bluuebunny/crossref_metadata_2025_split huggingface dataset:
A comparison between buoyant vortex rings and vortex pairs
Authors: Turner J. S. 
Published: March 2006

In this paper it is shown how earlier results for buoyant vortex rings may be extended to describe the corresponding two-dimensional case, which arises in the theory of bent-over plumes. It is again assumed that in uniform surroundings the circulation remains constant while the buoyancy acts to increase the momentum of the pair. The behaviour in two dimensions is quite different from that in three, however; a buoyant vortex ring spreads linearly with height, whereas a buoyant pair spreads exponentially with height, or linearly with time (and therefore, in a bent-over plume, linearly with distance downwind).The theory has been extended to describe the rise of buoyant rings and pairs through stably stratified surroundings having a linear density gradient. The behaviour near the maximum height reached is found to depend critically in both cases on the relative rates at which the circulation and the momentum fall to zero. If these reach zero together, the rings or pairs will steadily increase in size and come to rest at a finite height and with a finite radius. If the circulation is non-zero when the momentum vanishes, the radius begins to decrease soon after the buoyancy becomes zero, and the vortices will therefore tend to break up suddenly and mix into their surroundings. There is a considerable increase in the final height which should be attained by vortex rings or bentover plumes if the initial circulation is increased; it is suggested that releasing smoke intermittently, rather than continuously, at high velocity might be a means of increasing the effective height of chimneys in calm conditions. When the circulation reaches zero before the momentum does, the solutions indicate that the radius becomes very large near the level of zero buoyancy.
The stability of free boundary layers between two uniform streams
Authors: Tatsumi T. , Gotoh K. 
Published: March 2006

Hydrodynamic stability of free boundary-layer flows is treated in general. It is found that the situations at low Reynolds numbers are universal for all velocity profiles of free boundary-layer type. Curves of constant amplification are calculated as far as O(R3). In particular, the asymptotic form of the neutral curves for R [eDot ] 0 is found to be α = R/(4√3), so that the critical Reynolds numbers of these flows are identically zero. The phase velocity of the disturbance is also found to be zero, for all disturbances, up to the second approximation.A method of normalizing the velocity profiles is suggested, and existing results for the stability of various profiles at large Reynolds numbers are discussed from a new point of view.
The Stokes flow problem for a class of axially symmetric bodies
Authors: Payne L. E. , Pell W. H. 
Published: March 2006

The Stokes flow problem is concerned with fluid motion about an obstacle when the motion is such that inertial effects can be neglected. This problem is considered here for the case in which the obstacle (or configuration of obstacles) has an axis of symmetry, and the flow at distant points is uniform and parallel to this axis. The differential equation for the stream function ψ then assumes the form L2−1ψ = 0, where L−1 is the operator which occurs in axiallysymmetric flows of the incompressible ideal fluid. This is a particular case of the fundamental operator of A. Weinstein's generalized axially symmetric potential theory. Using the results of this theory and theorems regarding representations of the solutions of repeated operator equations, the authors (1) give a general expression for the drag of an axially symmetric configuration in Stokes flow, and (2) indicate a procedure for the determination of the stream function. The stream function is found for the particular case of the lens-shaped body.Explicit calculation of the drag is difficult for the general lens, without recourse to numerical procedures, but is relatively easy in the case of the hemispherical cup. As examples illustrative of their procedures, the authors briefly consider three Stokes flow problems whose solutions have been given previously.
On the dynamics of unsteady gravity waves of finite amplitude Part 1. The elementary interactions
Authors: Phillips O. M. 
Published: March 2006

This paper is concerned with the non-linear interactions between pairs of intersecting gravity wave trains of arbitrary wavelength and direction on the surface of water whose depth is large compared with any of the wavelengths involved. An equation is set up to describe the time history of the Fourier components of the surface displacement in which are retained terms whose magnitude is of order (slope)2 relative to the linear (first-order) terms. The second-order terms give rise to Fourier components with wave-numbers and frequencies formed by the sums and differences of those of the primary components, and the amplitudes of these secondary components is always bounded in time and small in magnitude. The phase velocity of the secondary components is always different from the phase velocity of a free infinitesimal wave of the same wave-number. However, the third-order terms can give rise to tertiary components whose phase velocity is equal to the phase velocity of a free infinitesimal wave of the same wave-number, and when this condition is satisfied the amplitude of the tertiary component grows linearly with time in a resonant manner, and there is a continuing flux of potential energy from one wave-number to another. The time scale of the growth of the tertiary component is of order of the (−2)-power of the geometric mean of the primary wave slopes times the period of the tertiary wave. The Stokes permanent wave appears as a special case, in which the tertiary wave-number is the same as that of the primary, but its phase is advanced by ½π. The energy transfer to the tertiary component in this case is usually interpreted as an increase in the phase velocity of the wave.The dynamical interactions in water of finite depth are considered briefly, and it is shown that the amplitude of the secondary components becomes large (though bounded in time) as the water depth becomes smaller than the wave-length of the longest primary wave.
The second approximation to cnoidal and solitary waves
Authors: Laitone E. V. 
Published: March 2006

