-dimensional flow is possible for a finite band of horizontal wavenumbers as long as the Rayleigh number is small enough. For Rayleigh numbers larger than about 380, however, no two-dimensional solutions are stable. Comparisons with previous theoretical and experimental work are given.
Instability of rigidly rotating flows to non-axisymmetric disturbances
Authors: Maslowe S. A.
Published: March 2006

An investigation of the hydrodynamic stability of swirling flows having arbitrary Rossby numbers is described. A necessary condition for instability is derived for rigidly rotating flows and this condition is further refined in the specific case of a parabolic axial flow. Numerical results are presented for two azimuthal wave-numbers corresponding to the maximum growth rates of unstable perturbations as a function of Rossby number. It is found that the largest growth rates occur when the Rossby number is O(1) and that instability persists for surprisingly large values of this parameter. Previous explanations of the instability mechanism are discussed and it is concluded that these are only adequate in the limit of small Rossby number.
Pendular rings between solids: meniscus properties and capillary force
Authors: Orr F. M. , Scriven L. E. , Rivas A. P.
Published: March 2006

The Laplace–Young equation is solved for axisymmetric menisci, analytically in terms of elliptic integrals for all possible types of pendular rings and liquid bridges when the effect of gravity is negligible, numerically for selected other cases in order to assess gravity's effect. Meniscus shapes, mean curvatures, areas and enclosed volumes are reported, as are capillary forces. It is shown that capillary attraction may become capillary repulsion when wetting is imperfect. The special configurations of vanishing capillary force and of zero mean curvature are treated. The range of utility of the convenient ‘circle approximation’ is evaluated.
Higher-order approximation for free shear layers in almost rigid rotations
Authors: Cook L. Pamela , Ludford G. S. S.
Published: March 2006

The free shear layer stemming from a discontinuity in angular velocity at either of two parallel disks in almost rigid rotation with fluid between is re-examined. The sole discrepancy between theory and experiment is unaffected by higher-order approximation unless curvature effects are included, when it is reduced.
Waves and wave resistance of thin bodies moving at low speed: the free-surface nonlinear effect
Authors: Dagan G.
Published: March 2006

The linearized theory of free-surface gravity flow past submerged or floating bodies is based on a perturbation expansion of the velocity potential in the slenderness parameterewith the Froude numberFkept fixed. It is shown that, although the free-wave amplitude and the associated wave resistance tend to zero asF→ 0, the linearized solution is not uniform in this limit: the ratio between the second- and first-order terms becomes unbounded asF→ 0 with ε fixed. This non-uniformity (called ‘the second Froude number paradox’ in previous work) is related to the nonlinearity of the free-surface condition. Criteria for uniformity of the thin-body expansion, combining ε andF, are derived for two-dimensional flows. These criteria depend on the shape of the leading (and trailing) edge: as the shape becomes finer the linearized solution becomes valid for smallerF.

Uniform first-order approximations for two-dimensional flow past submerged bodies are derived with the aid of the method of co-ordinate straining. The straining leads to an apparent displacement of the most singular points of the body contour (the leading and trailing edges for a smooth shape) and, therefore, to an apparent change in the effective Froude number.
The laminar decay of suddenly blocked channel and pipe flows
Authors: Weinbaum S. , Parker K. H.
Published: March 2006

