Numerical evidence of breaking of vortex lines in an ideal fluid
Emergence of singularity of vorticity at a single point, not related to any symmetry of the initial distribution, has been demonstrated numerically for the first time. Behaviour of the maximum of vorticity near the point of collapse closely follows the dependence (t 0−t)−1, where t 0 is the time of collapse. This agrees with the interpretation of collapse in an ideal incompressible fluid as of the process of vortex lines breaking.
KeywordsEuler Equation Vortex Line Vortex Tube Numerical Evidence Vortex Filament
Unable to display preview. Download preview PDF.
- Arnold, V.I. 1981 Theory of Catastrophe. Znanie, Moscow (in Russian) [English transl.: Theory of Catastrophe 1986, 2nd rev. ed. Springer].Google Scholar
- Arnold, V.I. 1989 Mathematical Methods of Classical Mechanics. 2nd ed., Springer-Verlag, New York.Google Scholar
- Crow, S.C. 1970 Stability Theory for a pair of trailing vortices. Amer. Inst. Aeronaut. Astronaut. J.8, 2172–2179.Google Scholar
- Frisch, U. 1995 Turbulence. The legacy of A.N.Kolmogorov. Cambridge Univ. Press.Google Scholar
- Kolmogorov, A.N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds number, Doklady AN SSSR30, 9–13 (in Russian) [reprinted in 1991 Proc. R. Soc. Lond. A 434, 9–13].Google Scholar
- L’vov, V.S. 1991 Scale invariant theory of fully developed hydrodynamic turbulence — Hamiltonian approach. Phys. Rep.207, 1–47.Google Scholar
- Monin, A.S. & Yaglom, A.M. 1992 Statistical hydro-mechanics. 2nd ed., vol.2, Gidrometeoizdat, St.Petersburg (in Russian) [English transl.: 1975 Statistical Fluid Mechanics. Vol. 2, ed. J.Lumley, MIT Press, Cambridge, MA].Google Scholar
- Zakharov, V.E. & Kuznetsov, E.A. 1986 Quasiclassical theory of three-dimensional wave collapse. Sov. Phys. JETP64, 773–780.Google Scholar
- Zheligovsky, V.A., Kuznetsov, E.A. & Podvigina, O.M. 2001 Numerical modeling of collapse in ideal incompressible hydrodynamics. Pis’ma v ZhETF (JET Letters) 74, 402–406.Google Scholar