The expansion method introduced by Friedrichs (1948) for the systematic development of shallow-water theory for water waves of large wavelength was used by Keller (1948) to obtain the first approximation for the finite-amplitude solitary wave of Boussinesq (1872) and Rayleigh (1876), as well as for periodic waves of permanent type, corresponding to the cnoidal waves of Korteweg & de Vries (1895).The present investigation extends Friedrich's method so as to include terms up to the fourth order from shallow-water theory for a flat horizontal bottom, and thereby obtains the complete second approximations to both cnoidal and solitary waves. These second approximations show that, unlike the first approximation, the vertical motions cannot be considered as negligible, and that the pressure variation is no longer hydrostatic.
Note on waves through gases at pressures small compared with the magnetic pressure, with applications to upper-atmosphere aerodynamics
Authors: Lighthill M. J. 
Published: March 2006

Most treatments of magnetohydrodynamics waves have confined physical interpretation to cases when the Alfvén velocity a1 is small compared with the sound velocity a0. Here we consider the ‘low-beta situation’, in which a1, the only possible waves are longitudinal ones, propagated unidirectionally along lines of magnetic force with velocity a0. These can be interpreted as sound waves, confined to effectively rigid magnetic tubes of force. Hall-current effects do not alter these conclusions (in contrast to the high-beta situation), and finite conductivity introduces only small dissipation.An application is made to the flow pattern around a body moving through the F2 layer of the ionosphere, where, although neutral particles have a very large mean free path, charged particles interact electrostatically and, it is argued, may be regarded as forming a continuous fluid whose movement is independent of that of the neutral particles. A body moving at satellite speed or below would then excite the above-mentioned unidirectional sound waves, but no waves at much faster Alfvén velocity. These considerations suggest that its movement would be accompanied by a [xvee ]-shaped pattern of electron density (figure 2), which might be in part responsible for some anomalous radar echoes that have been reported.
An example of steady laminar flow at large Reynolds number
Authors: Proudman Iam 
Published: March 2006

The purpose of this note is to describe a particular class of steady fluid flows, for which the techniques of classical hydrodynamics and boundary-layer theory determine uniquely the asymptotic flow for large Reynolds number for each of a continuously varied set of boundary conditions. The flows involve viscous layers in the interior of the flow domain, as well as boundary layers, and the investigation is unusual in that the position and structure of all the viscous layers are determined uniquely. The note is intended to be an illustration of the principles that lead to this determination, not a source of information of practical value.The flows take place in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. When fluid is extracted through both walls there are boundary layers on both walls and the flow outside these layers is irrotational. When fluid is extracted through one wall and injected through the other, there is a boundary layer only on the former wall and the inviscid rotational flow outside this layer satisfies the no-slip condition on the other wall. When fluid is injected through both walls there are no boundary layers, but there is a viscous layer in the interior of the channel, across which the second derivative of the tangential velocity is discontinous, and the position of this layer is determined by the requirement that the inviscid rotational flows on either side of it must satisfy the no-slip conditions on the walls.
The effect of a very strong magnetic cross-field on steady motion through a slightly conducting fluid
Authors: Ludford G. S. S. 
Published: March 2006

The flow engendered by the steady motion of a cylindrical insulator through an inviscid, incompressible fluid of small conductivity σ is not close to potential flow when the applied magnetic cross-fieldH0is sufficiently strong. Here we determine the limiting form of this flow as σ → 0 with$\sigma H^2_0 \rightarrow \infty$, the latter representing the ponderomotive force.The limit equations do not have a unique solution, but it is possible to make a selection by taking into account the inertia of the fluid during the limiting process, i.e. without recourse to considerations of how the motion was set up from rest. The forces on the cylinder are found to be asymptotically proportional to$\surd {\sigma} H_0$.The case of an elliptic cylinder and that of a flat plate are worked out in detail.
On the behaviour of liquid dispersions in mixing vessels
Authors: Shinnar Reuel 
Published: March 2006

