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Exact theory of material spike formation in flow separation

Published online by Cambridge University Press:  20 April 2018

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
Corresponding
E-mail address:

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.

Type
JFM Papers
Copyright
© 2018 Cambridge University Press 

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