0
2013
Impact Factor

    Approximate Weak Solutions to the Vorticity Evolution Equation for a Viscous Incompressible Fluid in the Class of Vortex Filaments

    Received 20 June 2022; accepted 05 August 2022; published 30 September 2022

    2022, Vol. 18, no. 3, pp.  423-439

    Author(s): Kotsur O. S., Shcheglov G. A., Marchevsky I. K.

    This paper is concerned with the equation for the evolution of vorticity in a viscous incompressible fluid, for which approximate weak solutions are sought in the class of vortex filaments. In accordance with the Helmholtz theorem, a system of vortex filaments that is transferred by the flow of an ideal barotropic fluid is an exact solution to the Euler equation. At the same time, for viscous incompressible flows described by the system of Navier – Stokes equations, the search for such generalized solutions in the finite time interval is generally difficult. In this paper, we propose a method for transforming the diffusion term in the vorticity evolution equation that makes it possible to construct its approximate solution in the class of vortex filaments under the assumption that there is no helicity of vorticity. Such an approach is useful in constructing vortex methods of computational hydrodynamics to model viscous incompressible flows.
    Keywords: weak solution, vortex filament, helicity of vorticity, diffusion velocity, viscosity
    Citation: Kotsur O. S., Shcheglov G. A., Marchevsky I. K., Approximate Weak Solutions to the Vorticity Evolution Equation for a Viscous Incompressible Fluid in the Class of Vortex Filaments, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 3, pp.  423-439
    DOI:10.20537/nd220307


    Download File
    PDF, 323.39 Kb




    Creative Commons License
    This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License