Abstract
When in a physical problem three variable quantities add to a constant, it is possible to introduce a convenient geometrical representation of the variables in terms of trilinear coordinates. This usually permits an overview of the ranges of variation of the variables that is useful for qualitative analysis, and may point to quantitative insights that would be difficult to obtain in any other way. A brief historical discussion of trilinear coordinates is given, and examples of their use in solving flow problems are cited, including laminar flow in a pipe; the interaction of point vortices; and Lumley’s representation of the eigenvalues of the anisotropy tensor for turbulent flow.
Work supported by NSF/PYI Award MSM 84-51107.
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References
Aref, H. 1979 “Motion of three vortices.”Phys. Fluids 22, 393–400.
Aref, H., Rott, N.,& Thomann, H. 1990 “Gröli’s solution of the three-vortex problem.” UCSD preprint
Berestetskii, V. B., Lifshitz, E. M., Pitaevskii, L. P. 1971Relativistic quantum theory. Part 1. Pergamon Press, Oxford, §68.
Coxeter, H. S. M., Greitzer, S. L. 1967Geometry revisited. The Mathematical Association of America, Washington D. C., Sec. 4.6.
Eckhardt, B. 1988 “Integrable four-vortex motion.”Phys. Fluids 31, 2796–2801.
Ferrers, N.M. 1866An elementary treatise on tri-linear coordinates, the method of reciprocal polars and the theory of projections. Second ed., Macmillan & Co., London, 182pp.
Goryachev, D. N. 1898 “On some cases of the motion of rectilinear, parallel vortices.”Proc. Imperial Moscow UniversityPhys.-Math. series, 106pp. (In Russian)
Gröli, W. 1877Specielle Probleme über die B ewe gun g geradliniger paralleler WirbelfädenZürcher und Furrer, Zürich. 86pp.
Lumley, J. L. 1978 “Computational modeling of turbulent flows.”Adv. Appl. Mech. 18, 123–176.
Rott, N. 1990 “Constrained three- and four-vortex problems.”Phys. Fluids A 2, 1477 - 1480.
Synge, J. L. 1949 “On the motion of three vortices.”Can. J. Math1, 257–270.
Taylor, G. I.1937 “The determination of stresses by means of soap films.”InThe Mechanical Properties of FluidsBlackie & Sons Ltd., London, 382pp.
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© 1992 Springer-Verlag New York, Inc.
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Aref, H. (1992). Trilinear Coordinates In Fluid Mechanics. In: Gatski, T.B., Speziale, C.G., Sarkar, S. (eds) Studies in Turbulence. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2792-2_42
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DOI: https://doi.org/10.1007/978-1-4612-2792-2_42
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