bluuebunny/crossref_metadata_2025_split huggingface dataset:
Effects of plane progressive irrotational waves on thermal boundary layers
Authors: Witting James 
Published: March 2006

The average changes in the structure of thermal boundary layers at the surface of bodies of water produced by various types of surface waves are computed. the waves are two-dimensional plane progressive irrotational waves of unchanging shape. they include deep-water linear waves, deep-water capillary waves of arbitrary amplitude, stokes waves, and the deep-water gravity wave of maximum amplitude.The results indicate that capillary waves can decrease mean temperature gradients by factors of as much as 9·0, if the average heat flux at the air-water interface is independent of the presence of the waves. Irrotational gravity waves can decrease the mean temperature gradients by factors no more than 1·381.Of possible pedagogical interest is the simplicity of the heat conduction equation for two-dimensional steady irrotational flows in an inviscid incompressible fluid if the velocity potential and the stream function are taken to be the independent variables.
On hydromagnetic oscillations in a rotating cavity
Authors: Gans Roger F. 
Published: March 2006

Time-dependent hydromagnetic phenomena in a rotating spherical cavity are investigated in the framework of an interior boundary-layer expansion. The interior problem is shown to contain waves whose frequencies are of order ω, Aω and A2ω, where ω is the rotation rate of the cavity and A2 = B2/4πρωA2 [Lt ] 1 is the Alfvén number. B is an imposed magnetic field, ρ the fluid density and R the radius of the cavity. The first type of wave is a modification of the hydro-dynamic inertial wave, the second is a pseudo-geostrophic wave and is involved in spin-up, and the third is related to the MAC waves of Braginskiy (1967).It is shown that the MAC waves must satisfy more than the usual normal boundary conditions and that reference must be made to the boundary-layer solution to resolve the ambiguity regarding which conditions are to be taken. For normal liquid metals of small magnetic Prandtl number the MAC waves must satisfy full magnetic boundary conditions; only the no-slip conditions may be deferred to the boundary layers.The boundary-layer structure is investigated in detail to display the interactions between applied field, viscosity, electrical conductivity, frequency and latitude. The decay of the pseudo-geostrophic modes, essentially the spin-up problem, is discussed for a non-axisymmetric constraining field and non-zero container conductivity. Three regimes exist, depending on container conductivity.
Linear stability of the dissipative, two-fluid, cylindrical Couette problem. Part 1. The stably-stratified hydrodynamic problem
Authors: Schneyer G. P. , Berger S. A. 
Published: March 2006

The stability of a two-fluid vortex is studied as a step towards understanding the separation and containment problems in a gaseous-core nuclear rocket. In particular, the linear hydrodynamic stability of two incompressible, immiscible, viscous fluids occupying separate annular regions of a cylindrical Couette apparatus is considered. Neglecting surface tension and gravity, a conservative assumption, the governing equations for arbitrary jumps in fluid properties are derived and numerical solutions to the resultant eigenvalue problems obtained. Results are presented for the effect on neutral stability of density and viscosity jumps, varying gap widths, and differing fluid-fluid interfacial positions. The solutions are limited, however, to the case of stably stratified fluids and a stationary outer cylinder.Two separate modes (multiple eigenvalues) have been discovered for all cases in which two fluids, differing in any property, are present. A rationale is presented for this phenomenon as well as for most of the other observed results.While most results are believed to be manifestations of the Taylor cylindrical Couette instability phenomenon, evidence is presented for the existence of additional ‘hidden’ eigenvalues attributable to the classical Kelvin–Helmholtz and/or the recently reported Yih viscosity-stratification instability phenomena.
Semi-infinite vortex trails, and their relation to oscillating airfoils
Authors: Weihs D. 
Published: March 2006

