scholarly journals Finite rotating and translating vortex sheets

2021 ◽  
Vol 923 ◽  
Author(s):  
Bartosz Protas ◽  
Stefan G. Llewellyn Smith ◽  
Takashi Sakajo
Keyword(s):  
Vortex Sheets

Abstract

6—The Instability of Two Vortex Sheets Enclosing a Subsonic Jet due to Acoustic Radiation

1974 ◽  
Vol 72 (1) ◽  
pp. 79-91 ◽  
Author(s):  
N. Hardisty
Keyword(s):  
Acoustic Radiation ◽  
Vortex Sheets ◽  
Instability Waves ◽  
Subsonic Jet

SummaryThe propagation of sound in a subsonic jet separated by two vortex sheets from two semi-infinite still media is considered and it is found that instability waves arise at particular points on the vortex sheets and that their effect is confined to certain regions.

Do vortex sheets roll up?

1959 ◽  
Vol 8 (1) ◽  
pp. 77-90 ◽  
Author(s):  
Garrett Birkhoff ◽  
Joseph Fisher
Keyword(s):  
Vortex Sheets

scholarly journals Remarks on Stationary and Uniformly-rotating Vortex Sheets: Rigidity Results

2021 ◽  
Author(s):  
Javier Gómez-Serrano ◽  
Jaemin Park ◽  
Jia Shi ◽  
Yao Yao
Keyword(s):  
Angular Velocity ◽  
Disjoint Union ◽  
Vortex Sheet ◽  
Vortex Sheets ◽  
Smooth Curves ◽  
Rigidity Results ◽  
Positive Vorticity ◽  
Constant Vorticity ◽  
Concentric Circles ◽  
Finite Disjoint Union

AbstractIn this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity $$\Omega $$ Ω , such that it has positive vorticity and is concentrated in a finite disjoint union of smooth curves with finite length is the trivial one: constant vorticity amplitude supported on a union of nested, concentric circles. The proof follows a desingularization argument and a calculus of variations flavor.

scholarly journals Collapse of n Point Vortices, Formation of the Vortex Sheets and Transport of Passive Markers

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 943
Author(s):  
Henryk Kudela
Keyword(s):  
Differential Equations ◽  
Point Vortex ◽  
Optimization Procedure ◽  
Vortex Sheet ◽  
Point Vortices ◽  
Vortex Sheets ◽  
Impermeable Barrier ◽  
Initial Location ◽  
Passive Tracers ◽  
Initial Iterate

In this paper, the motion of the n-vortex system as it collapses to a point in finite time is studied. The motion of vortices is described by the set of ordinary differential equations that we are able to solve analytically. The explicit formula for the solution demands the initial location of collapsing vortices. To find the collapsing locations of vortices, the algebraic, nonlinear system of equations was built. The solution of that algebraic system was obtained using Newton’s procedure. A good initial iterate needs to be provided to succeed in the application of Newton’s procedure. An unconstrained Leverber–Marquart optimization procedure was used to find such a good initial iterate. The numerical studies were conducted, and numerical evidence was presented that if in a collapsing system n=50 point vortices include a few vortices with much greater intensities than the others in the set, the vortices with weaker intensities organize themselves onto the vortex sheet. The collapsing locations depend on the value of the Hamiltonian. By changing the Hamiltonian values in a specific interval, the collapsing curves can be obtained. All points on the collapse curves with the same Hamiltonian value represent one collapsing system of vortices. To show the properties of vortex sheets created by vortices, the passive tracers were used. Advection of tracers by the velocity induced by vortices was calculated by solving the proper differential equations. The vortex sheets are an impermeable barrier to inward and outward fluxes of tracers. Arising vortex structures are able to transport the passive tracers. In this paper, several examples showing the diversity of collapsing structures with the vortex sheet are presented. The collapsing phenomenon of many vortices, their ability to self organize and the transportation of the passive tracers are novelties in the context of point vortex dynamics.

scholarly journals Traveling waves from the arclength parameterization: Vortex sheets with surface tension

2013 ◽  
Vol 15 (3) ◽  
pp. 359-380 ◽  
Author(s):  
Benjamin Akers ◽  
David Ambrose ◽  
J. Douglas Wright
Keyword(s):  
Surface Tension ◽  
Traveling Waves ◽  
Vortex Sheets

A Simple Approach to the Theory of Secondary Flows

1954 ◽  
Vol 5 (4) ◽  
pp. 218-234 ◽  
Author(s):  
J. H. Preston
Keyword(s):  
Simple Approach ◽  
Secondary Flows ◽  
Large Deflections ◽  
Simple Method ◽  
Vortex Sheets ◽  
Trailing Edges ◽  
Secondary Motion ◽  
Set Up ◽  
Uniform Stream

