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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J. O. Hinze, Turbulence, Second Ed., McGraw-Hill, New York, 1975
G. K. Batchelor, The theory of homogeneous turbulence, Cambridge University Press, London, 1960
P. S. Bernard and B. S. Berger, A method for computing three-dimensional turbulent flows, SIAM Jour. of Applied Math., 42, 453–470, (1982)
P. S. Bernard, Computation of the turbulent flow in an internal combustion engine during compression, ASME Jour. of Fluids Engineering, 103, 75–81 (1981)
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
L. Lichtenstein, Grundlagen der Hydromechanik, Springer-Verlag, Berlin, 1929
P. E. Appell, Traité de mécanique rationnelle, TOME 111, Troiséme Edition, Gauthier-Villars et Cie, Paris, 1928
D. Jacob, Introduction mathematique á la mécanique des fluides, Gauthier-Villars, Paris, 1959
H. Poincaré, Théorie des tourbillons, Paris, 1893
H. Villat, Lecons sur la théorie des tourbillons, Gauthier-Villars et Cie, Paris, 1930
U. Crudeli, Il problema fondametnale di Stekloff nella teoria dei campi vettoriali, Rendiconti del Circolo Mathematico di Palermo, 58, 166–174 (1934)
L. M. Milne-Thomson, Theoretical hydrodynamics, 4th Edition, Macmillan Co., New York, 1965
R. Courant and D. Hilbert, Methods of mathematical physics, Vol. II, Interscience Publishers, New York, 1962
H. B. Phillips, Vector analysis, John Wiley and Sons, New York, 1963
M. E. Gurtin, On Helmholtz’s theorem and the completeness of the Papkovich-Neuber stress functions for infinite domains, Archive Rational Mech. and Analysis 9, 225–233 (1962)
D. Lovelock and H. Rund, Tensors, differential forms and variational principles, John Wiley and Sons, New York, , 1975
J. L. Synge and A. Schild, Tensor calculus, University of Toronto Press, Toronto, 1962
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Article copyright:
© Copyright 1985
American Mathematical Society
