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  • Articles  (1,884)
  • Cambridge University Press  (1,884)
  • 1980-1984  (1,884)
  • 1982  (1,884)
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  • 1980-1984  (1,884)
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  • 1
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    Three-dimensional stability of vortex arrays (1982)
    Cambridge University Press
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    Publication Date: 1982-12-01
    Description: The stability to three-dimensional disturbances of three classical steady vortex configurations in an incompressible inviscid fluid is studied in the limit of small vortex cross-sectional area and long axial disturbance wavelength. The configurations examined are the single infinite vortex row, the Karman vortex street of staggered vortices and the symmetricvortex street. It is shown that the single row is most unstable to a two-dimensional disturbance, while the Karman vortex street is most unstable to a three-dimensional disturbance over a significant range of street spacing ratios. The symmetric vortex street is found to be most unstable to three-dimensional or two-dimensional symmetric disturbances depending on the spacing ratio of the street. Short remarks are made concerning the relevance of the calculations to the observed instabilities in free shear layer, wake and boundary-layer type flows. © 1982, Cambridge University Press. All rights reserved.
    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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  • 2
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    Effects of inertia on the diffusional deposition of small particles to spheres and cylinders at low Reynolds numbers (1982)
    Cambridge University Press
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    Publication Date: 1982-12-01
    Description: A formalism that accounts for inertial and diffusive effects in the dynamics of a dilute gas-particle suspension is introduced. The treatment is purely deterministic away from a very thin Brownian diffusion sublayer, while, within the sublayer, inertial effects are small, permitting a near-equilibrium expansion in powers of the Stokes number (particle relaxation time divided by flow characteristic residence time). This expansion provides phenomenological expressions for theparticle velocity including two terms: the standard Brownian diffusion, and an additional inertial drift velocity which is closely related to the pressure diffusion term of the Chapman-Enskog expansion. As an example, the general formalism is applied in detail to the case of Stokes flow about a sphere, and sketched for the similar case of a cylinder. Two competing mechanisms are seen to affect the total rate of particle capture by the sphere: (i) the stagnation-point region is considerably enriched in particles owing to the high compressibility of the particle phase, which leads to locally enhanced deposition; (ii) centrifugal forces tend to deplete the Brownian diffusion sublayer of particles, reducing diffusion rates away from the stagnation point to the surface. The first effect is seen to dominate over the second except in a very narrow zone of small Stokes numbers. Our method bridges the gap between Levich's solution for the ‘pure-diffusion’ limit and Michael's treatment in the ‘pure-inertia’ limit. © 1982, Cambridge University Press. All rights reserved.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 3
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    A simple model of mixing and chemical reaction in a turbulent shear layer (1982)
    Cambridge University Press
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    Publication Date: 1982-12-01
    Description: Arguments are presented to show that the concept of gradient diffusion is inapplicable to mixing in turbulent shear layers. A new model is proposed for treating molecular mixing and chemical reaction in such flows at high Reynolds number. It is based upon the experimental observations that revealed the presence of coherent structures and that showed that fluid elements from the two streams are distributed unmixed throughout the layer by large-scale in viscid motions. The model incorporates features of the strained flame model and makes use of the Kolmogorov cascade in scales. Several model predictions differ markedly from those of diffusion models and suggest experiments for testing the two approaches.† Present address: Dept of Aeronautics, University of Washington, Seattle, WA 98195. © 1982, Cambridge University Press. All rights reserved.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 4
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    Observations of inertial waves in a homogeneous rotating fluid (1982)
    Cambridge University Press
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    Publication Date: 1982-12-01
    Description: Observations of inertial waves generated by uniform horizontal flow over ridges and truncated axisymmetric obstacles in a homogeneous fluid rotating about a vertical axis are discussed and compared with linear theory. The dependence of the flow on obstacle shape, Ro, H, E and e is investigated. Here Ro = U/2ΩL is the Rossby number, H = Ro(D/L), E = v/2ΩL2 is the Ekman number, and e = h/L is the non-dimensional height of the obstacle, where U is the basic velocity Ω is the angular frequency, L is a streamwise length, D is the depth of the fluid, h is the height of theobstacle, and v is the kinematic viscosity. Previous linear analysis of this problem has been for the limit H fixed, Ro→ 0, referred to here as the small-Ro limit. However, it is shown that certain linear terms neglected in the small-Ro limit can be important for finite Ro, and are included in the analysis given here. The observed flow is then well described by linear theory for H/ e 1, particularly in the case of two-dimensional flow over a ridge. However, for H/e 1 the flow field is dominated by a vertical columnar motion, which is not adequately described by the analysi. © 1982, Cambridge University Press. All rights reserved.
