Motion of a helical vortex

2017 ◽  
Vol 836 ◽  
Author(s):  
Oscar Velasco Fuentes
Keyword(s):  
Velocity Field ◽  
Cross Section ◽  
Single Point ◽  
Small Circle ◽  
Inviscid Incompressible Fluid ◽  
Helical Vortex ◽  
Angular Velocities ◽  
Infinite Tube ◽  
Range Of Values ◽  
Theoretical Results

This paper deals with the motion of a single helical vortex in an unbounded inviscid incompressible fluid. The vortex is an infinite tube whose centreline is a helix and whose cross-section is a small circle where the vorticity is uniform and parallel to the centreline. Ever since Joukowsky (Trudy Otd. Fiz. Nauk Mosk. Obshch. Lyub. Estest., vol. 16, 1912, pp. 1–31) deduced that this vortex translates and rotates steadily without change of form, numerous attempts have been made to compute the velocities. Here, Hardin’s (Phys. Fluids, vol. 25, 1982, pp. 1949–1952) solution for the velocity field is used to find new expressions for the linear and angular velocities of the vortex. The theoretical results are verified by numerically computing the velocity at a single point using the Helmholtz integral and the Rosenhead–Moore approximation to the Biot–Savart law, and by numerically simulating the vortex evolution, under the Euler equations, in a triple-periodic cube. The new formulae are also shown to be more accurate than previous results over the whole range of values of the vortex pitch and cross-section.

Flow topology of helical vortices

2018 ◽  
Vol 842 ◽  
Author(s):  
Oscar Velasco Fuentes
Keyword(s):  
Angular Velocity ◽  
The Self ◽  
Flow Topology ◽  
Inviscid Incompressible Fluid ◽  
Helical Vortices ◽  
Angular Velocities ◽  
Flow Evolution ◽  
Range Of Values ◽  
Theoretical Results ◽  
Transport Fluid

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 this paper, the linear and angular velocities of this set of vortices ($U$ and $\unicode[STIX]{x1D6FA}$ respectively) are computed as the sum of the mutually induced velocities found by Okulov (J. Fluid Mech., vol. 521, 2004, pp. 319–342) and the self-induced velocities found by Velasco Fuentes (J. Fluid Mech., vol. 836 2018). Numerical computations of the velocities using the Helmholtz integral and the Biot–Savart law, as well as numerical simulations of the flow evolution under the Euler equations, are used to verify that the theoretical results are accurate for $N=1,\ldots ,4$ vortices over a broad range of values of the pitch and radius of the vortices. An analysis of the flow topology in a reference system that translates with velocity $U$ and rotates with angular velocity $\unicode[STIX]{x1D6FA}$ serves to determine the capacity of the vortices to transport fluid.

ANALYSIS OF THE GENERAL EQUATIONS OF THE TRANSVERSE VIBRATION OF A PIECEWISE UNIFORM VISCOELASTIC PLATE

2020 ◽  
Vol 7 (3) ◽  
pp. 52-56
Author(s):  
MMATMATISA JALILOV ◽  
◽  
RUSTAM RAKHIMOV ◽  
Keyword(s):  
Cross Section ◽  
Transverse Vibration ◽  
Three Dimensional ◽  
Viscoelastic Plate ◽  
Constant Thickness ◽  
Regional Problem ◽  
Rigid Contact ◽  
Under Construction ◽  
Derivatives Of ◽  
Theoretical Results