Semi-infinite double rows of vortices are used to study the periodic wake of both oscillating and stationary two-dimensional bodies immersed in a uniform incompressible stream. Analytical expressions for the induced Velocities on the body, for trails with constant spacing, which are valid for small values of the oscillation amplitude are presented while, for the general case of vortex shedding, an iterative procedure for the representation of trails of variable spacing is developed and used. Vortex streets due to oscillating bodies are obtained as a function of three non-dimensional parameters: the Strouhal number (initial spacing ratio), a non-dimensional vortex strength and the downstream spacing ratio. Criteria establishing when such trails are expected to widen, become narrow or stay of constant width are presented, as well as expressions for the induced velocities.The trails and their induced velocities enable the calculation of the vortex strength from measurable quantities. Thus they can serve as a method for estimating the hydrodynamic forces on the airfoil due to large amplitude oscillations, such as those observed in the propulsive movements of fish and cetaceans, as well as the small amplitude oscillations due to hydroelastic interactions.
Sedimentation in a dilute dispersion of spheres
Authors: Batchelor G. K. 
Published: March 2006

The dispersion considered consists of a large number of identical small rigid spheres with random positions which are falling through Newtonian fluid under gravity. The volume fraction of the spheres (c) is small compared with unity. The dispersion is statistically homogeneous, and the axes of reference are chosen so that the mean volume flux across any stationary surface is zero. The problem is to determine the mean value of the velocity of a sphere (U). In §3 there is described a systematic and rigorous procedure which overcomes the familiar difficulty presented by the occurrence of divergent integrals, essentially by the choice of a quantity V whose mean value can be found exactly and which has the same long-range dependence on the position of a second sphere as U so that the mean of U – V can be expressed in terms of an absolutely convergent integral. The result is that, correct to order c, the mean value of U is U0(1 – 6.55 c), where U0, is the velocity of a single sphere in unbounded fluid. The only assumption made in the calculation is that the centres of spheres in the dispersion take with equal probability all positions such that no two spheres overlap; arguments are given in support of this assumption, which is expected to be valid only when the spheres are identical. Calculations which assume a simple regular arrangement of the spheres or which adopt a cell model of the hydrodynamic interactions give the quite different result that the change in the mean speed of fall is proportional to $c^{\frac{1}{3}}$, for reasons which are made clear.The general procedure described here is expected to be applicable to other problems concerned with the effect of particle interactions on the average properties of dispersions with small volume fraction of the particles.
Laminarization of turbulent pipe flow by fluid injection
Authors: Pennell W. T. , Eckert E. R. G. , Sparrow E. M. 
Published: March 2006

The effects of fluid injection on the structure of an initially fully developed, low Reynolds number, turbulent pipe flow have been studied by means of a hot-film anemometer. Measurements were made of the axial turbulence intensity field and of the time-mean streamwise velocity distribution, both in the porous-walled pipe and in the solid-walled hydrodynamic development section. Oscilloscope traces showing the timewise pattern of the local velocity fluctuations were also monitored. The Reynolds number of the air flow at the inlet of the porous pipe was varied from 3090 to 6350, and the Reynolds number of the injected air ranged from 60 to 160.Near the tube wall, the initial effect of injection is a significant reduction of the axial turbulence level and an increase in the thickness of the viscous and buffer layers. The degree by which turbulence is reduced in this region is more or less proportional to the ratio of the injection to entrance Reynolds numbers. In the core region of the flow, which is centred about the tube axis, there is also an initial reduction in the magnitude of the axial component of turbulence which is thought to be due to injection-induced acceleration of the flow. There is also an annular region, which separates the wall and core regions, in which the turbulence intensity initially increases. In the downstream portion of the porous tube the entire flow undergoes a re-transition to fully developed turbulence.
Nonlinear resonant wave motion of a radiating gas
Authors: Eninger James E. , Vincenti Walter G. 
Published: March 2006

