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Spike formation theory in three-dimensional flow separation

Published online by Cambridge University Press:  22 August 2023

Sreejith Santhosh ,
Haodong Qin ,
Bjoern F. Klose ,
Gustaaf B. Jacobs Open the ORCID record for Gustaaf B. Jacobs [Opens in a new window] ,
Jérôme Vétel Open the ORCID record for Jérôme Vétel [Opens in a new window]  and
Mattia Serra Open the ORCID record for Mattia Serra [Opens in a new window]
Sreejith Santhosh
Affiliation:
Department of Physics, University of California, San Diego, CA 92093, USA
Haodong Qin
Affiliation:
Department of Physics, University of California, San Diego, CA 92093, USA
Bjoern F. Klose
Affiliation:
Department of Aerospace Engineering, San Diego State University, San Diego, CA 92182, USA Institute of Test and Simulation for Gas Turbines, German Aerospace Center (DLR), 86159 Augsburg, Germany
Gustaaf B. Jacobs
Affiliation:
Department of Aerospace Engineering, San Diego State University, San Diego, CA 92182, USA
Jérôme Vétel
Affiliation:
Department of Mechanical Engineering, Polytechnique Montréal, Montréal, QC H3C 3A7, Canada
Mattia Serra*
Affiliation:
Department of Physics, University of California, San Diego, CA 92093, USA
*
†Email address for correspondence: mserra@ucsd.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 three-dimensional flows with arbitrary time dependence. Based on the exact evolution of the largest principal curvature on near-wall material surfaces, our theory identifies fixed and moving separation. Our approach is effective over short time intervals and admits an instantaneous limit. As a byproduct, we derive explicit formulas for the evolution of the Weingarten map and the principal curvatures of any surface advected by general three-dimensional flows. The material backbone we identify acts first as a precursor and later as the centrepiece of Lagrangian flow separation. We discover previously undetected spiking points and curves where the separation backbones connect to the boundary and provide wall-based analytical formulas for their locations. We illustrate our results on several steady and unsteady flows.

JFM classification

Boundary Layers: Boundary layer separation Nonlinear Dynamical Systems: Pattern formation Wakes/Jets: Separated flows

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 969 , 25 August 2023 , A25
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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