Adjoint Equations in Stability Analysis

• Paolo Luchini ^[1] ; Alessandro Bottaro ^[2]
  1. [1] University of Salerno

     University of Salerno

     Fisciano, Italia

     
  2. [2] University of Genova
• Localización: Annual review of fluid mechanics, ISSN 0066-4189, Nº. 46, 2014, págs. 493-517
• Idioma: inglés
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• Resumen

  • The objective of this article is to review some developments in the use of adjoint equations in hydrodynamic stability theory. Adjoint-based sensitivity analysis finds both analytical and numerical applications much beyond those originally imagined. It can be used to identify optimal perturbations, pinpoint the most receptive path to break down, select the most destabilizing base-flow defect in a nominally stable configuration, and map the structural sensitivity of an oscillator. We focus on two flow cases more closely: the noise-amplifying instability of a boundary layer and the global mode occurring in the wake of a cylinder. For both cases, the clever interpretation and use of direct and adjoint modes provide key insight into the process of the transition to turbulence.