SummaryA simple method is developed for computing the trailing vorticity which arises when a non-uniform stream is turned.It is shown that, for a sudden and constant deflection of a non-uniform stream, no net trailing vorticity is set up in the exit flow and hence there is no secondary motion.In the case of an impulse cascade of finite dimensions with constant turning, it is found that the trailing vorticity has three distinct components—the passage vorticity and two components which appear as vortex sheets springing from the trailing edges of the aerofoils. It is shown that for small angles of deflection there is no net circulation associated with the trailing vorticity downstream, of the cascade, and it is inferred that this should still be so for large deflections.

scholarly journals Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

2019 ◽  
Vol 266 (9) ◽  
pp. 5397-5430 ◽  
Author(s):  
Alessandro Morando ◽  
Paola Trebeschi ◽  
Tao Wang
Keyword(s):  
Euler Equations ◽  
Nonlinear Stability ◽  
Two Dimensional ◽  
Vortex Sheets

scholarly journals Confined vortex surface and irreversibility. 1. Properties of exact solution

2021 ◽  
pp. 2150097
Author(s):  
Alexander Migdal
Keyword(s):  
Strain Tensor ◽  
Special Kind ◽  
Local Strain ◽  
Vortex Sheet ◽  
Exceptional Case ◽  
Surface Integral ◽  
Time Reversibility ◽  
Navier Stokes Equation ◽  
Vortex Sheets ◽  
Asymmetric Vortex

We revise the steady vortex surface theory following the recent finding of asymmetric vortex sheets (Migdal, 2021). These surfaces avoid the Kelvin–Helmholtz instability by adjusting their discontinuity and shape. The vorticity collapses to the sheet only in an exceptional case considered long ago by Burgers and Townsend, where it decays as a Gaussian on both sides of the sheet. In generic asymmetric vortex sheets (Shariff, 2021), vorticity leaks to one side or another, making such sheets inadequate for vortex sheet statistics and anomalous dissipation. We conjecture that the vorticity in a turbulent flow collapses on a special kind of surface (confined vortex surface or CVS), satisfying some equations involving the tangent components of the local strain tensor. The most important qualitative observation is that the inequality needed for this solution’s stability breaks the Euler dynamics’ time reversibility. We interpret this as dynamic irreversibility. We have also represented the enstrophy as a surface integral, conserved in the Navier–Stokes equation in the turbulent limit, with vortex stretching and viscous diffusion terms exactly canceling each other on the CVS surfaces. We have studied the CVS equations for the cylindrical vortex surface for an arbitrary constant background strain with two different eigenvalues. This equation reduces to a particular version of the stationary Birkhoff–Rott equation for the 2D flow with an extra nonanalytic term. We study some general properties of this equation and reduce its solution to a fixed point of a map on a sphere, guaranteed to exist by the Brouwer theorem.

The flow structure in the lee of an inclined 6:1 prolate spheroid

1994 ◽  
Vol 269 ◽  
pp. 79-106 ◽  
Author(s):  
T. C. Fu ◽  
A. Shekarriz ◽  
J. Katz ◽  
T. T. Huang
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Flow Structure ◽  
Incidence Angle ◽  
Prolate Spheroid ◽  
The Body ◽  
Boundary Layer Transition ◽  
Primary Vortex ◽  
Vortex Sheets ◽  
Vorticity Distribution

Particle displacement velocimetry is used to measure the velocity and vorticity distributions around an inclined 6: 1 prolate spheroid. The objective is to determine the effects of boundary-layer tripping, incidence angle, and Reynolds number on the flow structure. The vorticity distributions are also used for computing the lateral forces and rolling moments that occur when the flow is asymmetric. The computed forces agree with results of direct measurements. It is shown that when the flow is not tripped, separation causes the formation of a pair of vortex sheets. The size of these sheets increases with increasing incidence angle and axial location. Their orientation and internal vorticity distribution also depend on incidence. Rollup into distinct vortices occurs in some cases, and the primary vortex contains between 20 % and 50 % of the overall circulation. The entire flow is unsteady and there are considerable variations in the instantaneous vorticity distributions. The remainder of the lee side, excluding these vortex sheets, remains almost vorticity free, providing clear evidence that the flow can be characterized as open separation. Boundary-layer tripping causes earlier separation on part of the model, brings the primary vortex closer to the body, and spreads the vorticity over a larger region. The increased variability in the vorticity distribution causes considerable force fluctuations, but the mean loads remain unchanged. Trends with increasing Reynolds number are conflicting, probably because of boundary-layer transition. The separation point moves towards the leeward meridian and the normal force decreases when the Reynolds number is increased from 0.42 × 106 to 1.3 × 106. Further increase in the Reynolds number to 2.1 × 106 and tripping cause an increase in forces and earlier separation.

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