scholarly journals Formation of curvature singularity along vortex line in an axisymmetric, swirling vortex sheet

2002 ◽  
Vol 14 (8) ◽  
pp. 2886-2897 ◽  
Author(s):  
Takashi Sakajo
Keyword(s):  
Vortex Line ◽  
Vortex Sheet ◽  
Curvature Singularity ◽  
Swirling Vortex

On the formation of Moore curvature singularities in vortex sheets

1999 ◽  
Vol 378 ◽  
pp. 233-267 ◽  
Author(s):  
STEPHEN J. COWLEY ◽  
GREG R. BAKER ◽  
SALEH TANVEER
Keyword(s):  
Complex Plane ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Nonlinear Effects ◽  
Vortex Sheet ◽  
Finite Amplitude ◽  
Analytical Continuation ◽  
Curvature Singularity ◽  
Singularity Formation ◽  
Vortex Sheets

Moore (1979) demonstrated that the cumulative influence of small nonlinear effects on the evolution of a slightly perturbed vortex sheet is such that a curvature singularity can develop at a large, but finite, time. By means of an analytical continuation of the problem into the complex spatial plane, we find a consistent asymptotic solution to the problem posed by Moore. Our solution includes the shape of the vortex sheet as the curvature singularity forms. Analytic results are confirmed by comparison with numerical solutions. Further, for a wide class of initial conditions (including perturbations of finite amplitude), we demonstrate that 3/2-power singularities can spontaneously form at t=0+ in the complex plane. We show that these singularities propagate around the complex plane. If two singularities collide on the real axis, then a point of infinite curvature develops on the vortex sheet. For such an occurrence we give an asymptotic description of the vortex-sheet shape at times close to singularity formation.

The collapse of an axi-symmetric, swirling vortex sheet

Nonlinearity ◽  
1993 ◽  
Vol 6 (6) ◽  
pp. 843-867 ◽  
Author(s):  
R E Caflisch ◽  
L Xiaofan ◽  
M J Shelley
Keyword(s):  
Vortex Sheet ◽  
Swirling Vortex

scholarly journals A substrate for brane shells from $$ T\overline{T} $$

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Jeremias Aguilera-Damia ◽  
Louise M. Anderson ◽  
Evan Coleman
Keyword(s):  
Three Dimensional ◽  
Radial Position ◽  
Singular Behavior ◽  
Curvature Singularity ◽  
Closed Timelike Curves ◽  
Finite Radius ◽  
Linear Dilaton ◽  
Singularity Resolution ◽  
New Interpretation ◽  
Single Trace

Abstract A solvable current-current deformation of the worldsheet theory of strings on AdS3 has been recently conjectured to be dual to an irrelevant deformation of the spacetime orbifold CFT, commonly referred to as single-trace $$ T\overline{T} $$ T T ¯ . These deformations give rise to a family of bulk geometries which realize a non-trivial flow towards the UV. For a particular sign of this deformation, the corresponding three-dimensional geometry approaches AdS3 in the interior, but has a curvature singularity at finite radius, beyond which there are closed timelike curves. It has been suggested that this singularity is due to the presence of “negative branes,” which are exotic objects that generically change the metric signature. We propose an alternative UV-completion for geometries displaying a similar singular behavior by cutting and gluing to a regular background which approaches a linear dilaton vacuum in the UV. In the S-dual picture, a singularity resolution mechanism known as the enhançon induces this transition by the formation of a shell of D5-branes at a fixed radial position near the singularity. The solutions involving negative branes gain a new interpretation in this context.

Separated Flow Past a Slender Delta Wing at Incidence

1973 ◽  
Vol 24 (2) ◽  
pp. 120-128 ◽  
Author(s):  
J E Barsby
Keyword(s):  
Delta Wing ◽  
Separated Flow ◽  
Leading Edge ◽  
Vortex Sheet ◽  
Simultaneous Equations ◽  
Delta Wings ◽  
Nested Iteration ◽  
Finite Difference Technique ◽  
Flow Past ◽  
Vortex Systems

SummarySolutions to the problem of separated flow past slender delta wings for moderate values of a suitably defined incidence parameter have been calculated by Smith, using a vortex sheet model. By increasing the accuracy of the finite-difference technique, and by replacing Smith’s original nested iteration procedure, to solve the non-linear simultaneous equations that arise, by a Newton’s method, it is possible to extend the range of the incidence parameter over which solutions can be obtained. Furthermore for sufficiently small values of the incidence parameter, new and unexpected results in the form of vortex systems that originate inboard from the leading edge have been discovered. These new solutions are the only solutions, to the author’s knowledge, of a vortex sheet leaving a smooth surface.Interest has centred upon the shape of the finite vortex sheet, the position of the isolated vortex, and the lift, and variations of these quantities are shown as functions of the incidence parameter. Although no experimental evidence is available, comparisons are made with the simpler Brown and Michael model in which all the vorticity is assumed to be concentrated onto an isolated line vortex. Agreement between these two models becomes very close as the value of the incidence parameter is reduced.

Formation of Vortex Street in Laminar Boundary Layer

1980 ◽  
Vol 47 (2) ◽  
pp. 227-233 ◽  
Author(s):  
M. Kiya ◽  
M. Arie
Keyword(s):  
Boundary Layer ◽  
Shear Flow ◽  
Laminar Boundary Layer ◽  
Solid Wall ◽  
Vortex Sheet ◽  
Vortex Street ◽  
Bluff Bodies ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Vortex Patterns

Main features of the formation of vortex street from free shear layers emanating from two-dimensional bluff bodies placed in uniform shear flow which is a model of a laminar boundary layer along a solid wall. This problem is concerned with the mechanism governing transition induced by small bluff bodies suspended in a laminar boundary layer. Calculations show that the background vorticity of shear flow promotes the rolling up of the vortex sheet of the same sign whereas it decelerates that of the vortex sheet of the opposite sign. The steady configuration of the conventional Karman vortex street is not possible in shear flow. Theoretical vortex patterns are experimentally examined by a flow-visualization technique.

Transonic and subsonic dynamics of the current-vortex sheet

2002 ◽  
Vol 9 (5) ◽  
pp. 1575-1583 ◽  
Author(s):  
A. Antognetti ◽  
G. Einaudi ◽  
R. B. Dahlburg
Keyword(s):  
Vortex Sheet

Analytic structure of vortex sheet dynamics. Part 1. Kelvin–Helmholtz instability

1982 ◽  
Vol 114 (-1) ◽  
pp. 283 ◽  
Author(s):  
Daniel I. Meiron ◽  
Gregory R. Baker ◽  
Steven A. Orszag
Keyword(s):  
Vortex Sheet ◽  
Analytic Structure ◽  
Helmholtz Instability
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