This paper is a theoretical investigation of the stable laminar decay of a fully established channel or pipe flow following a sudden blockage such as would be caused by the rapid closure of a valve or imposition of an end wall or gate. The development of the subsequent velocity and pressure fields is examined from the instant the initial pressure wave passes until the final decay of all motion. Three time scales of hydrodynamic interest are identified and the relevant solutions are obtained. The time scales are as follows: (i) a very short time characteristic of the passage of the pressure wave during which the velocity field adjusts inviscidly to the new boundary conditions imposed by the presence of the end wall, (ii) a short diffusion time during which the displacement interaction generated by the diffusion of the primary Rayleigh layer induces a substantial secondary motion with distinct side-wall boundary layers and an inviscid core and (iii) a long diffusion time during which the boundary layers fill the entire channel or pipe and the residual motion then dies out. The secondary flow for short diffusion times is of special interest in that it is an example of an unsteady boundary layer where the external pressure gradient and inviscid outer flow are unknown and determined by the integrated time history of the combined mass flow displacement generated by the primary- and secondary-flow boundary layers. The paper closes with some preliminary comments and experimental observations on decelerating pipe flows.
Fluid shielding of low frequency convected sources by arbitrary jets
Authors: Balsa T. F.
Published: March 2006

A low frequency asymptotic theory is proposed for the shielding of noise by jets of arbitrary cross-section. The results of the theory provide a qualitative explanation for the appearance of the quiet and noisy planes of a slot jet. The arguments in favour of this explanation are derived from a model problem in which a pulsating mass source is convecting along the axis of an infinitely long column of fluid of arbitrary cross-section. The jet velocity is represented by a uniform velocity profile (i.e. slug flow). The method of matched asymptotic expansions is applied to derive expressions for the acoustic pressure and the radiative power of the source.

The solution for the elliptic jet indicates that the radiative power in the horizontal plane (containing the major axis) is less than that in the vertical plane (containing the minor axis). This difference in power varies with source Strouhal number and jet Mach number. The effects of jet temperature are also included in the analysis. The theoretical results are in good qualitative agreement with experimental findings for slot nozzles. The theory indicates that the noise shielding offered by jets is negligible at low frequencies and low Mach numbers.
A theoretical and experimental study of the velocity distribution and transition to turbulence in free oscillatory flow
Authors: Clarion Claire , Pelissier Robert
Published: March 2006

The free oscillatory flow of a viscous fluid in a U-shaped tube is considered. A theoretical analysis (in which an axial flow is assumed and the start-up of the column is taken into account) shows, depending on the value of the similarity parameter γ, various regimes of the flow. Measurements of the velocity distribution are made using hot-film velocity probes, operated with a constant-temperature anemometer, and visualizations of the flow are performed. Experimental results are in good agreement with theoretical ones when the flow is laminar, and show the possible existence of turbulent flows. Critical values, at which the flow is disturbed over a more or less extended range of the successive oscillations, are determined for the similarity parameters γ and h0/R.
On turbulence and noise of an axisymmetric shear flow
Authors: Michalke A. , Fuchs H. V.
Published: March 2006

The noise produced by mean flow-turbulence interaction of a circular subsonic jet is investigated theoretically, and expanded in azimuthal constituents of the turbulent pressure fluctuations. It is found that the low-order azimuthal constituents are the most efficient sound sources. On the basis of pressure correlation measurements, the azimuthal constituents are determined in a low Mach number jet. It is found that, in a range of Strouhal numbers between 0·2 and 1, the first three to four azimuthal constituents clearly dominate over the rest of the turbulent source quantity. A strictly axisymmetric ring vortex model for the coherent structure of the turbulence is, however, shown to be inappropriate.
The propagation of planetary waves over a random topography
Authors: Thomson Richard E.
Published: March 2006

The purpose of this paper is to consider the effect of one-dimensional random depth variation on the propagation of planetary waves in a homogeneous layer of fluid having a free upper surface. We begin by determining the dispersion relation for the coherent part of the wave using the vorticity equation for the transport stream function and a previously described perturbation method. Then, from the resulting first-order expressions for the wavenumber, we obtain the phase speeds for the two possible planetary-wave solutions. These are compared with the corresponding phase speeds of planetary waves over a smoothly varying topography; the validity limits of the approximations are discussed. For the most physically realizable situation, of random depth correlation lengths much shorter than a typical wavelength, we find that the phase speed of the shorter (longer) wave component is less (greater) over a randomly varying topography than over a smoothly varying topography. In the case of the shorter waves, greatest relative changes in phase speed occur when the associated fluid motions are at right angles to the ‘strike’ of the roughness elements, while for both long and short waves there is no relative change in phase speed if fluid motions are parallel to the roughness contours. Moreover, both types of waves are shown to lose energy in the direction of energy propagation as a result of scattering. Numerical values are then obtained using hydrographic charts of the western North Pacific, and show that the randomness may significantly decrease the phase speed of the shorter planetary-wave component. Finally, we give a brief descriptive explanation of the results based on the effect of the topography on the wave restoring mechanism.
On the possibility of complete condensation shock waves in retrograde fluids
Authors: Thompson Philip A. , Sullivan Daniel A.
Published: March 2006

