Abstract
Many hydrodynamic instability patterns can be put into correspondence with a subset of characteristic surfaces of tangential discontinuities. These topological limits sets to systems of hyperbolic PDE’s are locally unstable, but a certain subset associated with minimal surfaces are globally stabilized, persistent and non-dissipative. Sections of these surfaces are the spiral scrolls so often observed in hydrodynamic wakes. This method of wake production does not depend explicitly upon viscosity.
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References
J. L. Barbossa and M. do Carmo (1976), Amer. Journ. Math. 98, 515
G. K. Batchelor (1967), Fluid Dynamics, (Cambridge University Press) p.354.
H. K. Browand (1986), Physica D 118 173
R. E. Cayflish (1991), in “Vortex Dynamics and Vortex Methods”, C.R. Anderson and C. Greengard, editors, (Am. Math. Soc, Providence, RI) p. 67
L.D. Landau & E.M. Lifschitz (1959), Fluid Mechanics, Addison-Wesley, Reading Mass
J. Hadamard (1952) Lectures on Cauch’s Problem in Linear Partial Differential Equations (Dover, N.Y.) p.21
H.Kaden (1931), Ing. Arch. 2, p.140
T. Kambe (1989), Physica D 37 p.403
R.M.Kiehn (1990), %#x201C;Topological Torsion, Pfaff Dimension and Coherent Structures” in Topological Fluid Mechanics, H. K. Moffatt and A. Tsinober, editors, (Cambridge University Press), p. 225.
R. M. Kiehn (1991), “Compact Dissipative Flow Structures with Topological Coherence Embedded in Eulerian Environments” in The Generation of Large Scale Structures in Continuous Media , (Singapore World Press).
R. M. Kiehn (1992), “Topological Defects, Coherent Structures, and Turbulence in Terms of Cartan’s theory of Differential Topology” in Developments in Theoretical and Applied Mechanics, SECTAM XVI Conference Proceedings, B.N.Antar,R. Engels, A.A.Prinaris, T.H.Molden. editors (University of Tennessee Space Institute, TN)
R. Krasny (1991), in Vortex Dynamics and Vortex Methods, C.R. Anderson and C. Greengard, editors, (Am. Math. Soc., Providence, RI) p. 385
R. Osserman (1986) A Survey of Minimal Surfaces (Dover, N.Y.) p. 18
D. I. Pullin (1989), in Mathematical Aspects of Vortex Dynamics, R. E. Cayflisch, editors (SIAM)
N. Rott (1956), J. Fluid Mech. 1 p.111
D. Struik (1961), Differential Geometry, (Addison Wesley, Reading, Mass)
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© 1993 Springer Science+Business Media Dordrecht
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Kiehn, R.M. (1993). Instability Patterns, Wakes and Topological Limit Sets. In: Bonnet, J.P., Glauser, M.N. (eds) Eddy Structure Identification in Free Turbulent Shear Flows. Fluid Mechanics and Its Applications, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2098-2_30
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DOI: https://doi.org/10.1007/978-94-011-2098-2_30
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