Regional Stability Analysis of Transitional Fluid Flows

  title={Regional Stability Analysis of Transitional Fluid Flows},
  author={Leonardo F. Toso and Ross Drummond and Stephen R. Duncan},
  journal={IEEE Control Systems Letters},
A method to bound the maximum energy perturbation for which regional stability of transitional fluid flow models can be guaranteed is introduced. The proposed method exploits the fact that the fluid model’s nonlinearities are both lossless and locally bounded and uses the axes lengths of the ellipsoids for the trajectory set containment as variables in the stability conditions. Compared to existing approaches based on quadratic constraints, the proposed method leads to an average increase in… 

Figures and Tables from this paper


Global Stability Analysis of Fluid Flows using Sum-of-Squares
A new method for assessing the stability of finite-dimensional approximations to the Navier-Stokes equation for fluid flows and a structured method for generating Lyapunov functions using sum-of-squares optimization that exploits this energy conservation property is suggested.
Nonlinear Nonmodal Stability Theory
This review discusses a recently developed optimization technique for analyzing the nonlinear stability of a flow state. It is based on a nonlinear extension of nonmodal analysis and, in its simplest
Estimating Regions of Attraction for Transitional Flows Using Quadratic Constraints
An iterative method that refines the analysis by solving a sequence of semi-definite programs, and another based on solving a generalized eigenvalue problem with lower computational complexity, but at the cost of some precision in the final solution are presented.
Transition in shear flows. Nonlinear normality versus non‐normal linearity
A critique is presented of recent works promoting the concept of non‐normal operators and transient growth as the key to understanding transition to turbulence in shear flows. The focus is in
Hydrodynamic Stability Without Eigenvalues
A reconciliation of findings with the traditional analysis is presented based on the "pseudospectra" of the linearized problem, which imply that small perturbations to the smooth flow may be amplified by factors on the order of 105 by a linear mechanism even though all the eigenmodes decay monotonically.
Regional Analysis of Slope-Restricted Lurie Systems
This paper considers the stability analysis of nonlinear Lurie type systems where the nonlinearity is both (locally) sector and slope restricted and uses a Lyapunov function that is quadratic on both the states and theNonlinearity and has an integral term on the non linearity.
A low-dimensional model for turbulent shear flows
We analyse a low-dimensional model for turbulent shear flows. The model is based on Fourier modes and describes sinusoidal shear flow, in which the fluid between two free-slip walls experiences a
A mostly linear model of transition to tur
A simple model in three real dimensions is proposed, illustrating a possible mechanism of transition to turbulence. The linear part of the model is stable but highly non‐normal, so that certain
On a self-sustaining process in shear flows
A self-sustaining process conjectured to be generic for wall-bounded shear flows is investigated. The self-sustaining process consists of streamwise rolls that redistribute the mean shear to create
On the Origin of Streaks in Turbulent Shear Flows
It is shown that the ideas of selective amplification and direct resonance, based on linear theory, do not provide a selection mechanism for the well-defined streak spacing of about 100 wall units