Shock discontinuities for which the upstream state is vapour and the downstream state is liquid are considered. The possibility of such shock waves is associated with a large number of molecular degrees of freedom: it is necessary that the ideal-gas specific heatcv[ges ] 24Rat the critical temperature, a condition which is met by several common fluids. Shock properties are found from a corresponding-states thermodynamic model and from several calculations based on data for particular fluids. Condensation shock waves satisfy the usual stability conditions and should be found in laboratory experiments.
Pulsatile flow in curved pipes
Authors: Smith F. T.
Published: March 2006

The characteristics of some flows that occur when fluid is driven through a curved tube are disclosed for an imposed pressure gradient of pulsatile nature, varying sinusoidally with time about a non-zero mean. The fully developed motion depends on three parameters, a traditional Dean number D, a frequencyrelated parameter β and a secondary Reynolds number Rs, it being assumed that the pipe's radius of curvature is much greater than its cross-sectional dimensions. The theoretical description of the flow field is extended from the steady and purely oscillatory limits hitherto studied to all the key situations arising when Rs is of order unity and one of the other parameters β or D takes a large or small value. During this analysis, which in certain cases involves the interactions between steady boundary layers and Stokes layers, a number of pulsatile motions are revealed and the manner in which at high frequencies the secondary motion can change its direction, from inward ‘centrifuging’ to outward, is also explained. Two further illustrations of pulsating motions, stemming from the steady limit, produce an alternative mode of transition from steady boundary-layer flow to the boundary-layer flows occurring when Rs ∼ 1. The study, which mainly deals with the flow in an arbitrary cross-section, lays down a formal basis for deriving the fundamental attributes of many physical situations, some of which are expressible in terms of crucial modifications to, or combinations of, flow problems whose properties are already appreciated.
Wave propagation in a stratified shear flow
Authors: Hartman R. J.
Published: March 2006

The linearized initial-value problem for a two-dimensional, unbounded, exponentially stratified, plane Couette flow is considered. The solution is used to evaluate the evolution of wave-packet perturbations to the mean flow for all Richardson numbers J > ¼, demonstrating that a consistent wave-packet approach to wave propagation in these flows is possible for all J > ¼. It is found that the vertical influence of a wave-packet perturbation is limited to a distance of order (J − ¼)½/k0, where k0 is the magnitude of the initial central wave vector. These results are used to clarify the J [gsim ] ¼ conclusions of an earlier treatment by Booker & Bretherton.
Nonlinear interaction of magnetic field and convection
Authors: Busse F. H.
Published: March 2006

The interaction between convection in a horizontal fluid layer heated from below and an ambient vertical magnetic field is considered. The analysis is based on the Boussinesq equations for two-dimensional convection rolls and the assumption that the amplitudeAof the convection and the Chandrasekhar numberQare small. It is found that the magnetic energy is amplified by a factor of orderR½m, whereRmis the magnetic Reynolds number. The ratio between the magnetic and kinetic energies can reach values much larger than unity. Although the magnetic field always inhibits convection, this influence decreases with increasing amplitude of convection. Thus finite amplitude onset of steady convection becomes possible at Rayleigh numbers considerably below the values predicted by linear theory.
Turbulence measurements in an ‘equilibrium’ axisymmetric wall jet
Authors: Ramaprian B. R.
Published: March 2006

