Steady spheroidal vortices—More exact solutions to the Navier-Stokes equation
Author:
Vivian O’Brien
Journal:
Quart. Appl. Math. 19 (1961), 163-168
MSC:
Primary 76.35
DOI:
https://doi.org/10.1090/qam/137415
MathSciNet review:
137415
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Abstract: The vorticity equation, the curl of the Navier-Stokes equation, is considered in ellipsoidal coordinates. The steady spheroidal vortex solutions are demonstrated as examples of a class of exact flow solutions characterized by a simple linear vorticity distribution.
M. J. M. Hill, On a spherical vortex, Trans. Roy. Soc. (London) A185, 213–245 (1894)
H. Lamb, Hydrodynamics, 6th ed., Dover, New York, 1945
M. J. Hadamard, Mouvement permanent lent d’une sphere liquide et visqueuse dans un liquid visqueux, Comp. Rend. 152, 1735–1738 (1911)
D. P. Rybezynsky, Über die fortschreitende Bewegung einer flüssigen Kugel in einem zähen Medium, Bull. Acad. Sci. Crac (A) 403, 40–46 (1911)
G. G. Stokes, On the effect of the internal friction of fluids on the motion of pendulums, Camb. Phil. Soc. Trans 9, 8–106 (1850) (also Scientific Papers, vol. 3, University Press, Cambridge, 1901)
K. E. Spells, Study of circulation patterns within liquid drops moving through liquid, Phys. Soc. Proc. 65, 541–546 (1952)
P. Savic, Circulation and distortion of liquid drops falling through a viscous medium, NRC of Can. Rept. No. MT–22, 1953
S. Goldstein (ed.) Modern developments in fluid dynamics, Clarendon Press, Oxford, 1938
W. Magnus and F. Oberhettinger, Formulas and theorems for the functions of mathematical physics, Chelsea Publ. Co., New York, 1954
V. O’Brien, Steady spheroidal vortices, APL/CM–970, 1960
M. J. M. Hill, On a spherical vortex, Trans. Roy. Soc. (London) A185, 213–245 (1894)
H. Lamb, Hydrodynamics, 6th ed., Dover, New York, 1945
M. J. Hadamard, Mouvement permanent lent d’une sphere liquide et visqueuse dans un liquid visqueux, Comp. Rend. 152, 1735–1738 (1911)
D. P. Rybezynsky, Über die fortschreitende Bewegung einer flüssigen Kugel in einem zähen Medium, Bull. Acad. Sci. Crac (A) 403, 40–46 (1911)
G. G. Stokes, On the effect of the internal friction of fluids on the motion of pendulums, Camb. Phil. Soc. Trans 9, 8–106 (1850) (also Scientific Papers, vol. 3, University Press, Cambridge, 1901)
K. E. Spells, Study of circulation patterns within liquid drops moving through liquid, Phys. Soc. Proc. 65, 541–546 (1952)
P. Savic, Circulation and distortion of liquid drops falling through a viscous medium, NRC of Can. Rept. No. MT–22, 1953
S. Goldstein (ed.) Modern developments in fluid dynamics, Clarendon Press, Oxford, 1938
W. Magnus and F. Oberhettinger, Formulas and theorems for the functions of mathematical physics, Chelsea Publ. Co., New York, 1954
V. O’Brien, Steady spheroidal vortices, APL/CM–970, 1960
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Article copyright:
© Copyright 1961
American Mathematical Society
