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  • 1
    Electronic Resource
    Electronic Resource
    Convective instability of a spherical fluid inclusion (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 36-44 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: When a vertical temperature gradient is applied to a large solid containing a spherical fluid inclusion, the temperature in the fluid is a function only of height. The stability of this fluid against convection is investigated and it is found that the principle of exchange of stabilities applies. The linear differential system governing stability is then solved; the results show that the thermal conductivity of the surrounding solid is always stabilizing and that the most unstable mode is the first asymmetric mode, for which the critical Rayleigh number is given. The energy method can be applied, with due modifications to account for heat conduction in the surrounding solid. The same mathematical governing differential system would then be obtained, giving the same number for the upper bound of the Rayleigh numbers below which the fluid is stable. This number is then truly critical: The fluid is stable or unstable according to whether the Rayleigh number is below or above it, whatever the magnitude of the disturbance. The results are discussed in the context of the movement of the spherical inclusion in a soluble solid. The greater instability of the asymmetric mode indicates that when instability occurs, the fluid inclusion will have a sidewise component, which is greater for a greater supercritical Rayleigh number. The effect of double diffusion is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866056
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  • 2
    Electronic Resource
    Electronic Resource
    Movement of liquid inclusions in soluble solids: An inverse Stokes' law (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 2785-2787 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The temperature distribution in an ellipsoidal liquid inclusion in a soluble solid, with a constant gradient far away from the liquid, and the movement of the liquid inclusion as a whole, which results as a consequence, are investigated. Since the solid is soluble and its concentration in solution is temperature dependent, any temperature variation in the liquid induces a concentration variation, which will transfer mass by diffusion, eroding the wall where the temperature is high and depositing solid material at the wall where the temperature is lower. This erosion or deposition will cause the liquid inclusion to move, and will, through absorption or release of latent heat, in turn affect the temperature distribution. From the result obtained for the general ellipsoid, specific results for prolate and oblate ellipsoids of revolution, the sphere, and circular and elliptic cylinders are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865474
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  • 3
    Electronic Resource
    Electronic Resource
    Instability resulting from stratification in thermal conductivity (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 1769-1773 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: There are many instances of hydrodynamic instability induced by a variation, or stratification, in either a fluid property or a flow property. In this article a new instability is presented. It is shown that when there is a variation in thermal conductivity in the fluid, instability can occur in the presence of a longitudinal gravitational field.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865603
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  • 4
    Electronic Resource
    Electronic Resource
    Solitary waves in stratified fluids and their interaction (1993)
    Springer
    Acta mechanica Sinica 9 (1993), S. 193-209 
    Details
    ISSN: 1614-3116
    Keywords: internal solitary waves ; stratified liquids ; exponential stratification ; linear stratification ; systematic use of the solubility condition in successive approximations ; interaction of internal solitary waves ; detailed derivation of the KdV equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A systematic procedure is proposed for obtaining solutions for solitary waves in stratified fluids. The stratification of the fluid is assumed to be exponential or linear. Its comparison with existing results for an exponentially stratified fluid shows agreement, and it is found that for the odd series of solutions the direction of displacement of the streamlines from their asymptotic levels is reversed when the stratification is changed from exponential to linear. Finally the interaction of solitary waves is considered, and the Korteweg-de Vries equation and the Boussinesq equation are derived. Thus the known solutions of these equations can be relied upon to provide the answers to the interaction problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02486797
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  • 5
    Electronic Resource
    Electronic Resource
    General solution for interaction of solitary waves including head-on collisions (1995)
    Springer
    Acta mechanica Sinica 11 (1995), S. 193-199 
    Details
    ISSN: 1614-3116
    Keywords: solitary waves ; Boussinesq equation ; head-on collision
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A corrected version of the Boussinesq equation for long water waves is derived and its general solution for interaction of any number of solitary waves, including head-on collisions, is given. For two solitary waves in head-on collision (which includes the case of normal reflection) the results agree with the experiments known.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02487722
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  • 6
    Electronic Resource
    Electronic Resource
    General solution for interaction of solitary waves including head-on collisions (1993)
    Springer
    Acta mechanica Sinica 9 (1993), S. 97-101 
    Details
    ISSN: 1614-3116
    Keywords: interaction of solitary waves ; head-on collisions ; KdV equation ; Boussinesq equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A general solution of the Boussinesq equation is presented which solves the problem of interaction of any number of right-going and left-going solitary waves. The solution relies on the exact solution of Gardner, Greene, Kruskal, and Miura (1967), and has the same degree of accuracy as that solution, but has a wider scope of application. It is much simpler than, but as accurate as, Hirota's exact solution (1973) of the Boussinesq equation, to which the present solution is compared for the simplest case of two solitary waves in head-on collision.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02487487
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  • 7
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    Convective instability of a spherical fluid inclusion (1987)
    American Institute of Physics
    Details
    Publication Date: 1987-01-01
    Print ISSN: 0031-9171
    Topics: Physics
    Published by American Institute of Physics
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  • 8
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    Turbulent buoyant plumes (1977)
    American Institute of Physics
    Details
    Publication Date: 1977-01-01
    Print ISSN: 0031-9171
    Topics: Physics
    Published by American Institute of Physics
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  • 9
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    Round buoyant laminar and turbulent plumes (1981)
    American Institute of Physics
    Details
    Publication Date: 1981-01-01
    Print ISSN: 0031-9171
    Topics: Physics
    Published by American Institute of Physics
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  • 10
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    Fluid Motion Induced by Surface-Tension Variation (1968)
    American Institute of Physics
    Details
    Publication Date: 1968-01-01
    Print ISSN: 0031-9171
    Topics: Physics
    Published by American Institute of Physics
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