This paper reports measurements of turbulent quantities in an axisymmetric wall jet subjected to an adverse pressure gradient in a conical diffuser, in such a way that a suitably defined pressure-gradient parameter is everywhere small. Self-similarity is observed in the mean velocity profile, as well as the profiles of many turbulent quantities at sufficiently large distances from the injection slot. Autocorrelation measurements indicate that, in the region of turbulent production, the time scale of ν fluctuations is very much smaller than the time scale ofufluctuations. Based on the data on these time scales, a possible model is proposed for the Reynolds stress. One-dimensional energy spectra are obtained for theu, vandwcomponents at several points in the wall jet. It is found that self-similarity is exhibited by the one-dimensional wavenumber spectrum of$\overline{q^2}(=\overline{u^2}+\overline{v^2}+\overline{w^2})$, if the half-width of the wall jet and the local mean velocity are used for forming the non-dimensional wavenumber. Both the autocorrelation curves and the spectra indicate the existence of periodicity in the flow. The rate of dissipation of turbulent energy is estimated from the$\overline{q^2}$spectra, using a slightly modified version of a previously suggested method.
Evidence for scale similarity of internal intermittency in turbulent flows at large Reynolds numbers
Authors: Van Atta C. W. , Yeh T. T.
Published: March 2006

Some new measurements and a reassessment of previous data on statistical properties of the breakdown coefficients qr,l in high Reynolds number turbulence show the existence of a range of scale similarity for scales larger than those in the viscous range (l [ges ] 36η). The rate of variation of the probability density p(qr,l) with changing outer scale l/η decreases as l/η increases, becoming fairly insignificant for the largest values of l/η. Measurements of characteristic functions of the probability densities show a substantial degree of statistical independence for sequential adjoint values of qr,l, consistent with the small values of the correlation coefficients for these variables. The data for the moments of qr,l exhibit a behaviour very close to that predicted by the scale-similarity theory when only data for r [ges ] 36η are considered, i.e. data for smaller inner length scales are excluded. The moments and corresponding values of the parameters μp are in good agreement with our previous results and with some earlier data of Kholmyansky, but some rather large unresolved differences in the probability densities of qr,l are found on comparing the present data with those of Kholmyansky. The present measurements of breakdown coefficients for ζ1 = [uscr ]− 1∂u/∂t = ∂(In [uscr ])/∂tand ζ2 = U−1∂u/∂t the time derivatives of the streamwise velocity and its logarithm measured in the atmospheric boundary layer, resolve some previous questions concerning the sensitivity of the results obtained to the choice of positive variable, varying sampling rates and the values of external parameters.

For low sampling rates, a systematic change in the shape of the probability densities p(qr,l) with varying digital sampling rate is found using either ζ1 or ζ2. For sufficiently high sampling rates, the probability densities are independent of the sampling rate; and invariant results are obtained when the sampling rate is at least one-quarter of the Kolmogorov frequency associated with the viscous length scale based on the turbulent dissipation rate. The probability densities p(qr,l) measured using either ζ1 or ζ2 are very similar to the corresponding spectra of ζ1 or ζ2 respectively. Comparison of the mean-square values of ζ1 and ζ2 with an extended form of Taylor's hypothesis shows that the variable ζ1 is not a good approximation to the true spatial derivative ∂u/∂x, and the use of such an approximation can lead to results that are both qualitatively and quantitatively incorrect.
An experimental study of the instability of a stably stratified free shear layer
Authors: Wang Yu-Hwa
Published: March 2006

