# Weak nonlinearity for strong nonnormality

@inproceedings{Ducimetire2021WeakNF, title={Weak nonlinearity for strong nonnormality}, author={Yves-Marie Ducimeti{\`e}re and Edouard Boujo and F. Gallaire}, year={2021} }

We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of nonnormal dynamical systems, when they experience transient growth or respond to harmonic forcing. This approach reconciles the nonmodal nature of these growth mechanisms and the need for a center manifold to project the leading-order dynamics. Under the hypothesis of strong nonnormality, we take advantage of the fact that small operator perturbations suffice to make the inverse resolvent…

## References

SHOWING 1-10 OF 55 REFERENCES

Nonlinear Nonmodal Stability Theory

- Mathematics
- 2018

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…

Sensitivity and optimal forcing response in separated boundary layer flows

- Physics
- 2009

The optimal asymptotic response to time harmonic forcing of a convectively unstable two-dimensional separated boundary layer on a flat plate is numerically revisited from a global point of view. By…

Stochastic forcing of the linearized Navier–Stokes equations

- Physics
- 1993

Transient amplification of a particular set of favorably configured forcing functions in the stochastically driven Navier–Stokes equations linearized about a mean shear flow is shown to produce high…

Modal and transient dynamics of jet flows

- Physics
- 2013

The linear stability dynamics of incompressible and compressible isothermal jets are investigated by means of their optimal initial perturbations and of their temporal eigenmodes. The transient…

Global Measures of Local Convective Instabilities

- Physics
- 1997

We examine the linear stability of the Ginzburg-Landau operator with spatially varying coefficients, which mimics strongly nonparallel open flows such as wakes, jets, and boundary layers. The…

Rapid path to transition via nonlinear localized optimal perturbations in a boundary-layer flow.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

This work aims at verifying the hypothesis that in some cases transition can be triggered by some purely nonlinear mechanisms, looking for a localized perturbation able to lead a boundary-layer flow to a chaotic state, following a nonlinear route.

Saturation of the response to stochastic forcing in two-dimensional backward-facing step flow: A self-consistent approximation

- Mathematics
- 2016

Selective noise amplifiers are characterized by large linear amplification to external perturbations in a particular frequency range despite their global linear stability. Applying a stochastic…

Nonmodal Stability Theory

- Physics
- 2007

Hydrodynamic stability theory has recently seen a great deal of development. After being dominated by modal (eigenvalue) analysis for many decades, a different perspective has emerged that allows the…

Self-consistent model for the saturation mechanism of the response to harmonic forcing in the backward-facing step flow

- PhysicsJournal of Fluid Mechanics
- 2016

Certain flows denominated as amplifiers are characterized by their global linear stability while showing large linear amplifications to sustained perturbations. As the forcing amplitude increases, a…

The preferred mode of incompressible jets: linear frequency response analysis

- PhysicsJournal of Fluid Mechanics
- 2013

Abstract The linear amplification of axisymmetric external forcing in incompressible jet flows is investigated within a fully non-parallel framework. Experimental and numerical studies have shown…