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.
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