A stably stratified free shear layer is created in a continuously circulating water channel in the laboratory. Two streams of salt water of different concentrations are brought together at the entrance to the open channel and a layered uniform flow field with a distinct sharp interface is produced in the test section. The maximum density difference between the two layers is Δρx = 0·0065ρw, where ρw is the density of water. The velocity of each layer can be adjusted at will to create free shear across the interface. At the end of the open channel, a mechanical device to separate the layers for recirculation is provided. The resulting flow field has a viscous region approximately 15 times larger than the scale of the salinity diffusion layer. Visual observations are made with hydrogen bubbles and dye traces. Interfacial waves are initiated by artificial excitation. The perturbation frequencies range from 0·476 to 10·40Hz. The measured wavelengths range from 0·46 to 3·02 cm. Damped waves as well as growing waves are observed at various exciting frequencies. Velocity profiles and instantaneous velocities are measured by a hot-film anemometer designed for use in salt water. Experimental values of the Richardson number, the dominant parameter characterizing the instability process, range from 1·23 to 14·45. The stability boundary is determined experimentally. Comparisons with Hazel's numerical results and the earlier results of Scotti & Corcos for low values of the Richardson number are also made.
Forces on bodies moving transversely through a rotating fluid
Authors: Mason P. J.
Published: March 2006

Measurements have been made of the net force F acting on a bluff rigid body moving with velocity U (relative to a fluid rotating about a vertical axis with uniform angular velocity Ω) in a plane perpendicular to the axis of rotation. The force F is of magnitude 2ΩρVU, where ρ is the density of the fluid and V is a volume which depends on the size and shape of the body. The relative direction of F and U is found to depend on the quantity
\[
{\cal S}\equiv \frac{2\Omega L}{U}\bigg(\frac{h}{D}\bigg),
\]
where L and h are horizontal and vertical lengths characterizing the object and D is the depth of the fluid in which the object is placed.
Horizontal momentum jets in rotating basins
Authors: Savage Stuart B. , Sobey Rodney J.
Published: March 2006

In order to prevent stagnation and improve water quality, the intakes of many water-supply reservoirs have the form of momentum jets directed approximately radially into the storage. An analysis which idealizes this flow as consisting of a turbulent jet issuing horizontally from a circular orifice into a large rotating basin of deep water shows that the jet path is a spiral whose length scale L depends upon the rate of rotation and the kinematic momentum of the jet. Good agreement is found with flow-visualization experiments when the basin depth h is ‘large’ (h/L [gsim ] 0·21). For small depths (h/L [lsim ] 0·024) the flow tends to be twodimensional and the jet path is found to be straight. Full-scale reservoirs are usually shallow enough that the effect of the earth's rotation on the jet path is likely to be small. However these reservoirs are not inordinately shallow and tests with distorted hydraulic models are likely to show significant effects of rotation and can be misleading to the unsuspecting.
Transonic equivalence rule: a nonlinear problem involving lift
Authors: Cheng H. K. , Hafez M. M.
Published: March 2006

The inviscid transonic flow past a thin wing having swept leading edges, with smooth lift and thickness distributions, is shown to possess an outer nonlinear structure determined principally by a line source and a line doublet. Three domains (the thickness-dominated, the intermediate, and the lift-dominated), representing different degrees of lift control of the outer flow, are identified; a transonic equivalence rule valid in all three domains is established. Except in one domain, departure from the Whitcomb-Oswatitsch area rule is significant; the equivalent body corresponding to the source effect has an increased cross-sectional area depending nonlinearly on the lift. This nonlinear lift contribution results from the second-order corrections to the inner (Jones) solution, but produces effects of first-order importance in the outer flow. Of interest is an afterbody effect dependent on the vortex drag, which is not accounted for by the classical transonic small-disturbance theory.
A comparison of the wake structure of a stationary and oscillating bluff body, using a conditional averaging technique
Authors: Davies M. E.
Published: March 2006

