Objective early identification of kinematic instabilities in shear flows

TL;DR

This paper introduces a kinematic method to detect flow instabilities early by analyzing the curvature change of fluid particle lines, applicable to complex shear flows without prior flow knowledge.

Contribution

It proposes an objective, parametrization-independent approach based on Lagrangian curvature to identify flow instabilities early in various shear flow scenarios.

Findings

Successfully detects instabilities in jet flows, airfoil shear flows, and wake flows.

Provides an analytic link between velocity mode growth and Lagrangian curvature.

Applicable to flows of general complexity without needing base flow information.

Abstract

A kinematic approach for the identification of flow instabilities is proposed. By defining a flow instability in the Lagrangian frame as the increased folding of lines of fluid particles, subtle perturbations and unstable growth thereof are detected early based solely on the curvature change of material lines over finite time. The material line curvature is objective, parametrization independent, and can be applied to flows of general complexity without knowledge of the base flow. An analytic connection between the growth of Eulerian velocity modes perturbing a general shear flow and the induced flow map and Lagrangian curvature change is derived. The approach is verified to capture instabilities promptly in a temporally developing jet flow, an unstable separated shear flow over a cambered airfoil, and in the onset of a wake instability behind a circular cylinder.