bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the propulsion efficiency of swimming flexible hydrofoils of finite thickness
Authors: Uldrick J. P. 
Published: March 2006

This paper presents some recent theoretical results on the energy exchange between a swimming flexible two-dimensional hydrofoil of finite profile thickness and the inviscid incompressible fluid in which the body swims. The rate at which kinetic energy is transferred to the fluid by the undulating hydrofoil, the power required to maintain the prescribed motion, and the resulting power available for propulsion are calculated in terms of the thickness to chord ratio and the displacement and rate of displacement of the hydrofoil. With a small unsteady perturbation theory, the analysis is decomposed to show separately the effects of the circulatory and non-circulatory flows, both depending on the first-order terms of the unsteady perturbation velocity components. In addition, an analysis is presented showing the effect of the non-linear unsteady pressure distribution on the surface of the hydrofoil. Contrary to what might be expected, this latter effect is of the same order of magnitude for a thick rounded-nose profile as for the flat plate where the effect is concentrated at the sharp leading edge and is related to the so-called suction force. However, except for small values of the reduced frequency, the non-linear contribution is negligible in comparison with the linear contribution.New functions associated with the retarded flow in the wake are introduced and special techniques for their solution are presented, these being related to Theodorsen's function of unsteady airfoil theory for the special case of the undulating flat plate.The numerical results reveal that the kinetic energy imparted to the fluid, the power required to maintain the motion, and the resulting propulsive power, follow closely those of an infinitesimal model for small values of the reduced frequency of oscillation, but diverge somewhat from the classical thin plate analysis for large reduced frequencies. Of particular interest is the fact that a very large percentage of the power required to maintain the motion is used in the generation of the wake, whereas a very small percentage of the power available for propulsion comes from the wake. This indicates that, if some mechanism could be devised to control the wake, very high swimming efficiencies could be attained. Fish, in all probability, have been succeeding in doing this for millions of years.
On the stability of viscous flow between eccentric rotating cylinders
Authors: Ritchie G. S. 
Published: March 2006

The stability of viscous flow between eccentric cylinders is analysed for the case in which the inner cylinder rotates while the outer cylinder remains stationary, and where the difference in radii of the cylinders is small in comparison with their mean radius. The linearised equations governing the marginal stability of axially periodic disturbances are derived in general for the case where the cylinders are infinitely long, and are solved approximately to give estimates of the critical Taylor number at which vortex flow occurs for a range of relative eccentricity of the cylinders.The results give an upper bound to the stability boundary, and certain results of DiPrima are used to establish a lower bound, and consequently the stability boundary is well established for eccentricity ratios less than about 0·6. One important conclusion is that for a considerable range of eccentricity ratio the flow is less stable than when the cylinders are concentric.
Selective withdrawal from a stably stratified fluid
Authors: Wood I. R. 
Published: March 2006

In this paper a reservoir connected through a horizontal contraction to a channel is considered. Both the reservoir and the channel are considered to contain a stable multi-layered system of fluids. The conditions under which there is a flow in only one layer, and the depth in this flowing layer decreases continuously from its depth in the reservoir to its depth in the channel, give the maximum discharge that can be obtained with a flow only from this single layer. For this case the volume discharge calculations are carried out at a single section (the section of minimum width). Where there are velocities in only two layers and the depth in each of these layers decreases continuously from their depths in the reservoir to their depths in the channel, the theory involves computations at two sections in the flow. These are the section of minimum width and a section upstream of the position of minimum width (the virtual point of control). For this flow it is shown that the solution is the one in which the velocity and density distributions are self similar and that the depths of the layers at the point of maximum contraction are two-thirds of those far upstream. It is then shown that for any stable continuous or discrete density stratification in the reservoir a self similar solution will satisfy the conditions for the depths of the flowing layers to decrease smoothly from the reservoir to downstream of the contraction. Again the ratio of the depth at the contraction to that far upstream is two-thirds.When there is a very large density difference between the fluid in the lower dead water and that in the lowest flowing streamline then this streamline becomes horizontal and may be considered as a frictionless bed. The flow when the bed is not horizontal but where there is a small rise in the channel at the position of maximum contraction is considered for the case where two discrete layers flow under a volume of dead water. In this case the velocity and density profiles are not self similar.Experiments have been carried out with a contraction in a flume for the withdrawal of two discrete layers from a three layer system and the withdrawal from a fluid with a linear density gradient. In both cases the reservoir and channel bed and hence the lowest streamline was effectively horizontal. These experiments confirmed the theoretical predictions.
Smoke observations of the wake of a group of three cylinders at low Reynolds number
Authors: Zdravkovich M. M. 
Published: March 2006