A conditional averaging technique to extract the underlying vortex pattern from a turbulent bluff body wake is described. Ensemble averages of wake velocities are developed on the basis of a reference phase position, determined from the outer flow irrotational fluctuations. The method is applied to the wakes of a stationary and oscillating D-shape cylinder, where, in the latter case, the vortex shedding is locked to the frequency of body movement. Direct comparisons of average circulation and vortex street spacings are obtained and these demonstrate the significant change in wake structure that accompanies and sustains vortex-induced vibrations. It is observed in both conditions that only 25% of the estimated shed vorticity is found in the fully developed wake. In addition the analysis produces profiles of vorticity and velocity in an ‘average vortex cycle’. A model, developed to help interpret these results, suggests that a good representation of an average wake situation is obtained by the addition of considerable mean shear to a street of finite area axisymmetric vortices.
Axisymmetric Stokes flow past a spherical cap
Authors: Dorrepaal J. M. , O'neill M. E. , Ranger K. B.
Published: March 2006

The axisymmetric streaming Stokes flow past a body which contains a surface concave to the fluid is considered for the simplest geometry, namely, a spherical cap. It is found that a vortex ring is attached to the concave surface of the cap regardless of whether the oncoming flow is positive or negative. A stream surface ψ = 0 divides the vortex from the mainstream flow, and a detailed description of the flow is given for the hemispherical cup. The local velocity and stress in the vicinity of the rim are expressed in terms of local co-ordinates.
Stability of natural convection in a narrow rotating annulus
Authors: Korpela Seppo A. , Arpaci Vedat S.
Published: March 2006

The stability of the conduction regime of natural convection of a fluid contained in a narrow rotating annulus with a heated inner wall has been investigated according to the linear theory. The results include computations for Prandtl numbersP= 0, 0·72 and 6·7 over a large range of the rotational parameters. For low rotation rates the instability sets in as multicellular convection with the cell axes horizontal in the absence of rotation but tilting monotonically towards the vertical as the rotation rate is in creased. Two other types of instability were found at high rotation rates. For large Froude numbers the unstable thermal stratification leads to a Bénard type of convection with vertically oriented rolls. For large Taylor numbers, through a mainly hydrodynamic mechanism, a nearly vertically oriented cellular structure develops in the flow which is destabilized as a result of rotation.
The phase configuration of waves around a body moving in a rotating stratified fluid
Authors: Peat K. S. , Stevenson T. N.
Published: March 2006

A body is started impulsively from rest and moves on an arbitrary path in an incompressible, stably stratified, rotating fluid. The phase configuration of the waves which are generated is studied using small amplitude wave theory. The theory is compared with experiment for a few special cases which include a horizontal cylinder (a) oscillating about a position fixed in the fluid, (b) moving with constant velocity and (c) moving with a constant angular velocity in a circular path relative to the fluid. Theory and experiment show reasonable agreement except where wakes interfere with the wave pattern.
The influence of jet flow on jet noise. Part 2. The noise of heated jets
Authors: Mani R.
Published: March 2006

This paper continues the study of part 1 into the area of the noise of heated jets. First, this part of the study discusses how a convected wave equation approach based on Lilley's equation leads to additional dipole and simple source terms associated with the velocity fluctuations due to transverse gradients of the mean density of the flow. Once these source terms have been identified and roughly estimated, we revert to a plug-flow model of the jet flow (where now the jet temperature and jet density differ from the ambient values) to estimate the radiation of these singularities. Several novel physical aspects of hot-jet noise are uncovered by the analysis. Indeed the problem of hot-jet noise is the one where the greatest deviations from Lighthill's ideas on jet noise generation are evident. The results are applied to available data and a very satisfactory measure of agreement is obtained with respect to the various predictions of the theory. Mechanisms for ‘excess’ pure jet noise scaling onM6andM4are found to result from the density gradients of the mean flow. The satisfactory agreement with the data suggests a solution of the problem of scaling jet noise with regard to jet temperature effects. The ability to predict correctly the data also suggests that the jet temperature has very little effect on the turbulence source spectrum generating jet noise at least for jet exit velocities up to about 1·5 times the atmospheric speed of sound.
Laminar film flow on a cylindrical surface
Authors: Becker Ernst
Published: March 2006