A method due to Chester is applied to the theoretical study of resonant wave motion of a radiatively active gas. The inviscid non-conducting grey gas is confined between two infinite parallel walls, and a one-dimensional wave motion is driven by a sinusoidally varying input of black-body radiation from one of the walls. For sufficiently weak driving radiation, the motion can be described by the general solution of the classical wave equation (with the functional form of the solution still undetermined) plus a particular solution due to the driving radiation. When the driving is done at or near a resonant frequency, however, nonlinearities and perturbations in spontaneous emission from the gas must be taken into account before application of the boundary conditions. Such application then leads to a nonlinear integral equation governing the undetermined function in the general solution of the wave equation. This equation is solved numerically by the method of parametric differentiation.In a frequency range around resonance and for a sufficiently weak relative level of spontaneous emission, the nonlinearities give rise to shock waves (numberingNat theNth resonant frequency) that are repeatedly reflected at the walls. The perturbations in spontaneous emission give rise to damping, however, and for sufficiently high levels of emission the shock waves disappear. Specific results for various values of optical thickness and various relative levels of spontaneous emission are presented at frequencies in a range around the first resonance.
Mean motions and impulse of a guided internal gravity wave packet
Authors: Mcintyre Michael E. 
Published: March 2006

Second-order mean fields of motion and density are calculated for the two-dimensional problem of an internal gravity wave packet (the waves are predominantly of a single frequency o and wavenumberk) propagating as a wave-guide mode in an inviscid, diffusionless Boussinesq fluid of constant buoyancy frequencyN, confined between horizontal boundaries. (The same mathematical analysis applies to the formally identical problem for inertia waves in a homogeneous rotating fluid.)To leading order the mean motions turn out to be zero outside the wave packet, which consequently possesses a well-defined fluid impulse [Iscr ]. This is directed horizontally, and is given in magnitude and sense by\[ {\cal I} = \alpha{\cal M};\quad\alpha = \frac{2c_{\rm g}(c-c_{\rm g})(c+2c_{\rm g})}{c^3-4c^3_{\rm g}}. \]Here [Mscr ] is the so-called ‘wave momentum’, defined as wave energy divided by horizontal phase velocity c ≡ ω/k, andcg=c(N2–ω2)/N2, the group velocity.If the wave packet is supposed generated by a horizontally towed obstacle, [Mscr ] appears as the total fluid impulse, but of this a portion [Mscr ]-[Iscr ] in general propagates independently away from the wave packet in the form of long waves. When the wave packet itself is totally reflected by a vertical barrier immersed in the fluid, the time-integrated horizontal force on the barrier equals 2 [Iscr ] (and not 2 [Mscr ] as might have been expected from a naive analogy with the radiation pressure of electromagnetic waves.)
Waves generated in rotating fluids by travelling forcing effects
Authors: Rao G. V. Prabhakara 
Published: March 2006

The two-dimensional wave pattern produced in a homogeneous rotating fluid by a forcing effect oscillating with a frequency σ′0 and travelling with a uniform speed U along a line inclined to the axis of rotation at an arbitrary angle α is studied following Lighthill's technique. It is shown how the far field changes with α and σ′0.For all σ′0 < 2Ω, except for σ′0 = 2Ω sin α (Ω being the angular velocity of the fluid), the forcing effect excites two systems of waves. When σ′0 → 2Ω sin α one of these systems spreads out, influencing the upstream side while the other shrinks in the downstream direction. This upstream influence is to the left or to the right of the line of motion of the forcing effect (the forcing line) according as σ′0 − 2Ω sin α[lg ] 0 and increases as σ′0 − 2Ω sin α decreases. For σ′0 > 2Ω there is only a single system propagating downstream. As α varies these systems undergo a kind of rotation retaining the main features. α ≠ 0 or ½π makes the pattern asymmetric about the forcing line while a non-zero σ′0 splits the steady-case identical wave systems into two, which are otherwise coincident.When σ′0 = 2Ω sin α the forcing effect excites straight unattenuated waves of fixed frequency travelling both ahead and behind in a ‘column’ parallel to the forcing line and enclosing it. Also there are two other systems, which propagate without penetrating into an upstream wedge. It is shown that this ‘column’ is the counterpart of the ‘Taylor column’.
Transient internal waves produced by a moving body in a tank of density-stratified fluid
Authors: Graham E. W. 
Published: March 2006

