Fluid velocity fields derived from vorticity singularities
Author:
K. B. Ranger
Journal:
Quart. Appl. Math. 62 (2004), 671-685
MSC:
Primary 76D17; Secondary 76M35
DOI:
https://doi.org/10.1090/qam/2104268
MathSciNet review:
MR2104268
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Abstract: The present article addresses the existence by construction of random velocity fields produced by prescribed flow singularities which are consistent with the equations governing the motion of a two-dimensional viscous incompressible liquid. By showing first that the vorticity can be arbitrary and consistent with the flow equations it is then possible to determine the velocity field explicitly in terms of the vorticity and its derivatives.
H. L. Dryden, F. P. Murnaghan and H. Bateman, Hydrodynamics, Dover Publications, Inc., 242–244 (1956)
G. B. Jeffrey, The two-dimensional stead motion of a viscous fluid, Phil. Mag. 29 (6), 445–455 (1915)
J. Leray, Étude de diverses integrates non-lineaires et de quelques problems que pose l’Hydrodynamiques, Jour. de Math. Pures et Appl. 12, 1 (1933)
- K. Oswatitsch, Physikalische Grundlagen der Strömungslehre, Handbuch der Physik (herausgegeben von S. Flügge), Bd. 8/1, Strömungsmechanik I (Mitherausgeber C. Truesdell), Springer-Verlag, Berlin-Göttingen-Heidelberg, 1959, pp. 1–124 (German). MR 0108115
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G. Batchelor, An Introduction to Fluid Dynamics CUP, 205–208 (1967)
H. L. Dryden, F. P. Murnaghan and H. Bateman, Hydrodynamics, Dover Publications, Inc., 242–244 (1956)
G. B. Jeffrey, The two-dimensional stead motion of a viscous fluid, Phil. Mag. 29 (6), 445–455 (1915)
J. Leray, Étude de diverses integrates non-lineaires et de quelques problems que pose l’Hydrodynamiques, Jour. de Math. Pures et Appl. 12, 1 (1933)
J. Serrin, Mathematical principles of classical fluid mechanics, Handbuch der Physik VIII/I, Springer-Verlag, Berlin 125–263 (1959)
D. J. Acheson, Elementary Fluid Dynamics, Oxford University Press, 53 (1959)
G. Batchelor, An Introduction to Fluid Dynamics CUP, 205–208 (1967)
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Article copyright:
© Copyright 2004
American Mathematical Society