The paper deals with steady laminar film flow which is set up at the cylindrical surface of an idealized horizontal ‘road’ when homogeneous ‘rain’ is falling onto the road in a vertical downward direction. It is shown that a particular solution of the Navier-Stokes equations is possible for which the depth of the liquid film is constant. In that case the Navier-Stokes equations reduce to the equations governing plane stagnation-point flow. However, the boundary conditions differ from those for the classical stagnation-point problem. Solutions for nearly inviscid flow and predominantly viscous flow are derived analytically. In particular, simple formulae for the depth of the film are found in both cases. Finally, the importance of the particular solution as a member of a whole class of solutions is discussed on the basis of a momentum integral approximation.
A macromolecule transport model for the arterial wall and endothelium based on the ultrastructural specialization observed in electron microscopic studies
Authors: Weinbaum Sheldon , Caro Colin G.
Published: March 2006

A composite hydrodynamic-diffusion model of the arterial wall is presented to describe the vesicular transport of relatively inert macromolecules across the inner endothelial lining of the larger arteries of humans and animals and their subsequent diffusion in the underlying tissue of the intima and media. This model is motivated by the highly specialized ultrastructure of the arterial wall observed in electron microscopic studies and the recent experimental measurements of the time-dependent uptake of labelled macromolecules in animal arteries under carefully controlledin vitroconditions. The proposed dynamic model for the vesicular transport across the endothelial cell layer considers the constrained Brownian diffusion of 700 Å vesicles subject to long-range hydrodynamic and short-range London-van der Waals force interactions with the plasmalemma membranes of the endothelial cell. Approximate solutions are developed for the motion and the steady-state vesicle density distribution near the plasmalemma and in the interior of the cell using boundary-layer-like methods. The model for the vesicular transport just described appears as a novel boundary condition in the basic diffusion model for the underlying tissue. The latter is treated as a two-phase medium comprised of an interstitial fluid continuum with a uniformly dispersed smooth muscle phase as first proposed by Hills (1968). This model for the underlying tissue assumes that the smooth muscle cells contribute insignificantly to the macromolecule diffusion across the arterial wall but act as the principal storage reservoir for the macromolecules for large diffusion times because of their large volume fraction. The dimensionless parameters that arise in the theoretical model are determined by comparing the solutions for the time-dependent total wall uptake with Fry's (1973) experimental data for canine carotid artery.
A technique to identify and preserve the spinal accessory nerve during neck dissection
Authors: Chaukar D A , Pai A , D'Cruz A K
Published: March 2006

Introduction: Preservation of the spinal accessory nerve during neck dissection should be the rule rather than the exception. Despite the presence of many described techniques to locate the nerve, a tedious dissection is often required; as a consequence, it remains vulnerable to damage.

Method: We describe a novel method, not previously reported, based on identifying a constant vein which crosses the nerve. This aids in the nerve's early identification.

Conclusion: Our method enables the surgeon to locate the nerve precisely and to avoid damage to it, thereby maximizing post-operative function.
Satisfaction with cosmesis following nasal manipulation: do previous fractures matter?
Authors: Supriya M , Clement W A , Ahsan F , Cain A J
Published: March 2006

Objective: To determine if patients who have had multiple previous nasal fractures and who undergo manipulation of fractured nasal bones under general anaesthetic (MUA) are as likely to be satisfied with their post-operative nasal cosmesis as patients who have only sustained a single injury.

Design: Telephone survey.

Setting: District general hospital.

Participants: Adult patients who had undergone MUA over the preceding three years.

Main outcome measures: Patient satisfaction with nasal cosmesis and nasal airway and willingness to consider corrective surgery.

Results: One hundred and two patients were contacted. Overall patient satisfaction with cosmesis and nasal airway was 82 and 77 per cent, respectively, with 15 per cent willing to consider a procedure to improve their nasal cosmesis and 12 per cent willing to consider a procedure to improve nasal airway. Twenty-three (22.5 per cent) gave a history of one or more nasal bone fractures, either treated or untreated, prior to the most recently treated injury. Patient satisfaction with cosmesis in this group was 65 per cent, compared with 87 per cent satisfaction in the single injury group (p = 0.03). No statistically significant differences were demonstrated when comparing these groups for: satisfaction with nasal airway (70 vs 80 per cent, p = 0.46); willingness to consider a procedure to improve cosmesis (26 vs 11 per cent, p = 0.16); and willingness to consider a procedure to improve nasal airway (17 vs 10 per cent, p = 0.46).

Conclusions: A history of multiple previous nasal fractures does appear to alter patient satisfaction with the cosmetic outcome of nasal manipulation. These patients should be informed that they have a decreased chance of attaining a cosmetically acceptable result.
Myxofibrosarcoma of the neck
Authors: Udaka T , Yamamoto H , Shiomori T , Fujimura T , Suzuki H
Published: March 2006

We report a rare case of myxofibrosarcoma arising in the neck. A 55-year-old man presented with a two-year history of left-sided, painless, submandibular swelling. Computed tomography and magnetic resonance imaging (MRI) revealed an 80 × 35 mm, well defined, lobulated, submandibular tumour extending to the parapharyngeal space. The tumour showed uniformly low intensity and marked hyperintensity in T1- and T2-weighted MRI scans, respectively, and was scarcely enhanced by gadolinium. A tentative diagnosis of lymphangioma or plunging ranula was made, and the patient underwent local injection of OK-432, which proved to be ineffective. Resection of the tumour was then performed via a transcervical approach. The tumour was histopathologically and immunohistochemically diagnosed as a low-grade myxofibrosarcoma. The patient's post-operative clinical course was uneventful, and the patient was free of disease 27 months after surgery. The pathology, clinical characteristics and treatment of myxofibrosarcoma are bibliographically reviewed.
Functional MRI correlates of the recall of unresolved life events in borderline personality disorder
Authors: BEBLO THOMAS , DRIESSEN MARTIN , MERTENS MARKUS , WINGENFELD KATJA , PIEFKE MARTINA , RULLKOETTER NINA , SILVA-SAAVEDRA ANAMARIA , MENSEBACH CHRISTOPH , REDDEMANN LUISE , RAU HARALD , MARKOWITSCH HANS J. , WULFF HELLA , LANGE WOLFGANG , BEREA CRISTINA , OLLECH ISABELLA , WOERMANN FRIEDRICH G.
Published: March 2006

Background. Patients with borderline personality disorder (BPD) frequently report unresolved life events but it is still poorly understood, how these experiences are represented in the brain. Using functional magnetic resonance imaging (fMRI), the present study aimed at investigating the neural correlates of the recall of unresolved life events in patients with BPD and healthy controls.

Method. Twenty female BPD patients and 21 healthy control subjects underwent fMRI. During measurement subjects recalled unresolved and resolved negative life events. Individual cue words were used to stimulate autobiographical memory. After scanning, subjects rated their emotional states during the recall of both types of memories.

Results. When contrasting unresolved and resolved life events, patients showed significant bilateral activation of frontotemporal areas including the insula, amygdala, and the anterior cingulate cortex, the left posterior cingulate cortex, right occipital cortex, the bilateral cerebellum and the midbrain. In healthy subjects, no differential brain activation was related to these conditions. The 2×2 factorial analysis (ΔBPD−Δcontrols) revealed similar results with bilateral activation of the frontal cortex including parts of the insula and of the orbitofrontal cortex, temporal activation including the amygdala, activation of the right occipital cortex, and parts of the cerebellum. Patients but not controls reported higher levels of anxiety and helplessness during the unresolved versus resolved memory condition.

Conclusions. The activation of both, the amygdala and prefrontal areas, might reflect an increased effortful but insufficient attempt to control intensive emotions during the recall of unresolved life events in patients with BPD.