The internal waves produced by a moving body are generally longer in the direction of motion than the corresponding surface waves. This difference is accentuated when the density variation is slight and the body velocity is large in which case a very long towing tank may be required for the simulation of a steady-state condition. The following theoretical study of transient waves is intended as a step in relating test conditions and requisite towing-tank sizes.A source–sink pair travelling for a finite time is used to represent the restricted motion of a body in a tank. The approximate length and volume of the body are fixed, but its precise shape (somewhat irregular and slightly time dependent) is assumed to be of secondary importance and is not calculated here. The density-stratified fluid is assumed to have a constant Brunt–Väisälä frequency.A solution in the form of a triple sum over the tank eigenfunctions applies quite generally for the internal wave system (neglecting surface waves and the potential-flow-type solution near the body). Examples covering the large-scale structure of the flow field have been solved for two values of an approximate similarity parameter. The value of the similarity parameter indicates how closely steady-state conditions are approached. The first (larger) value chosen produces a well-defined quasi-steady state near the body with transient fluctuations of the order of ± 10%. The second (smaller) value gives a poorly defined quasisteady state with fluctuations of the order of ±50%. More elaborate studies varying the tank length, width and depth could be made by programming the calculations.The effect of a collapsing wake has not been considered here, but might possibly be treated by similar methods.
Nearly spherical constant-power detonation waves as driven by focused radiation
Authors: George Y. H. , Moore F. K. 
Published: March 2006

An analysis is made of the flow within a three-dimensional explosion, or spark, created in a gas absorbing energy from a steady conical beam of radiation with nearly spherical symmetry. The radiation, typically from an array of lasers with a common focus, is assumed to be very intense, and absorbed immediately behind an outwardly advancing strong shock. The resulting self-similar flow has previously been studied for spherical symmetry; somewhat improved calculations for that case are presented here.Departures of the laser power from spherical uniformity, which would result from practical problems of arrangement, are conveniently represented by an ascending series of Legendre polynomials in the polar angle. For non-uniformities of small amplitude, first-order perturbations of the flow field are analysed in detail. Self-similarity is shown to be retained, for zero counter-pressure and power constant with time.For the first five harmonics in power distortion, the resulting fourth-order system of equations is solved numerically for profiles of velocity components, density and pressure, and for shock shape. Results are presented graphically. These solutions are singular near the focus, but are nevertheless fully determined. In the limit of large wavenumber, the core of the flow has vanishing tangential velocity and pressure perturbations, and hence the governing equations are only of second order, except presumably in a boundary layer appearing near the shock.Study of the nonlinear case of large wavenumber along the axis of symmetry shows that the singularity at the focus reflects the existence of a ‘forbidden zone’ whose extent depends on the degree of asymmetry. It is argued that this zone is one within which diffusional processes must dominate.
On the motion of turbulent thermals
Authors: Escudier M. P. , Maxworthy T. 
Published: March 2006

An analysis is presented of the motion of a turbulent thermal in an unstratified environment. Although based upon the entrainment hypothesis introduced by G. I. Taylor (see Morton, Taylor & Turner 1956), the analysis differs from previous work in that it is not limited to small density differences between the thermal and its surroundings. Also, the influence of the virtual mass of the unsteadily moving fluid, ignored by previous investigators, is included and shown to be of significance for any density difference.Calculations of the temporal variations of size, velocity and density are presented in non-dimensional form for thermals with initial density ratios covering the practically attainable range. It is shown a posteriori that losses of momentum and buoyancy to a wake are probably of negligible influence in any real case.
Report on the NATO Advanced Study Institute on magnetohydrodynamic phenomena in rotating fluids
Authors: Moffatt H. K. 
Published: March 2006

