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Exact theory of material spike formation in flow separation

Published online by Cambridge University Press:  20 April 2018

Mattia Serra Open the ORCID record for Mattia Serra [Opens in a new window] ,
Jérôme Vétel Open the ORCID record for Jérôme Vétel [Opens in a new window]  and
George Haller Open the ORCID record for George Haller [Opens in a new window]
Mattia Serra*
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
Jérôme Vétel
Affiliation:
Department of Mechanical Engineering, Polytechnique Montréal, Montréal, QC, H3C 3A7, Canada
George Haller
Affiliation:
Institute for Mechanical Systems, ETH Zürich, 8092 Zürich, Switzerland
*
†Email address for correspondence: serram@seas.harvard.edu
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Abstract

We develop a frame-invariant theory of material spike formation during flow separation over a no-slip boundary in two-dimensional flows with arbitrary time dependence. Based on the exact curvature evolution of near-wall material lines, our theory identifies both fixed and moving flow separation, is effective also over short time intervals, and admits a rigorous instantaneous limit. As a byproduct, we derive explicit formulae for the evolution of material line curvature and the curvature rate for general compressible flows. The material backbone that we identify acts first as the precursor and later as the centrepiece of unsteady Lagrangian flow separation. We also discover a previously undetected spiking point where the backbone of separation connects to the boundary, and derive wall-based analytical formulae for its location. Finally, our theory explains the perception of off-wall separation in unsteady flows and provides conditions under which such a perception is justified. We illustrate our results on several analytical and experimental flows.

JFM classification

Nonlinear Dynamical Systems: Pattern formation Wakes/Jets: Separated flows Mathematical Foundations: Topological fluid dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 845 , 25 June 2018 , pp. 51 - 92
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Copyright
© 2018 Cambridge University Press 

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