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Non-modal instability mechanisms in stratified and homogeneous shear flow

Abstract : This thesis reports a study of nonmodal instability mechanisms in shear flows, mainly mixing layers. We focus on the linearized perturbations that maximize the energy amplification at finite time, the 'optimal perturbations', which in non-normal systems are different from the most unstable eigenmode. An original description of non-normality and its consequences is provided in chapter 2. Chapter 3 deals with the well known lift-up mechanism, for the case of longitudinal inviscid perturbations to any parallel flow. A new one-dimensional equation determining the orthogonal set of optimal and sub-optimal perturbations is found in that case, allowing to obtain new exact and asymptotic results. In chapter 4 we address the secondary instability of mixing layers, for which we use the naturally evolving 2D flow as a base state to compute the 3D optimal perturbations. Among the optimal responses we recover the usual 'elliptic' and 'hyperbolic' types of perturbation structure, the largest growth depending on the spanwise wavenumber and optimization times (initial and final). In chapters 5 and 6 we consider density stratification in the direction orthogonal to the plane of the base flow, and we use a 'Craya-Herring' decomposition to analyse the flow in terms of its internal wave and vertical vorticity content. The perturbation equations for a general 2D base flow are first derived and interpreted in terms of wave/vortex energetics in chapter 5. These results are used in chapter 6 to analise the strong generation and emission of internal waves produced by the optimal perturbations to a horizontal shear layer.
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Contributor : Cristobal Arratia <>
Submitted on : Monday, February 20, 2012 - 2:39:35 PM
Last modification on : Wednesday, March 27, 2019 - 4:39:25 PM
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  • HAL Id : pastel-00672072, version 1



Cristobal Arratia. Non-modal instability mechanisms in stratified and homogeneous shear flow. Fluid Dynamics [physics.flu-dyn]. Ecole Polytechnique X, 2011. English. ⟨pastel-00672072⟩



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