An Advanced Study Institute sponsored by NATO on “Magnetohydrodynamic Phenomena in Rotating Fluids” was held in Cambridge, England, from 26 June to 4 July 1972. The aim of the meeting was to provide, through invited lectures, a systematic account of those aspects of the geophysics of the earth's core and of astrophysics in which both rotation effects and magnetic effects play an important part. In addition to the invited lectures, shorter contributions and discussions were strongly encouraged. The main Sessions and the Session Chairmen were as follows:A    The earth's magnetism and planetary magnetism magnetism    Sir Edward BullardB    Convection, differential rotation, and magneto-hydrodynamics in the sun    Dr N. O. WeissC    Stellar and interstellar magnetism; pulsars    Prof. E. SpiegelD    Boundary layers and detached shear layers and spin-up problems    Prof. E. R. BentonE    Waves and instabilities influenced by Lorentz and/or Coriolis forces    Dr R. HideF    Dynamo theory    Prof. P. H. RobertsThese Chairmen, together with Professor P. A. Gilman and Dr H. K. Moffatt, who acted as Director of the Institute, constituted the Organising Committee. The summary of the meeting which follows has been substantially written by Dr Weiss (sessions B and C), Dr Hide (A and E), Professor Benton (D) and Professor Roberts (F), whose willing collaboration is gratefully acknowledged.There were just over a hundred participants, the great majority of whom were accommodated at Trinity College, Cambridge, for the duration of the meeting.
The near wall jet of a normally impinging, uniform, axisymmetric, supersonic jet
Authors: Carling J. C. , Hunt B. L. 
Published: March 2006

The near wall jet produced by directing a uniform axisymmetric jet of air normally onto a large flat plate has been investigated experimentally and theoretically for four jets in the Mach number range 1·64–2·77. Detailed measurements of the surface pressure and shadowgraph and surface flow pictures are presented. The results show that the mechanism which mainly determines the supersonic near wall jet is the jet-edge expansion and its reflexions from the sonic line and the wall-jet boundaries. The near wall jet is found to consist of an alternating series of expansion and recompression regions whose strengths depend on the jet Mach number and decay with distance. At Mach numbers of 2·4 and above, shock waves are observed in the first recompression region and at a Mach number of 2·77 the boundary layer separates locally. Further out, viscous effects become increasingly important and a constant-pressure shear flow is established at a distance which increases with jet Mach number. The application of the method of characteristics in an approximate manner reproduces a number of the features of the near wall jet which are observed experimentally.Pressure distributions obtained in the shock layer show that a stagnation bubble can occur and that its occurrence depends on factors such as the flow upstream of the nozzle. The wall-jet region is found to be largely independent of whether or not a bubble occurs in the shock layer.
Optimal swimming of flagellated micro-organisms
Authors: Pironneau O. , Katz D. F. 
Published: March 2006

This paper studies flagellar undulations that propel a micro-organism at a given speed while minimizing its expenditure of hydrodynamical energy. The study is in two basic parts. The first part is a qualitative inquiry into the general nature of undulations that are hydrodynamically optimal in the instantaneous sense. The results indicate that an apparent sliding of the entire flagellum along its instantaneous axis is fundamental to such motions, although an additional deformation is necessary to compensate for the presence of the organism's head. Periodic or semi-periodic undulations are clearly suggested, and must consist of travelling waves propagated in the direction opposite to propulsion.The second part of the paper is a quantitative inquiry as to the values of parameters that optimize given periodic wave shapes in the time-average sense. The trade-off between wave amplitude and the number of wavelengths is of particular interest. Results are obtained for small amplitude sinusoidal waves and finite amplitude sawtooth waves. For the latter, a single wavelength with amplitude roughly one-sixth of the wavelength is optimal. The significance of the twitching movements of the head is investigated. The results are consistent with the qualitative study and emphasize the need to inhibit such motions. The implications of the dependence of resistive-force coefficients upon wave shape are considered, and the physical significance of rotational pitching motions is assessed.