Vortex motions and conformal mappings
An evolution equation describing vortex motions of invariant curves is established. Exact solutions of this equation, generalizing those of Kirchoff and Moore and Saffman, are found. A non linear dispersion relation extending a classical result of Lamb is demonstrated. Other results are proven.
KeywordsEuler Equation Stream Function Steady State Solution Boundary Component Real Constant
Unable to display preview. Download preview PDF.
- Ahlfors, L., and Beurling, A., Conformal Invariants and functiontheoretic null sets, Acta Math. 83 (1950), 101–129.Google Scholar
- Burbea, J., On stability of certain vortex motions, Proceedings on Nonlinear PIE in Engineering and Applied Science, Rhode Island, 1979, Marcel Dekker, to appear.Google Scholar
- Deem, G.S., and Zabusky, N.J., Vortex waves, stationary “V-states”, interactions, recurrence and breaking, Phys.Rev.Letters 40 (1978), 854–862.Google Scholar
- Keller, H.B., and Langford, W.F., Iterations, perturbations and multiplicities for nonlinear bifurcation problems, Arch. Rational Mech.Anal. 48 (1972), 83–108.Google Scholar
- Lamb, H., Hydrodynamics, Dover Publications, New York, 1945.Google Scholar
- Love, A.E.H., On the stability of certain vortex motions, Proc.London Math.Soc. (1)25 (1893), 18–42.Google Scholar
- Moore, D.W., and Saffman, P.C., Structure of a line vortex in an imposed strain, “Aircraft Wake Turbulence and its Detection”, Plenum Press (1971), 339–354.Google Scholar
- Zabusky, N.J., Coherent structures in fluid dynamics, “The Significance of Nonlinearity in the Natural Sciences”, Plenum Press (1977), 145–205.Google Scholar