Singularity Formation on Vortex Sheets: The Rayleigh-Taylor Problem

1992 ◽  
pp. 337-349
Author(s):  
M. S. Siegel
Keyword(s):  
Singularity Formation ◽  
Vortex Sheets ◽  
Taylor Problem

scholarly journals Singularity formation in three-dimensional vortex sheets

2003 ◽  
Vol 15 (1) ◽  
pp. 147-172 ◽  
Author(s):  
Thomas Y. Hou ◽  
Gang Hu ◽  
Pingwen Zhang
Keyword(s):  
Three Dimensional ◽  
Singularity Formation ◽  
Vortex Sheets

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.

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.

scholarly journals Naked singularity formation in $${f({\mathcal R})}$$ gravity

2011 ◽  
Vol 43 (11) ◽  
pp. 2943-2963 ◽  
Author(s):  
A. H. Ziaie ◽  
K. Atazadeh ◽  
S. M. M. Rasouli
Keyword(s):  
Naked Singularity ◽  
Singularity Formation

Comment on “Two-finger selection theory in the Saffman-Taylor problem”

2001 ◽  
Vol 63 (4) ◽  
Author(s):  
Giovani L. Vasconcelos
Keyword(s):  
Selection Theory ◽  
Taylor Problem ◽  
Finger Selection

Do vortex sheets roll up?

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

scholarly journals Singularity Formation for the Compressible Euler Equations

2017 ◽  
Vol 49 (4) ◽  
pp. 2591-2614 ◽  
Author(s):  
Geng Chen ◽  
Ronghua Pan ◽  
Shengguo Zhu
Keyword(s):  
Euler Equations ◽  
Compressible Euler Equations ◽  
Singularity Formation ◽  
Compressible Euler
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