This article discusses the analysis of the general equations of the transverse vibration of a piecewise homogeneous viscoelastic plate obtained in the “Oscillation of inlayer plates of constant thickness” [1]. In the present work on the basis of a mathematical method, the approached theory of fluctuation of the two-layer plates, based on plate consideration as three dimensional body, on exact statement of a three dimensional mathematical regional problem of fluctuation is stood at the external efforts causing cross-section fluctuations. The general equations of fluctuations of piecewise homogeneous viscoelastic plates of the constant thickness, described in work [1], are difficult on structure and contain derivatives of any order on coordinates x, y and time t and consequently are not suitable for the decision of applied problems and carrying out of engineering calculations. For the decision of applied problems instead of the general equations it is expedient to use confidants who include this or that final order on derivatives. The classical equations of cross-section fluctuation of a plate contain derivatives not above 4th order, and for piecewise homogeneous or two-layer plates the elementary approached equation of fluctuation is the equation of the sixth order. On the basis of the analytical decision of a problem the general and approached decisions of a problem are under construction, are deduced the equation of fluctuation of piecewise homogeneous two-layer plates taking into account rigid contact on border between layers, and also taking into account mechanical and rheological properties of a material of a plate. The received theoretical results for the decision of dynamic problems of cross-section fluctuation of piecewise homogeneous two-layer plates of a constant thickness taking into account viscous properties of their material allow to count more precisely the is intense-deformed status of plates at non-stationary external loadings.

Finite difference code for velocity and surface traction of a Fluid between Two Eccentric Spheres

2015 ◽  
Vol 11 (1) ◽  
pp. 2960-2971
Author(s):  
M.Abdel Wahab
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Finite Difference ◽  
Numerical Study ◽  
Outer Sphere ◽  
Equation Of Motion ◽  
Annular Region ◽  
Surface Traction ◽  
Angular Velocities ◽  
Axis Passing

The Numerical study of the flow of a fluid in the annular region between two eccentric sphere susing PHP Code isinvestigated. This flow is created by considering the inner sphere to rotate with angular velocity 1  and the outer sphererotate with angular velocity 2  about the axis passing through their centers, the z-axis, using the three dimensionalBispherical coordinates (, ,) .The velocity field of fluid is determined by solving equation of motion using PHP Codeat different cases of angular velocities of inner and outer sphere. Also Finite difference code is used to calculate surfacetractions at outer sphere.

Kelvin and V-like Ship Wakes Affected by Surfactants

2001 ◽  
Vol 45 (02) ◽  
pp. 150-163
Author(s):  
Gregory Zilman ◽  
Touvia Miloh
Keyword(s):  
Cross Section ◽  
Single Layer ◽  
Ship Wake ◽  
Backscattering Cross Section ◽  
Alternative Approach ◽  
Ship Wakes ◽  
Half Angle ◽  
Radar Backscattering ◽  
The Green Function ◽  
Theoretical Results

Synthetic aperture radar (SAR) ship wake images in light wind and calm sea conditions frequently appear in the form of a bright V with a half-angle of 2 to 3 deg. Sophisticated and conflicting explanations of this phenomenon, based on the Bragg scattering mechanism, have been proposed. There is a belief that the narrow V-wake is not a part of the Kelvin wake. An alternative approach, which is not generally accepted, suggests that short divergent Kelvin waves may contribute to the V-wake imaging although these waves are mixed with unsteady surface waves generated by the ship-induced turbulence. Ship-generated divergent waves contaminated by surfactants and their radar backscattering cross section are studied. The hull of the ship is represented by a single layer of hydrodynamic singularities. The Green function of a point source moving below a free surface covered by surfactants is derived. A closed-form asymptotic solution for the far ship wave wake is obtained. It is used to calculate analytically the corresponding radar backscattering cross section. The radiative, viscous, and surfactant-induced decay of the V-wake brightness along the V-arms is discussed. The theoretical results are compared against available experimental data.

scholarly journals The velocity field induced by a helical vortex tube

2005 ◽  
Vol 17 (10) ◽  
pp. 107101 ◽  
Author(s):  
Y. Fukumoto ◽  
V. L. Okulov
Keyword(s):  
Velocity Field ◽  
Vortex Tube ◽  
Helical Vortex

Magnetohydrodynamic flow due to the discharge of an electric current in a hemispherical container

1976 ◽  
Vol 73 (4) ◽  
pp. 641-650 ◽  
Author(s):  
C. Sozou ◽  
W. M. Pickering
Keyword(s):  
Free Surface ◽  
Velocity Field ◽  
Flow Field ◽  
Electric Current ◽  
Cross Section ◽  
Analytic Solution ◽  
Closed Loops ◽  
Slow Viscous Flow ◽  
Axial Cross Section ◽  
Section Form

