Motion of a helical vortex

@article{Fuentes2015MotionOA,
  title={Motion of a helical vortex},
  author={Oscar Velasco Fuentes},
  journal={arXiv: Fluid Dynamics},
  year={2015}
}
We study the motion of a single helical vortex in an unbounded, inviscid, incompressible fluid. The vortex is an infinite tube whose centerline is a helix and whose cross section is a circle of small radius (compared to the radius of curvature) where the vorticity is uniform and parallel to the centerline. Ever since Joukowsky (1912) deduced that this vortex translates and rotates steadily without change of form, numerous attempts have been made to compute these self-induced velocities. Here we… 

Figures from this paper

Flow topology of helical vortices

Equal coaxial symmetrically located helical vortices translate and rotate steadily while preserving their shape and relative position if they move in an unbounded inviscid incompressible fluid. In

Generalized helical vortex pairs

New solutions describing the interaction of helical pairs of counter-rotating vortices are obtained using a vortex filament approach. The vortices are assumed to have a small core size allowing the

The self-induced motion of a helical vortex

Helical vortices have been studied for more than a century to understand basic aspects of fluid motion. Helical vortices appear both in nature, e.g. as tornadoes, and in many industrial applications

Differences between the motion of a helical vortex and the movement of fluid particles along its axis

The motion of a helical vortex and the movement of the fluid particles along its axis are analyzed. The same form of the helical axis of the vortex and the trajectory of the particles sometimes leads

Vortex bursting near a free surface

When the cross-section is reduced, a vortex displays spiralling and elasticity, bursting when the external velocity drops. How are these properties affected near a free surface? To answer, a

Solitons and nonlinear waves along quantum vortex filaments under the low-temperature two-dimensional local induction approximation.

TLDR
This work shows that by putting the two-dimensional LIA into correspondence with the first equation in the integrable Wadati-Konno-Ichikawa-Schimizu (WKIS) hierarchy, the approach can be coupled to existing inverse scattering transform results from the literature in order to obtain solitary wave solutions including the analog of the Hasimoto one-soliton for the 2D-LIA.

Structure and stability of Joukowski's rotor wake model

Abstract In this work, Joukowski's rotor wake model is considered for a two-blade rotor of radius $R_b$ rotating at the angular velocity $\varOmega _R$ in a normal incident velocity $V_{\infty }$.

Travelling helices and the vortex filament conjecture in the incompressible Euler equations

TLDR
The Euler equations are considered in vorticity form in jats:disp-formula and the Euler equation is considered in jat:tex-math.

An acentric rotation of helical vortex pair

References

SHOWING 1-10 OF 28 REFERENCES

On the self-induced motion of a helical vortex

The velocity field in the immediate vicinity of a curved vortex comprises a circulation around the vortex, a component due to the vortex curvature, and a ‘remainder’ due to the more distant parts of

The stability of a helical vortex filament

The stability of a helical vortex filament of finite core and infinite extent to small sinusoidal displacements of its centre-line is considered. The influence of the entire perturbed filament on the

The Steady Motion and Stability of a Helical Vortex

1. Introductory .—This is the third of a series of papers dealing with the stability or instability of certain forms of vortex motion associated with the wake of a body moving in a fluid. In the

The effect of torsion on the motion of a helical vortex filament

In this paper we analyse in detail, and for the first time, the rôle of torsion in the dynamics of twisted vortex filaments. We demonstrate that torsion may influence considerably the motion of

Topology of helical fluid flow

Considering a coordinate-free formulation of helical symmetry rather than more traditional definitions based on coordinates, we discuss basic properties of helical vector fields and compare results

Stability of helical tip vortices in a rotor far wake

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

The Dilemma of Defining a Vortex

The problem of defining a vortex in a real fluid is discussed. The definition and identification of a vortex in unsteady motions is difficult since streamlines and pathlines are not invariant with

Self-induced motion and asymptotic expansion of the velocity field in the vicinity of a helical vortex filament

A derivation of an expression for the self-induced velocity of a helical vortex filament with moderate and small pitch is presented for the cases of an infinite space as well as a space bounded by a