2000/09/02 by E. A. Kuznetsov, Kuznetsov, E. A., V. P. Ruban +1
Engineering · Mathematics · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.physics/0009007
revtex, 9 pages, no figures
arxiv created 2000/09/02 · openalex publication_date 2000/09/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new mechanism of the collapse in hydrodynamics is suggested, due to breaking of continuously distributed vortex lines. Collapse results in formation of the point singularities of the vorticity field |\bfΩ|. At the collapse point, the value of the vorticity blows up as (t0-t)-1 where t0 is a collapse time. The spatial structure of the collapsing distribution approaches a pancake form: contraction occurs by the law l1∼(t0-t)3/2 along the "soft" direction, the characteristic scales vanish like l2∼(t0-t)1/2 along two other ("hard") directions. This scenario of the collapse is shown to take place in the integrable three-dimensional hydrodynamics with the Hamiltonian \cal H=∫|\bfΩ|d\bf r. Most numerical studies of collapse in the Euler equation are in a good agreement with the proposed theory.