The classical problem of linear stability of a regular $N$-gon of point vortices to infinitesimal space displacements from an equilibrium of the vortex configuration is generalized to the one for $N$ helical vortices (couple, triplet, etc., $N\,{>}\, 1$) for the first time. As a consequence of this consideration, the analytical form for the stability boundaries has been obtained. This solution allows an efficient analysis to be made of the existence of stable helical vortex arrays, which were repeatedly observed in practice.Such a stability problem was earlier considered in theory, but only for the case of a plane polygonal array of $N$ point vortices. As for helical vortices, owing to their complexity, intensive study has been mainly on the self-induced motion of the vortex.The algebraic representation for the velocity of motion of the $N$ helical vortex array was originally obtained as an additional intermediate result. The new formula allows accurate calculations to be made within the whole range of helical pitch variations and has a simpler form than the known asymptotic expressions.Solution of these two classical problems of vortex dynamics has significance both for theoretic and applied mechanics, as well as for many other areas of natural science, where the rotor (vortex) concept is the basic one.

Helical vortices in swirl flow are studied theoretically and experimentally.A theory of helical vortices has been developed. It includes the following results: an analytical solution describing an elementary helical vortex structure – an infinitely thin filament; a solution for axisymmetrical vortices accounting for the helical shape of vortex lines and different laws of vorticity distribution; a formula for calculation of the self-induced velocity of helical vortex rotation (precession) in a cylindrical tube; an explanation of the zone with reverse flow (recirculation zone) arising in swirl flows; and the classification of vortex structures.The experimental study of helical vortices was carried out in a vertical hydrodynamical vortex chamber with a tangential supply of liquid through turning nozzles. Various vortex structures were formed owing to changing boundary conditions on the bottom and at the exit section of the chamber. The hypothesis of helical symmetry is confirmed for various types of swirl flow. The stationary helical vortex structures are described (most of them for the first time) the features of which agree with the results and predictions of the theoretical model developed. They are the following: a rectilinear vortex; a composite columnar vortex; helical vortices screwed on the right or on the left; a vortex with changing helical symmetry; a double helix – two entangled vortex filaments of the same sign.

As a means of analysing the stability of the wake behind a multi-bladed rotor the stability of a multiplicity of helical vortices embedded in an assigned flow field is addressed. In the model the tip vortices in the far wake are approximated by infinitely long helical vortices with constant pitch and radius. The work is a further development of a model developed in Okulov (J. Fluid Mech., vol. 521, p. 319) in which the linear stability of N equally azimuthally spaced helical vortices was considered. In the present work the analysis is extended to include an assigned vorticity field due to root vortices and the hub of the rotor. Thus the tip vortices are assumed to be embedded in an axisymmetric helical vortex field formed from the circulation of the inner part of the rotor blades and the hub. As examples of inner vortex fields we consider three generic axial columnar helical vortices, corresponding to Rankine, Gaussian and Scully vortices, at radial extents ranging from the core radius of a tip vortex to several rotor radii.The analysis shows that the stability of tip vortices largely depends on the radial extent of the hub vorticity as well as on the type of vorticity distribution. As part of the analysis it is shown that a model in which the vortex system is replaced by N tip vortices of strength Γ and a root vortex of strength − N/Γ is unconditionally unstable.

The flow behind a model of a wind turbine rotor is investigated experimentally in a water flume using particle image velocimetry (PIV) and laser Doppler anemometry (LDA). The study performed involves a three-bladed wind turbine rotor designed using the optimization technique of Glauert (Aerodynamic Theory, vol. IV, 1935, pp. 169-360). The wake properties are studied for different tip speed ratios and free stream speeds. The data for the various rotor regimes show the existence of a regular Strouhal number associated with the development of an instability in the far wake of the rotor. From visualizations and a reconstruction of the flow field using LDA and PIV measurements it is found that the wake dynamics is associated with a precession (rotation) of the helical vortex core.