The present paper is concerned with the conditions of flow in tanks containing stirred fluids. An attempt is made to apply the theoretical concepts of local isotropy to explain the behaviour of liquid in liquid dispersions, subjected to turbulent agitation. Relations describing quantitatively the influence of turbulence on both break-up and coalescence of individual droplets are derived and are compared with experimental evidence. A special type of dispersion is described in which droplet size is controlled by the prevention of coalescence due to turbulence. The dependence of droplet size on energy dissipation per unit mass, as predicted by the theory of local isotropy, is put to an experimental test using geometrically similar vessels of different sizes.Though the results are not entirely conclusive, experimental evidence suggests that the hypothesis of locally isotropic flow may be applicable to the flow conditions described in the paper, and that statistical theories of turbulence can be of practical value in estimating droplet sizes in agitated dispersions.
Spectral flatness factor and ‘intermittency’ in turbulence and in non-linear noise
Authors: Kennedy D. A. , Corrsin S. 
Published: March 2006

The flatness factor F of the signal transmitted through a band-pass filter has been measured for the turbulence in a free shear layer and for a squared Gaussian noise. They both show flatness factor increasing with centre frequency fc. In the turbulence, band-passed signals look intermittent and have larger F than the full signal, but in the squared noise, band-passed signals all have smaller F than the full signal although they look more intermittent.It is shown analytically that the derivative of a smoothed, squared Gaussian noise may have flatness factor either greater or less than the undifferentiated signal.
Interaction between gravity waves and a shear flow
Authors: Hughes B. A. , Stewart R. W. 
Published: March 2006

A series of experiments has been undertaken in which three major properties of a surface tension-gravity wave system have been examined. The results of these experiments have been compared with existing theories. The three properties are: (i) viscous decay in the absence of mean flow, the relevant theory being given in Lamb (1932, § 348); (ii) propagation velocities in the presence and absence of flow (Lamb 1932, § 267), and (iii) the change of wave energy on crossing a stable Couette shear flow. The measurements in the last case were compared with two theories, one obtained from the Navier–Stokes equations including terms up to second order in wave slope, the other, following previous authors, obtained on the assumption that any direct interaction of the waves with the shear flow is negligible. According to the theory obtained from the Navier–Stokes equations, the divergence of surface wave energy is equal to the rate of change of wave energy due to the interaction between the mean flow and the wave system plus the rate of change of wave energy due to viscous decay.An optical system was used to measure the maximum wave slopes, the wave-numbers and the shear velocities.Results indicate that an anomalous region of wave properties exists for wave-numbers near 2.7 cm−1. For a set of data in which the wave-numbers were always less than 1.8 cm−1, it was found that the viscous decay rate and the propagation laws agree with theory to within the experimental error, and the interaction measurements fit the theory with the non-linear term included rather than the traditional theories.
A theory of anisotropic fluids
Authors: Hand George L. 
Published: March 2006

A theory is proposed in which the stress tensor is a function of the components of the rate of deformation tensor and a symmetric tensor describing the microscopic structure of a fluid. The expression for the stress tensor can be written in closed form using results from the Hamilton-Cayley theorem. This theory is shown to contain Prager's theory of dumbbell suspensions as a special case. By limiting the type of terms in the constitutive equations, various stress components can be evaluated for simple shear. These exhibit non-Newtonian behaviour typical of certain higher polymer solutions.Some of the results of the anisotropic fluid theory are compared with experimental measurements of normal stress and apparent viscosity. Certain high polymers in solution show good agreement between theory and experiment, at least for low enough values of the rate of shear.
A consequence of the zero fourth cumulant approximation
Authors: O'Brien Edward E. , Francis George C. 
Published: March 2006

Recent investigations by Kraichnan (1961) and Ogura (1961) have raised doubts concerning the usefulness of the zero fourth cumulant approximation in turbulence dynamics. It appears extremely tedious to examine, by numerical computation, the consequences of this approximation on the turbulent energy spectrum although the appropriate equations have been established by Proudman & Reid (1954) and Tatsumi (1957). It has proved possible, however, to compute numerically the sequences of an analogous assumption when applied to an isotropic passive scalar in isotropic turbulence.The result of such computation, for specific initial conditions described herein, and for stationary turbulence, is that the scalar spectrum does develop negative values after a time approximately $2 \Lambda | {\overline {(u^2)}} ^{\frac {1}{2}}$, Where Λ is a length scale typical of the energy-containing components of both the turbulent and scalar spectra and $\overline {(u^2)}^{\frac {1}{2}}$ is the root mean square turbulent velocity.
The final approach to steady, viscous flow near a stagnation point following a change in free stream velocity
Authors: Kelly R. E 
Published: March 2006

