Absolute instability of plane incompressible jets. (10th May 2023)

• Record Type: Journal Article
• Authors: Vedeneev, Vasily; Nikitin, Nikolay
• Is Part Of: Journal of fluid mechanics. Volume 962(2023)
• Publication Date: 2023-05-10
• Subjects: absolute/convective instability -- shear-flow instability; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2023.163
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : In this paper, the possibility of absolute instability in a plane unidirectional jet is analysed. We consider a parametrized family of velocity profiles with variable inflection point location and shear layer thickness. Using the inviscid saddle-point analysis, we show that absolute instability can occur in the case of a sufficiently low velocity at the inflection point or a sufficiently thin shear layer. Then we proceed to the viscous analysis and find the critical Reynolds numbers separating the zones of convective and absolute instability. We obtained a minimum value $Re = 315$ . As an independent verification of the theoretical results, we conduct a direct numerical simulation of the evolution of a localized pulse perturbation in the framework of the linearized Navier–Stokes equations. The calculated absolute/convective instability boundary is in a good agreement with theoretical results of the saddle-point analysis.