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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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    Coaxial scattering of Euler-equation translating V -states via contour dynamics (1982)
    Cambridge University Press
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    Publication Date: 1982-12-01
    Description: The robustness of localized states that transport energy and mass is assessed by a numerical study of the Euler equation in two space dimensions. The localized states are the translating ‘F-states’ discovered by Deem & Zabusky. These piecewise-constant dipolar (i.e. oppositely-signed or) vorticity regions are steady translating solutions of theEuler equations. A new adaptive contour-dynamical algorithm with curvature-controlled node insertion and removal is used. The evolution of one F-state, subject to a symmetric-plus-asymmetric perturbation is examined and stable (i.e. non-divergent) fluctuations are observed. For scattering interactions, coaxial head-on (or on) and head-tail (or on) arrangements are studied. The temporal variation of contour curvature and perimeter after F-states separate indicate that internal degrees of freedom have been excited. For weak interactions we observe phase shifts and the near recurrence to initial states. When two similar, equal-circulation but unequal-area F-states have a head-on interaction a new asymmetric state is created by contour ‘exchange’. There is strong evidence that this is near to a F-state. For strong interactions we observe phase shifts, ‘breaking’ (filament formation) and, for head-tail interactions, merger of like-signed vorticity regions. © 1982, Cambridge University Press. All rights reserved.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 6
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    Double-diffusive convection with large variable gradients (1982)
    Cambridge University Press
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    Publication Date: 1982-12-01
    Description: The onset of double-diffusive convection is discussed for a layer of fluid in which the vertical salinity gradient varies with depth and for which the thermal and saline Rayleigh numbers R and Rs are large. These conditions are similar to those that exist in a solar pond prior to the onset of any instability. It is shown that when convection occurs it takes the form of an overstable mode and is essentially confined to a narrow region of vertical extent Rs- 1/4 x depth of the fluid layer, centred at the critical depth where the salt gradient is smallest. The leading terms in asymptotic expansions of the ratio R/Rs, the frequency of oscillation p and the horizontal wavenumber a are determined for Rs 1. The results predicted by the theory are shown to be in good agreement with numerical results and with observations of solar ponds. © 1982, Cambridge University Press. All rights reserved.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 7
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    Time-dependent solutions of multimode convection equations (1982)
    Cambridge University Press
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    Publication Date: 1982-12-01
    Description: Truncated modal equations are used to study the time evolution of thermal convection. In the Boussinesq approximation these nonlinear equations are obtained by expanding the fluctuating velocity and temperature fields in a finite set of planforms of the horizontal coordinates. Here we report on numerical studies dealing with two or three modes with triad interactions. We have found rich time dependence in these cases: periodic and aperiodic solutions can be obtained, along with various steady solutions. Three-mode solutions reproduce the qualitative appearance of spoke-pattern convection as observed in experiments at high Prandtl numbers. Though the values of the periods of the time-dependent solutions do not agree with those of the experiments, their variation with Rayleigh number compares favourably. Except at the highest Rayleigh number we have considered (107), the theoretical Nusselt numbers agree well with experiment.† N values from II, table 1.‡ P-estimates from Rossby (1969) and Krishnamurti (1973). © 1982, Cambridge University Press. All rights reserved.
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    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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    Fluid dynamics and mass transfer in a gas centrifuge (1982)
    Cambridge University Press
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    Publication Date: 1982-12-01
    Description: The fluid motion, temperature distribution and the mass-transfer problem of a binary gas mixture in a rapidly rotating centrifuge are investigated. The model centrifuge considered consists of a pair of concentric circular cylinders bounded on the top and bottom by horizontal end plates; the apparatus rotates rapidly about the axis of the cylinders. During steady operation a binary gas mixture containing species A and B is injected into and withdrawn from the centrifuge through axisymmetric slots located on the sidewalls. Solutions for the velocity, temperature and mass-fraction fields within the centrifuge are obtained for mechanically or thermally driven centrifuges. For the mass-transfer problem, a detailed analysis of the fluid-mechanical boundary layers is required, and, in particular, mass fluxes within the boundary layers are obtained for a wide range of source-sink geometries. Solutions to the mass-transfer problem are obtained for moderately and strongly forced flows in the container; the dependence of the separation (or enrichment) factor on centrifuge configuration, rotational speed and fraction of the volumetric flow rate extracted at the product port (the cut) are predicted. © 1982, Cambridge University Press. All rights reserved.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 9
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    On the stability of boundary-layer flow over a spring-mounted piston (1982)
    Cambridge University Press
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    Publication Date: 1982-12-01
    Description: The stability of weakly compressible boundary-layer flow over a spring-mounted piston is examined theoretically by modelling the mean boundary layer at low Strouhal numbers by means of a step-function velocity profile. This constitutes a prototype problem for the treatment of the interaction of unsteady boundary-layer flow with a compliant surface, and the present discussion complements a recent analysis due to Ffowcs Williams and Purshouse by incorporating the influence of flow separation at the edges of the piston. This is effected analytically by application of the unsteady Kutta condition at both the leading and trailing edges of the piston. At high Reynolds numbers and in the case of light fluid loading itis predicted that the separated flow can cause piston flutter. Stability criteria are derived for a rectangular piston of large aspect ratio. © 1982, Cambridge University Press. All rights reserved.
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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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    Single-mode theory of diffusive layers in thermohaline convection (1982)
    Cambridge University Press
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    Publication Date: 1982-12-01
    Description: Joint Institute for Laboratory Astrophysics, and Department of Astrophysical, Planetary and Atmospheric Sciences, University of Colorado, Boulder, CO 80309.A two-layer configuration of thermohaline convection is studied, with the principal aim of explaining the observed indeendence of the buoyancy-flux ratio on the stability parameter when the latter is large. Temperature is destabilizing and salinity is stabilizing, so diffusive interfaces separate the convecting layers. Theconvection is treated in the single-mode approximation, with a prescribed horizontal planform and wavenumber. Surveys ofnumerical solutions are presented for a selection of Rayleigh numbers R, stability parameters γ and horizontal wavenumbers a. The solutions yield a buoyancy flux ratio Xthat is insensitive to γ, in accord with laboratory experiments. However X increases with increasing R, in contradiction to laboratory observations. © 1982, Cambridge University Press. All rights reserved.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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