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arXiv · 2302.12395

Spike formation theory in 3D flow separation

Sreejith Santhosh·Haodong Qin·Bjoern F. Klose·Gustaaf B. Jacobs·Jérôme Vétel·Mattia Serra
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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 centerpiece 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.

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Sreejith Santhosh, Haodong Qin, Bjoern F. Klose, Gustaaf B. Jacobs, Jérôme Vétel, Mattia Serra. 2023-02-24. Spike formation theory in 3D flow separation. https://arxiv.org/abs/2302.12395

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