A smoke visualization technique was used to study the laminar wake behind a group of three cylinders. The main characteristic of the interaction between the three cylinders was the appearance of strong sinuous oscillations some distance downstream in the wake, which led to the formation of a new single vortex street. The mechanism of the formation process of this vortex street and the part played in it by the sinuous oscillations is demonstrated by a series of photographs. The effects of variation of the spacing of the configuration have been examined in detail.In an interaction between three fully developed vortex streets, some of the rows of vortices crossed, and there was an extremely complicated re-arrangement of vorticity in the wake.Transition to turbulence in such wakes was also studied. The most interesting result observed was an asymmetric transition. Wakes were sometimes observed which were laminar on one side and turbulent on the other.
On the mixing of angular momentum in a stirred rotating fluid
Authors: Bretherton F. P. , Turner J. S. 
Published: March 2006

It has been suggested on theoretical grounds that a vortex could be initiated in a cylindrical region of fluid, originally in solid rotation, by the horizontal mixing of angular momentum produced by external stirring. In this paper various arguments for and against the mechanism are examined and their difficulties exposed. No firm conclusion is reached. A series of mathematical models of the mixing motions has been used, to bring out the differences between mechanical stirring and the agitation of a gas by random molecular motions. They suggest the introduction of a diffusion coefficient for angular momentum, to be determined empirically. These theoretical ideas are then applied to the interpretation of the results of a laboratory experiment which has been designed to test the proposed mechanism directly.A wide, flat tank of liquid was set up on a rotating table and stirred with a vertically oscillated grid, whose elements were much smaller than the width of the tank. A neutrally buoyant particle was used as a tracer of fluid motions, to measure relative circulation velocities and the properties of the turbulence. The motion observed was dominated by the loss of angular momentum to the walls and the grid, an effect which has not been taken into account in previous theoretical assessments of the effects of mixing of angular momentum. The relative circulation present was not significantly different from zero, and the limits of error of the measurements imply that the rate of diffusion of angular momentum is less than 5% of that for fluid particles, with 95% probability.
Axially-symmetric eddies embedded in a rotational stream
Authors: Leibovich S. 
Published: March 2006

The structure of eddies embedded in a swirling stream of an incompressible, inviscid fluid is examined. Laminar motion is assumed, as is axial symmetry of the flow field.It is supposed that the eddies are formed either (i) as wakes behind solid obstacles placed in the stream, or (ii) as the products of vortex breakdown occurrences, in which case the eddies are completely surrounded by fluid of the outer stream. In either event, it is assumed that the presence of an eddy only slightly disturbs the motion of the outer stream, i.e. that the eddies are slender. In particular, this requires that r0Ω∞/W∞ [Lt ]1, where r0 is the maximum radial extent of the eddy, and Ω∞ and W∞ are defined below.The analysis is carried to completion when the undisturbed outer stream is a wheel flow. Principal results derived are summarized below. (1) Eddy lengths are related directly and simply to the internal vorticity, providing that there is swirl in the outer flow. (2) A corollary is that very slender eddies have a maximum possible length. In the case (ii) above, this length is 2πW∞/Ω∞, where W∞ is the axial velocity and Ω∞ the angular velocity of the undisturbed outer flow. (3) The shapes of the free streamlines bounding the eddy are calculated. A feature is the cusped nature of an eddy free end. (4) The motion inside the eddy and the disturbance to the outer stream are calculated.Irrotational base flows are exceptional. Results (1) and (2) above cannot be found for a potential outer flow, but (3) and (4) remain.
The suppression of wind-generated waves by a surface film
Authors: Gottifredi J. C. , Jameson G. J. 
Published: March 2006

In the presence of a surface-active agent waves generated on the surface of a liquid by a wind may be stabilized. This problem is explored, and in particular the critical wind velocity is calculated for wave inception in the presence of such a film.The dominant parameter associated with the surface layer is the surface elasticity χ the ‘inextensible film’ of Lamb is obtained as a limit as χ → ∞. Such a value is hypothetical as for real films χ is not large, being in the range 0 to 80 dyne/cm approximately. Nevertheless, we show that damping exceeding that of the inextensible film can be obtained for short wavelengths, and that the critical wind speed for capillary ripples can be increased by a factor of ten in the presence of a film of experimentally attainable characteristics.The reason for the effectiveness of films of low χ is that the damping in the liquid is related to χ and the wavelength λ in such a way that for small λ, damping is a maximum for small χ.
Inclined buoyant puffs
Authors: Richards J. M. 
Published: March 2006

