6533b826fe1ef96bd12850ff

RESEARCH PRODUCT

Regularized Euler-alpha motion of an infinite array of vortex sheets

Francesco GarganoVincenzo SciaccaMarco SammartinoRussel E. Caflisch

subject

PhysicsGeneral Mathematics010102 general mathematicsMathematical analysisGeometryVortex-sheet Birkhoff–Rott equation Euler-alpha regularization Complex singularities01 natural sciencesRegularization (mathematics)010305 fluids & plasmasVortexsymbols.namesakeSingularityFlow (mathematics)0103 physical sciencesVortex sheetEuler's formulasymbolsGravitational singularity0101 mathematicsComplex planeSettore MAT/07 - Fisica Matematica

description

We consider the Euler- $$\alpha $$ regularization of the Birkhoff–Rott equation and compare its solutions with the dynamics of the non regularized vortex-sheet. For a flow induced by an infinite array of planar vortex-sheets we analyze the complex singularities of the solutions.Through the singularity tracking method we show that the regularized solution has several complex singularities that approach the real axis. We relate their presence to the formation of two high-curvature points in the vortex sheet during the roll-up phenomenon.

yearjournalcountryeditionlanguage
2016-08-09
10.1007/s40574-016-0097-6http://hdl.handle.net/10447/206004