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  • Cambridge University Press  (5,342)
  • Cell Press
  • 1965-1969  (5,742)
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  • 1
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    The motion of a spherical liquid drop at high Reynolds number (1968)
    Cambridge University Press
    In:  Journal of Fluid Mechanics, 32 (2). pp. 367-391.
    Details
    Publication Date: 2020-03-11
    Description: The steady motion of a liquid drop in another liquid of comparable density and viscosity is studied theoretically. Both inside and outside the drop, the Reynolds number is taken to be large enough for boundary-layer theory to hold, but small enough for surface tension to keep the drop nearly spherical. Surface-active impurities are assumed absent. We investigate the boundary layers associated with the inviscid first approximation to the flow, which is shown to be Hill's spherical vortex inside, and potential flow outside. The boundary layers are shown to perturb the velocity field only slightly at high Reynolds numbers, and to obey linear equations which are used to find first and second approximations to the drag coefficient and the rate of internal circulation.
    Type: Article , PeerReviewed
    Format: text
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  • 2
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    The transformation of a solitary wave over an uneven bottom (1969)
    Cambridge University Press
    Details
    Publication Date: 1969-12-15
    Description: Based on a set of approximate equations for long waves over an uneven bottom, numerical results show that as a solitary wave climbs a slope the rate of amplitude increase depends on the initial amplitude as well as on the slope. Results are also obtained for a solitary wave progressing over a slope onto a shelf. On the shelf a disintegration of the initial wave into a train of solitary waves of decreasing amplitude is found. Experimental evidence is also presented.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 3
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    The effect of base bleed on the steady separated flow past bluff objects (1969)
    Cambridge University Press
    Details
    Publication Date: 1969-12-15
    Description: The modifying effect of base bleed on the steady separated flow past a two-dimensional bluff body is considered. Detailed experimental results are presented for Reynolds numbers R between 50 and 250 and for bleed coefficients b in the range 0 to 0·15. The streamline pattern near the object is found to be strongly affected by small changes in the rate of bleed, with the recirculating closed wake disappearing altogether for b 〉 0·15. Nevertheless, the qualitative dependence on R of the physical dimensions of the near-wake region and the associated streamwise pressure profile appear to be unaffected by base bleed.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 4
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    Gravity waves over a non-uniform flow (1969)
    Cambridge University Press
    Details
    Publication Date: 1969-12-15
    Description: This paper is concerned with the propagation of small amplitude gravity waves over a flow with non-uniform velocity distribution. For such a flow Burns derived a relation for the velocity of propagation in terms of the velocity distribution of the mean flow. This result is derived here in another way and some of its implications are discussed. It is shown that one of these is hardly acceptable physically. Burns's result holds only when a real value of the propagation velocity is assumed; the mentioned difficulties vanish if complex values are allowed for, implying damping or growth of the waves. Viscous effects which are the cause of damping or growth are important in the wall layer near the bottom and also at the critical depth, which is present when the wave speed is between zero and the fluid velocity at the free surface.In § 2 the basic equations for the present problem are given. In § 3 exchange of momentum and energy between wave and primary flow is discussed. This is analogous to what happens at the critical height in a wind flow over wind-driven gravity waves. In § 4 the viscous effects at the bottom are included in the analysis and the complex equation for the propagation velocity is derived. Finally in § 5 illustrations of the theory are given for long waves over running flow and for the flow along a ship advancing in a wavy sea. In these examples a negative curvature of the mean velocity profile is shown to have a stabilizing effect.