The motion of puffs which move in the direction of the buoyancy force was considered in a previous paper (Richards 1965). We now consider cases in which the directions of motion and of buoyancy are inclined or opposed. The main assumption is that the distributions of velocity inside the puffs are similar throughout the motion. Although this assumption is thought to be accurate only when the surroundings are neutral, we have reason to think that the same assumption may sometimes be used as an approximation to the internal distribution of velocity in other types of environment.The particular case of motion when the buoyancy force is constant is calculated in detail. The calculations are supported by observations from new laboratory experiments.
Double Kelvin waves with continuous depth profiles
Authors: Longuet-Higgins M. S. 
Published: March 2006

The possibility of long waves in a rotating ocean being trapped along a straight discontinuity in depth was demonstrated in a recent paper (Longuet-Higgins 1968). The analysis is now extended to the situation where the depth varies continuously, in a zone separating two regions of different depths. The trapping of waves in the transition zone is investigated, taking full account of the horizontal divergence of the motion.If the profile of the depth is assumed to be monotonic, then it is shown that the trapped waves always travel along the transition zone with the shallower water to their right in the northern hemisphere and to their left in the southern hemisphere. The wave period must always exceed a pendulum-day. The period is also bounded below by a quantity depending inversely on the maximum bottom gradient.By allowing the width W of the transition zone to vary, asymptotic forms for the trapped modes are obtained, both as W → 0 and as W → ∞. In the limit as W → 0 the depth becomes discontinuous, and it is shown that the lowest mode then becomes a double Kelvin wave (Longuet-Higgins 1968) propagated along the discontinuity. The periods of the higher modes, on the other hand, all tend to infinity; these modes become steady currents.Numerical calculations of the trapped modes are presented for two different laws of depth in the transition zone. It is found that as W → 0 the lowest mode is insensitive to the form of the depth profile. Higher modes depend on the details of the profile. Hence the lowest mode is the most likely to be observed in the real ocean.The dispersion relation is also investigated. It is shown that the group-velocity of all modes must change sign at some point in the range of wave-numbers, if the divergence is taken into account. When the divergence was neglected the lowest mode appeared to be exceptional, in that the group-velocity was always in the same direction. This anomaly is now removed.
The stability of steady and time-dependent plane Poiseuille flow
Authors: Grosch Chester E. , Salwen Harold 
Published: March 2006

The linear stability of plane Poiseuille flow has been studied both for the steady flow and also for the case of a pressure gradient that is periodic in time. The disturbance streamfunction is expanded in a complete set of functions that satisfy the boundary conditions. The expansion is truncated after N terms, yielding a set of N linear first-order differential equations for the time dependence of the expansion coefficients.For the steady flow, calculations have been carried out for both symmetric and antisymmetric disturbances over a wide range of Reynolds numbers and disturbance wave-numbers. The neutral stability curve, curves of constant amplification and decay rate, and the eigenfunctions for a number of cases have been calculated. The eigenvalue spectrum has also been examined in some detail. The first N eigenvalues are obtained from the numerical calculations, and an asymptotic formula for the higher eigenvalues has been derived. For those values of the wave-number and Reynolds number for which calculations were carried out by L. H. Thomas, there is excellent agreement in both the eigenvalues and the eigenfunctions with the results of Thomas.For the time-dependent flow, it was found, for small amplitudes of oscillation, that the modulation tended to stabilize the flow. If the flow was not completely stabilized then the growth rate of the disturbance was decreased. For a particular wave-number and Reynolds number there is an optimum amplitude and frequency of oscillation for which the degree of stabilization is a maximum. For a fixed amplitude and frequency of oscillation the wave-number of the disturbance and the Reynolds number has been varied and a neutral stability curve has been calculated. The neutral stability curve for the modulated flow shows a higher critical Reynolds number and a narrower band of unstable wave-numbers than that of the steady flow. The physical mechanism responsible for this stabiIization appears to be an interference between the shear wave generated by the modulation and the disturbance.For large amplitudes, the modulation destabilizes the flow. Growth rates of the modulated flow as much as an order of magnitude greater than that of the steady unmodulated flow have been found.
Theoretical study of the slow motion of a sphere and a fluid in a cylindrical tube
Authors: Greenstein T. , Happel J. 
Published: March 2006

The results of a theoretical treatment are presented for the slow flow of a viscous fluid through a circular cylinder within which a small spherical particle is confined. The sphere is situated in an arbitrary position within the cylinder, rotates with an arbitrary constant angular velocity and moves at constant velocity parallel to the wall. Approximate expressions are presented which give the frictional force, torque, and permanent pressure drop caused by the presence of this obstacle in the original Poiseuillian field of flow.An eccentricity function for the torque on a sphere in a circular cylinder was evaluated numerically. It can be used to predict the wall-effect for the torque as well as the angular velocity with which a ‘dense’ spherical particle will rotate. Expressions are presented which predict the angular velocity of ‘dense’ as well as neutrally buoyant hydrodynamically supported spherical particles.
Aerodynamic noise dependent on mean shear
Authors: Jones Ian S. F. 
Published: March 2006

