On the viscosity influence on a helical vortex flament evolution

Abstract

Abstract. Helical vortices whose parameters have a strong influence on the efficiency of the apparatus is often occur in technical devices using swirling flow (cyclones, separators, etc.). To date the internal structure of such vortices is poorly understood. In [1] a model of helical vortex with uniform vorticity distribution in the core is proposed. Vortices arising in real flow always have a smooth vorticity distribution due to the viscosity action. The problem on steady moving helical vortices with the vortex core of small size in an inviscid fluid was solved in [2]. The non-orthogonal 'helical' coordinate system was introduced that allowed author to reduce the problem to two dimensional one. However, the velocity of the vortex motion was written only in the form of a quadratures computation of which is difficult. This paper presents first attempt for research on the diffusion and dynamics of a viscous helical vortex.In this paper we consider the non-stationary problem of diffusion of helical vortex with a small diameter of core in viscous fluid. The aim is to describe the structure of the vortex and to find the speed of its movement.Consider coordinate system introduced in [2]:Here H ( ) is a helix, unit vectors ( T ( ), N( ), B( )) are directed along the tangent, normal and binormal to the helix (components of some vector in this coordinate system will be shown by use angle brackets < •, •, • >). Jacobian determinant of this system depends only on one coordinate:is the curvature of helical line, a is the helix radius and 2 l -is the helix pitch. Helical symmetry condition [1] written in the Cartesian coordinates looks as follows: