Instability threshold of a model for deep convection with depth-dependent viscosity. (May 2017)

• Record Type: Journal Article
• Authors: Rionero, Salvatore
• Is Part Of: International journal of non-linear mechanics. Volume 91(2017)
• Page Start: 163
• Page End: 169
• Publication Date: 2017-05
• Subjects: Deep convection -- Depth-dependent viscosity -- Instability threshold; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2017.03.003
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: The effect of depth-dependent viscosity on the onset of convection in deep horizontal layers heated from below is investigated. In the Zeytounian deep convection model (1989), the depth-dependent viscosity is introduced. The instability threshold of the thermal conduction rest state, is evaluated (in the free-free case). It is obtained that: (1) the strong principle of exchange of stability holds ; (2) the instability threshold depends – via a simple closed form (1.1) – on the viscosity law; (3) a fall in the instability threshold is driven by the depth-dependent viscosity. The action of (quadratic) polynomial and exponential depth-dependent viscosity on the instability threshold is evaluated. Although needs to be verified by experiments, the results obtained appear to be of interest not only for theoreticians but also for experimentalists. Abstract : Highlights: A " deep-convection model with depth-dependent viscosity " is introduced. The instability threshold, in a simple closed form, is provided. The results appear to be of interest not only for theoreticians but alsofor experimentalists.