New factors illustrating the effect of convection on acoustic radiation are deduced from Lighthill's theory of aerodynamic noise. For sound dependent on mean velocity variations for its generation, that is shear noise, the new factors are (1 − M cos θ)−3 and (1 − M cos θ)−1 in contrast with (1 − M cos θ)−5 for self noise.Comparison with the measured far-field directionality patterns reported by Howes (1960) shows that the factor (1 − M cos θ)−3 provides considerably better agreement with the experimental observations than the self noise factor.The source terms discussed by Lighthill (1954) when considering shear amplification are examined and shown to contain the terms produced by the analysis of Csanady (1966) as well as a new term dependent on the second derivative of the mean velocity.
Wave propagation and boundary instability in erodible-bed channels
Authors: Gradowczyk Mario H. 
Published: March 2006

Wave propagation in one-dimensional erodible-bed channels is discussed by using the shallow-water approximation for the fluid and a continuity equation for the bed. In addition to gravity waves, a third wave, which gives the velocity of propagation of a bed disturbance, is found. An appropriate dimensional analysis yields the quasi-steady approximation for the complete shallow-water equations.The well-known linear stability analysis of free-surface flows is extended to include the erodibility of the bed. The critical Froude numberFcabove which the free-surface of the fluid may become unstable is obtained. It is shown that erodibility increases the stability of the free surface, in qualitative agreement with previous experiments ifqb>qs,qbandqsbeing respectively the contact-bed discharge and suspended-material discharge. The stability theory is also used to discuss coupled beds and surface waves. From it, five different configurations have been obtained: a sinusoidal wave pattern moving downstream, a transition zone and antidunes moving upstream, moving downstream and stationary. These bed forms are in agreement with experimental results; hence shallow-water theory seems to give a reasonable explanation of the boundary instability.It is shown that the quasi-steady approximation and Kennedy's (1963) stability analysis will be in agreement if (kh)2[Lt ]1, wherekis the wave number, andhis the depth of the water. When the phase shift δ is introduced in the quasi-steady approximation, the five bed patterns derived from the full equations are found again.
Turbulent buoyant convection from a source in a confined region
Authors: Baines W. D. , Turner J. S. 
Published: March 2006

This paper considers the effect of continuous convection from small sources of buoyancy on the properties of the environment when the region of interest is bounded. The main assumptions are that the entrainment into the turbulent buoyant region is at a rate proportional to the local mean upward velocity, and that the buoyant elements spread out at the top of the region and become part of the non-turbulent environment at that level. Asymptotic solutions, valid at large times, are obtained for the cases of plumes from point and line sources and also periodically released thermals. These all have the properties that the environment is stably stratified, with the density profile fixed in shape, changing at a uniform rate in time at all levels, and everywhere descending (with ascending buoyant elements).The analysis is carried out in detail for the point source in an environment of constant cross-section. Laboratory experiments have been conducted for this case, and these verify the major predictions of the theory. It is then shown how the method can be extended to include more realistic starting conditions for the convection, and a general shape of bounded environment. Finally, the model is applied quantitatively to a variety of problems in engineering, the atmosphere and the ocean, and the limitations on its use are discussed.
Axisymmetric inertial oscillations of a fluid in a rotating spherical container
Authors: Aldridge Keith D. , Toomre Alar 
Published: March 2006

This paper describes an experiment performed with a fluid-filled sphere whose rotation speed about a fixed axis was forcibly varied in a slight but sinusoidal manner about a non-zero mean value. The object of this experiment was both to excite axisymmetric inertial eigen-oscillations within the relatively low viscosity fluid through the mild pumping action of the oscillatory Ekman boundary layer near the wall, and to measure and compare with theory some of the properties of such modes.Seven distinct fluid resonances were detected via pressure measurements made along the axis for various ratios of the excitation to the mean rotation frequency. For the three most pronounced of those modes, the observed frequency ratios agree within ½ of 1% with the corresponding ratios predicted from linear, small viscosity theory. The response amplitudes at the various resonances and the rates of decay upon switching off the excitation also compare favourably with theory, although the observed amplitudes are systematically lower and the decays more rapid by a few per cent to several tens of per cent.The theory referred to above is largely that of Greenspan (1964, 1968). It is in part rederived here from energy considerations.