    Print ISSN: 0022-1120
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 5
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    Non-linearity, relaxation and diffusion in acoustics and ultrasonics (1969)
    Cambridge University Press
    Details
    Publication Date: 1969-12-15
    Description: As they propagate through a gas, fluctuating pressure signals of moderate amplitude and of ultrasonic frequency are affected by amplitude dispersion, by relaxation damping and, particularly in ‘shock layers’, by diffusive damping. We derive a ‘high frequency’ theory including all these effects, for disturbances of arbitrary wave form excited by a wide variety of boundary conditions. By introducing a phase variable α, and taking account of non-linearity, we show how the signal propagates along the rays of linear acoustics theory, with constantly changing wave profile.Relaxation dampens the signal, as for linear acoustics, and also diminishes amplitude dispersion. A criterion for shock formation is given, and the importance of non-linearity for signal attenuation exhibited. As shocks form, α surfaces coalesce and diffusive mechanisms are accentuated. Whitham's area rule is shown to be relevant for unsteady three-dimensional flows in relaxing gases, and is used to compute the attentuation of an ultrasonic beam. Supersonic relaxing flow over a wavy wall is also analyzed, and focusing effects are discussed.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 6
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    Steady free convection above a point heat source and a horizontal line heat source in a vertical magnetic field (1969)
    Cambridge University Press
    Details
    Publication Date: 1969-12-15
    Description: An electrically conducting fluid is contained above a horizontal plane. A uniform vertical magnetic field is applied externally and the plane is maintained at a uniform temperature except for a point or a line heat source. Density variations are ignored except where they give rise to buoyancy forces.(i) The point heat source. Non-linear effects are small sufficiently far from the source. The resulting buoyancy forces interact with the magnetic forces to maintain a radial inflow towards the heat source. This fluid then escapes vertically as a jet, its structure now depending on the additional influence of viscosity. The perturbations of the temperature distribution and the magnetic field due to the motion are obtained. Finally, the effects of these perturbations back on to the fluid velocity are considered. The most striking features of the perturbations are (a) the action of the jet as a line source of heat for the fluid in the outer regions, (b) the large (compared to other perturbations) eddy in the jet.(ii) The line heat source. The temperature distribution and magnetic field are weakly perturbed only if the thermal and electrical conductivities are sufficiently small. Similar results are obtained, as in (i) above, provided ε (a dimensionless number characterising the strength of thermal convection: see (1.32), (3.24)) is less than ¼. However, even for small ε, the effects of thermal convection cannot be ignored. Hence, superimposed on the jet is an eddy (driven by buoyancy forces) whose flux of fluid increases indefinitely with its height above the plane. When ε 〉 ¼, the results suggest that numerous eddies will be formed.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 7
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    The flow induced by the transverse motion of a thin disk in its own plane through a contained rapidly rotating viscous liquid (1969)
    Cambridge University Press
    Details
    Publication Date: 1969-12-15
    Description: A thin circular disk translates slowly in its own plane transverse to the axis of rotation of parallel plane boundaries filled with viscous incompressible liquid. It is shown that the indeterminateness of the geostrophic flow is removed by constraints imposed by the dynamics of free shear layers (Stewartson layers), which surround a Taylor column whose boundary is not a stream surface. Fluid particles cross the Taylor column at the expense of deflexion through a finite angle. A comparison is made with the flow past a fat body (Jacobs 1964), where the geostrophie flow is determined without appeal to the dynamics of the shear layers. The problem is also considered for a disk in an unbounded fluid, and it is shown that to leading order there is no disturbance.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 8
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    On steady recirculating flows (1969)
    Cambridge University Press
    Details
    Publication Date: 1969-12-15
    Description: Integral constraints are derived for steady recirculating flows of nearly incompressible fluids, arising from the action of a small amount of viscosity and heat conduction. These constraints are then combined with the inviscid nondiffusive incompressible flow equations to show that two-dimensional flows containing closed nested streamlines, or three-dimensional flows with closed nested stream surfaces, are isothermal. In the former case it is shown that the vorticity is constant, and in the latter case there is an analogous result when the flow is axially symmetric and confined to axial planes. For a circular cell free convection problem, the interior temperature and vorticity are determined from the boundary conditions by an approximate integration of the boundary layer equations.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 9
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    Cylindrical shock and detonation waves in magnetogasdynamics (1969)
    Cambridge University Press
    Details
    Publication Date: 1969-12-15
    Description: Self-similar flow patterns are studied which arise when a cylindrically symmetric strong shock or detonation wave propagates outwards into a gas at rest in which the ambient density varies as the inverse square of the distance from the axis of symmetry along which flows a line current of either zero or finite constant strength. The electrical conductivity of the gas on either side of the wave is supposed perfect and the discontinuities discussed are either gasdynamic or magnetogas-dynamic in nature. It is shown that self-similar solutions exist for piston driven gasdynamic detonation and shock waves. Whilst no self-similar solutions may occur for magnetogasdynamic detonation waves, it is demonstrated that magnetogasdynamic shock waves do possess such solutions for which detailed flow patterns are presented.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 10
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    Shock collision at a molecular level (1969)
    Cambridge University Press
    Details
    Publication Date: 1969-12-15
    Description: The development of reflected waves are studied when two shocks of unequal strength collide and when a shock collides with a constant temperature wall. Both these problems are examined using the Monte Carlo technique developed by Bird (1967). Some limitations upon this technique are suggested and a modified time advance parameter used.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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