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On the non-persistence of irrotational motion in a viscous heat-conducting fluid

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Abstract

We consider the possibility of irrotational flow in a fluid exterior to a moving rigid obstacle, or interior to a moving rigid shell. Observations show that when a rigid body is impulsively set into motion an irrotational flow may exist initially but does not persist. The breakup of this irrotational flow and the associated phenomenon of generation of vorticity at the wall are generally attributed to the condition of adherence at the fluid-solid interface. Since this condition itself is derived from observation, one can ask whether there is another explanation for the phenomenon. The purpose of this paper is to show that a persistent irrotational flow is incompatible with the second law of thermodynamics.

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References

  • Batchelor, G. K., 1967. An Introduction to Fluid Dynamics. Cambridge University Press.

  • Gurtin, M. E., 1981. An Introduction to Continuum Mechanics. Academic Press.

  • Keller, J. B., 1954. Geometrical Acoustics I. The theory of weak shock waves. J. Appl. Physics 25, pp. 938–947.

    Google Scholar 

  • Lamb, H., 1932. Hydrodynamics. Cambridge University Press.

  • Serrin, J., 1959. Mathematical Principles of Classical Fluid Mechanics, sections 58–65. Handbuch der Physik VIII/1, Springer-Verlag.

    Google Scholar 

  • Truesdell, C., & R. Toupin, 1960. The Classical Field Theories, pp. 492–530. Handbuch der Physik III/1, Springer-Verlag.

    Google Scholar 

  • Truesdell, C., 1966 A. The Mechanical Foundations of Elasticity and Fluid Dynamics. Gordon and Breach.

  • Truesdell, C., 1966B. The Elements of Continuum Mechanics. Springer-Verlag.

  • Weatherburn, C. E., 1955. Differential Geometry of three Dimensions, Vol. 1, Cambridge University Press.

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  1. 10 Emerson Place, 02114, Boston, MA, USA

    Gerald G. Kleinstein

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  1. Gerald G. Kleinstein
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Communicated by J. Serrin

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Kleinstein, G.G. On the non-persistence of irrotational motion in a viscous heat-conducting fluid. Arch. Rational Mech. Anal. 101, 95–105 (1988). https://doi.org/10.1007/BF00251455

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  • DOI: https://doi.org/10.1007/BF00251455

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