Plume formation in strongly temperature-dependent viscosity fluids over a very hot surface

Abstract

Plume formation in a strongly temperature-dependent viscosity fluid placed on a very hot surface involves an intermediate step-small-scale convection in the thermal boundary layer. We perform numerical simulations and suggest a simple analysis of this process using the stagnant lid convection theory and Canright and Morris' theory of Rayleigh-Taylor instability of two layers with different viscosities. We show that plume formation can approximately be predicted from the requirement that the growth of the large-scale instability becomes faster than the growth of the convecting thermal boundary layer.

Theoretical and numerical study of a thermal convection problem with temperature-dependent viscosity in an infinite layer

“…[10]. The mentioned bibliography shows interest in different phenomena related to the mantle, such as magma [14], plate formation [23], and plumes formation [20,6]. Ref.…”

“…Several types of dependencies have been taken into account: polynomial dependence is considered in Ref. [9] but the most common is an exponential dependence as the dependence that best explains the behaviour of mantle convection [24,20,6,7,11]. There are some experiments adapting scales to small cells [19,25,21].…”

“…The Rayleigh-Bénard convection is the most simple approach to mantle convection. Most studies on the Rayleigh-Bénard problem consider a constant viscosity [15][16][17][18], but temperature-dependent viscosity has aroused interest as a better approach to mantle convection [19,20,7,[21][22][23]. Several types of dependencies have been taken into account: polynomial dependence is considered in Ref.…”

Thermal radiation effect on unsteady MHD free convection flow past a vertical plate with temperature‐dependent viscosity

“…To accurately predict the flow behaviour, it is necessary to take into account this variation of viscosity with temperature. The effects of temperature-dependent viscosity on the boundary layer flow and heat transfer is investigated by many authors such as Jang and Lin (1988), Pop et al (1992), Massoudi and Christie (1995), Kafoussias and Williams, (1995), Hady et al (1996), , , Abel et al (2002), Massoudi and Phuoc (2004), Begai (2004), Ke and Solomatov (2004), Ali (2006), Jayanthi and Kumari (2006), Mahmoud (2007a,b,c), Hayat et al (2007a), Massoudi et al (2008), Hayat and Ali (2008), and Mukhopadhyay and Layek (2008). Gebhart (1962) has shown that the viscous dissipation effect plays an important role in natural convection in various devices processes on large scales (or large planets).…”

On predicting mantle mushroom plumes

“…Thermal plumes in deep mantle have been simulated by computational geodynamics (CGD) models with influence of various parameters, such as viscosity, composition and phase changes, which are based on abruptly increased surface temperatures of 200e2000 C (Olson et al, 1987;Ji and Nataf, 1998;Kiefer and Kellogg, 1998;Montague et al, 1998;Goes et al, 2004;Ke and Solomatov, 2004;Davies, 2005). CGD simulations showed the formation of unstable thermal boundary layer up to the evolution of plumes, plume detachment and dissipation of heat in the bulk fluid (see review by Schubert et al (2001) and Davies (2005)) identical to observations of Foster (1969) and Sparrow et al (1970).…”