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A generalised multiparameter linear stability and sensitivity analysis method

Published online by Cambridge University Press:  15 May 2025

Zi-Han Zhang ,
Jun-Hua Pan Open the ORCID record for Jun-Hua Pan [Opens in a new window]  and
Ming-Jiu Ni Open the ORCID record for Ming-Jiu Ni [Opens in a new window]
Zi-Han Zhang
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China
Jun-Hua Pan
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics and University of Chinese Academy of Sciences, Beijing 100190, PR China
Ming-Jiu Ni*
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics and University of Chinese Academy of Sciences, Beijing 100190, PR China
*
Corresponding author: Ming-Jiu Ni, mjni@ucas.ac.cn
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Abstract

A generalised multiparameter model for linear modal stability and sensitivity analysis is developed. The stability and sensitivity equations are derived from a generalised vector-form governing equation comprised of multiple dimensionless parameters that represent different physical forces affecting the system’s stability. By introducing adjoint variables and constructing the Lagrangian identity, a differential relationship between the eigenvalue of the perturbation mode and dimensionless parameters is determined and defined as the global sensitivity gradient. It provides the constraint that must be satisfied for changes in different dimensionless parameters along the isoeigenvalue curve, which aids in the fast computation of the neutral curve. Moreover, the global sensitivity gradient can directly and intuitively evaluate the competitive relationship among the influences of various parameters on system instability. Based on the global sensitivity gradient, an optimal stability control strategy for transitioning from an unstable state to a stable state is discussed. Additionally, the relative sensitivity function is also introduced to investigate the influence of relative parameter variations on instability. To demonstrate the effectiveness of this method, three applications are presented: two-dimensional flow around a circular cylinder with a single dimensionless parameter Re; three-dimensional axisymmetric magnetohydrodynamic (MHD) flow around a sphere with two parameters Re and $N$; and two-dimensional MHD mixed convection with three parameters Re, ${\textit{Gr}}$ and $\textit{Ha}$.

JFM classification

Instability: Parametric instability

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1011 , 25 May 2025 , A12
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

†

These authors contributed equally to this work and should be considered co-first authors.

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