Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Velocity and vorticity correlations

Author: B. S. Berger
Journal: Quart. Appl. Math. 43 (1985), 97-102
MSC: Primary 76F05; Secondary 76-08
DOI: https://doi.org/10.1090/qam/782259
MathSciNet review: 782259
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Abstract: It is shown that one point velocity correlations may be expressed as a volume integral of the product of the singular part of Green's function and a function, $ {h_{jM}}\left( {x,X} \right)$, which satisfies Poisson's equation and vanishes for points on the boundary. An explicit expression is found for $ {h_{jM}}\left( {x,X} \right)$. These results provide a computational method for determining the velocity correlations.

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  • [1] J. O. Hinze, Turbulence, Second Ed., McGraw-Hill, New York, 1975
  • [2] G. K. Batchelor, The theory of homogeneous turbulence, Cambridge University Press, London, 1960
  • [3] Peter S. Bernard and Bruce S. Berger, A method for computing three-dimensional turbulent flows, SIAM J. Appl. Math. 42 (1982), no. 3, 453–470. MR 659406, https://doi.org/10.1137/0142033
  • [4] P. S. Bernard, Computation of the turbulent flow in an internal combustion engine during compression, ASME Jour. of Fluids Engineering, 103, 75-81 (1981)
  • [5] C. Truesdell and R. Taupin, The classical fields theories, Encyclopedia of Physics, Vol. 111/1 Principles of Classical Mechanics and Field Theory, Springer-Verlag, Berlin, 1960
  • [6] Leon Lichtenstein, Grundlagen der Hydromechanik, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 30, Springer-Verlag, Berlin, 1968 (German). MR 0228225
  • [7] P. E. Appell, Traité de mécanique rationnelle, TOME 111, Troiséme Edition, Gauthier-Villars et Cie, Paris, 1928
  • [8] D. Jacob, Introduction mathematique á la mécanique des fluides, Gauthier-Villars, Paris, 1959
  • [9] H. Poincaré, Théorie des tourbillons, Paris, 1893
  • [10] H. Villat, Lecons sur la théorie des tourbillons, Gauthier-Villars et Cie, Paris, 1930
  • [11] U. Crudeli, Il problema fondametnale di Stekloff nella teoria dei campi vettoriali, Rendiconti del Circolo Mathematico di Palermo, 58, 166-174 (1934)
  • [12] L. M. Milne-Thomson, Theoretical hydrodynamics, 4th Edition, Macmillan Co., New York, 1965
  • [13] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
  • [14] H. B. Phillips, Vector analysis, John Wiley and Sons, New York, 1963
  • [15] M. E. Gurtin, On Helmholtz’s theorem and the completeness of the Papkovich-Neuber stress functions for infinite domains, Arch. Rational Mech. Anal. 9 (1962), 225–233. MR 0187467, https://doi.org/10.1007/BF00253346
  • [16] David Lovelock and Hanno Rund, Tensor, differential forms, and variational principles, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1975. Pure and Applied Mathematics. MR 0474046
  • [17] J. L. Synge and A. Schild, Tensor Calculus, Mathematical Expositions, no. 5, University of Toronto Press, Toronto, Ont., 1949. MR 0033165

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DOI: https://doi.org/10.1090/qam/782259
Article copyright: © Copyright 1985 American Mathematical Society

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