In this paper we consider the flow field induced in an incompressible viscous conducting fluid in a hemispherical bowl by a symmetric discharge of electric current from a point source at the centre of the plane end of the hemisphere. This plane end is a free surface. We construct an analytic solution for the slow viscous flow and a numeriacl solution for the nonlinear problem. The streamlines in an axial cross-section form two sets of closed loops, one on either side of the axis. Our computations indicate that, for a given fluid, when the discharged current reaches a certain magnitude the velocity field breaks down. This breakdown probably originates at the vertex of the hemispherical container.

scholarly journals Big Bang Bifurcations in the Tantalus Oscillator Under Biphasic Perturbations

2019 ◽  
Vol 29 (02) ◽  
pp. 1950023
Author(s):  
Humberto Arce ◽  
Araceli Torres ◽  
Augusto Cabrera ◽  
Martín Alarcón ◽  
Carlos Málaga
Keyword(s):  
Bifurcation Diagram ◽  
Limit Cycle ◽  
Excellent Agreement ◽  
Big Bang ◽  
Wide Range ◽  
Coupling Time ◽  
First Time ◽  
Hydrodynamic Oscillator ◽  
Range Of Values ◽  
Theoretical Results

The Tantalus Oscillator is a nonlinear hydrodynamic oscillator with an attractive limit cycle. In this study, we pursue the construction of a biparametric bifurcation diagram for the Tantalus Oscillator under biphasic perturbations. That is the first time that this kind of diagram is built for this kind of oscillator under biphasic perturbations. Results show that biphasic perturbations have no effect when the coupling time is chosen over a wide range of values. This modifies the bifurcation diagram obtained under monophasic perturbations. Now we have the appearance of periodic increment Big Bang Bifurcations. The theoretical results are in excellent agreement with experimental observations.

Limit Analysis for Combined Edge and Pressure Loading on a Cylindrical Shell

1971 ◽  
Vol 93 (4) ◽  
pp. 998-1006
Author(s):  
H. S. Ho ◽  
D. P. Updike
Keyword(s):  
Cylindrical Shell ◽  
Velocity Field ◽  
Axial Force ◽  
Shear Force ◽  
Circular Cylindrical Shell ◽  
Yield Condition ◽  
External Pressure ◽  
Tresca Yield Condition ◽  
Stress States ◽  
Range Of Values

Equations describing the stress field and velocity field occurring in a circular cylindrical shell at plastic collapse are derived corresponding to stress states lying on each face of a yield surface for a uniform shell of material obeying the Tresca yield condition. They are then applied to the case of a shell under combined axisymmetric loadings (moment, shear force, and axial force) at one end and uniform internal or external pressure on the lateral surface. For a sufficiently long shell, complete solutions are obtained for a fixed far end, and for a certain range of values of axial force and pressure, they are obtained for a free far end. All the solutions are represented by either closed form or by quadratures. It is shown that in many cases the radial velocity field is proportional to the shear force.

Vibration Characteristics of Straight Blades of Asymmetrical Aerofoil Cross-Section

1969 ◽  
Vol 20 (2) ◽  
pp. 178-190 ◽  
Author(s):  
W. Carnegie ◽  
B. Dawson
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Limited Range ◽  
First Order ◽  
Special Cases ◽  
Theoretical Results ◽  
Theoretical Procedure ◽  
Good Agreement

SummaryTheoretical and experimental natural frequencies and modal shapes up to the fifth mode of vibration are given for a straight blade of asymmetrical aerofoil cross-section. The theoretical procedure consists essentially of transforming the differential equations of motion into a set of simultaneous first-order equations and solving them by a step-by-step finite difference procedure. The natural frequency values are compared with results obtained by an analytical solution and with standard solutions for certain special cases. Good agreement is shown to exist between the theoretical results for the various methods presented. The equations of motion are dependent upon the coordinates of the axis of the centre of flexure of the beam relative to the centroidal axis. The effect of variations of the centre of flexure coordinates upon the frequencies and modal shapes is shown for a limited range of coordinate values. Comparison is made between the theoretical natural frequencies and modal shapes and corresponding results obtained by experiment.

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