The flow field near a stagnation point in two-dimensional, incompressible, viscous flow is considered to change with time in such a way that the inviscid flow is steady after some given finite instant of time. The final approach to steady flow throughout the field is shown to be characterized by exponential decay with time of perturbations from the steady velocity field. The characteristic factors in the exponents arise from the solution of an eigenvalue problem in ordinary linear differential equations.Similar behaviour exists for the axially symmetric case. A comparable analysis furnishes, however, a meaningless result in the case of a two-dimensional, semiinfinite flat plate which is moving in its own plane, normal to its leading edge.
Radiation stress and mass transport in gravity waves, with application to ‘surf beats’
Authors: Longuet-Higgins M. S. , Stewart R. W. 
Published: March 2006

This paper studies the second-order currents and changes in mean surface level which are caused by gravity waves of non-uniform amplitude. The effects are interpreted in terms of the radiation stresses in the waves.The first example is of wave groups propagated in water of uniform mean depth. The problem is solved first by a perturbation analysis. In two special cases the second-order currents are found to be proportional simply to the square of the local wave amplitude: (a) when the lengths of the groups are large compared to the mean depth, and (b) when the groups are all of equal length. Then the surface is found to be depressed under a high group of waves and the mass-transport is relatively negative there. In case (a) the result can be simply related to the radiation stresses, which tend to expel fluid from beneath the higher waves.The second example considered is the propagation of waves of steady amplitude in water of gradually varying depth. Assuming no loss of energy by friction or reflexion, the wave amplitude must vary horizontally, to maintain the flux of energy constant; it is shown that this produces a negative tilt in the mean surface level as the depth diminishes. However, if the wave height is limited by breaking, the tilt is positive. The results are in agreement with some observations by Fairchild.Lastly, the propagation of groups of waves from deep to shallow water is studied. As the mean depth decreases, so the response of the fluid to the radiation stresses tends to increase. The long waves thus generated may be reflected as free waves, and so account for the 'surf beats’ observed by Munk and Tucker.Generalle speaking, the changes in mean sea level produced by ocean waves are comparable with those due to horizontal wind stress. It may be necessary to allow for the wave stresses in calculating wind stress coefficients.
Vertical motion of a floating sphere in a sine-wave sea
Authors: Barakat Richard 
Published: March 2006

The vertical motion (heave) of a freely floating sphere is studied under the action of incident sine waves. Forced heave is defined as the vertical motion of sphere in still water, while free heave is defined as the vertical motion of sphere in the sine-wave sea. The total velocity potential describing the motion is decomposed into three terms: incident wave potential, diffracted wave potential (potential as if the sphere were fixed in sine-wave sea), and forced heave potential (potential as if the sphere were in forced vertical motion in still water). The forced heave and diffraction problems are solved separately. The linearized equation of motion is then used to effect the synthesis of the free motion via two unknowns: amplitude of vertical displacement and phase difference.Both the radiation and diffraction problems are solved by expansions of non-orthogonal functions (wave-free potentials). These functions are trivial solutions of the Sommerfeld radiation condition in the sense that they attenuate faster than O(r−½) and it is necessary to add multipole terms which have the proper behaviour at infinity. Infinite systems of linear equations are obtained for the unknown expansion coefficients and the unknown source strengths of the multipole. The added mass, damping coefficient and wave-making coefficient in forced heave are studied as well as the force on the fixed sphere. In addition the added mass and damping coefficient in free heave are obtained.The horizontal motion (surge) of the freely floating sphere can be obtained by methods similar to those employed for the vertical motion. The author is presently working on this problem. Surge and heave are not independent motions but can be treated separately because of the symmetry of the sphere.
Hydromagnetic waves in a cylindrical plasma
Authors: Woods L. C. 
Published: March 2006

This paper contained several extensions of the theory of hydromagnetic waves in a partially ionized gas. The gas is confined in a cylindrical tube through which passes an axial magnetic field. The tube wall is assumed to be either a perfect conductor or a material of small or zero conductivity.The effects of the viscosity and compressibility of the ionized and neutral gases are included in the theory, as also are the contributions of finite conductivity and the ion-cyclotron term. The non-isotropic character of the viscosity and conductivity coefficients of the ionized gas is taken into account. New boundary conditions are derived for tubes with insulating walls, and it is shown that the only pure modes that can be propagated along such tubes are just two special cases of those waves having no azimuthal dependence.The principal result of the paper is a new dispersion relation which allows for all the dissipative effects just mentioned and which is valid for a range of frequencies which extends well beyond the ion cyclotron frequency, but falls short of the frequency at which electron inertia and displacement currents became effective.