A boundary-layer analysis of Benard convection in a fluid of strongly temperature-dependent viscosity

Morris, Stephen; Canright, David

doi:10.1016/0031-9201(84)90057-8

Cited by 131 publications

(91 citation statements)

References 13 publications

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“…This regime was reached in several previous studies of variable viscosity convection [e.g., Christensen, 1984;Hansen and Yuen, 1993]. At asymptotically large viscosity contrasts, the slow motion of a very viscous surface does not affect heat transport and convection occurs beneath a stagnant lid (stagnant lid regime) which was predicted theoretically by Morris and Canright [1984] and Fowler [1985]. This regime was observed in numerical experiments by Ogawa e!…”

mentioning

confidence: 55%

Three regimes of mantle convection with non‐Newtonian viscosity and stagnant lid convection on the terrestrial planets

Solomatov

Moresi

1997

Geophysical Research Letters

140

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mentioning

confidence: 55%

Three regimes of mantle convection with non‐Newtonian viscosity and stagnant lid convection on the terrestrial planets

Solomatov

Moresi

1997

Geophysical Research Letters

140

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“…The nondimensional temperature difference across the lower TBL depends on parameter ¾, as previously suggested by Morris and Canright [ 1984] 0 0c) CI -=--+c 2 , The strain rates • relevant to subsolidus convection within icy satellites are very low: • <10 'lls 'l. The creep mechanism driving plastic deformation at such strain rates is not very well known and will be discussed below (section 2.2).…”

Section: Otog•t•tblmentioning

confidence: 87%

Thermal convection in the outer shell of large icy satellites

Deschamps¹,

Sotin²

2001

J. Geophys. Res.

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Abstract. Evolution of large icy satellites is controlled by heat transfer across the outer ice I layer. After the core overturn a possible structure consists of a silicate core and a shell of molten ices. As the satellite cools down, the primordial ocean crystallizes. If the outer layer is thick enough, convection is very likely to occur in it. We have used the results of a recent twodimensional numerical model of convection including variable viscosity to estimate the vigor and the efficiency of convection in this layer. Viscosity variations induce the apparition of a stagnant lid at the top of the fluid, which reduces the efficiency of heat transfer. In the present study, the Rayleigh number Ra and the heat flux cp are computed as a function of the thickness of the layer, assuming that the ice flow is Newtonian. Calculations are first made for a generic satellite of radius R = 2500 km and mean density

= 1.9 g/cm 3. It is then shown that variations of _+500 km on the radius and _+0.5 g/cm 3 on the mean density do not induce significant differences in the

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“…However, owing to our used homogeneous experimental fluid, chemical aspects are not regarded here. During the past decades, various studies have addressed the topic of temperaturedependent viscosity mostly for Cartesian geometries (Booker 1976;Nataf & Richter 1982;Stengel, Oliver & Booker 1982;Richter, Nataf & Daly 1983;Morris & Canright 1984;Busse & Frick 1985;White 1988;Christensen & Harder 1991;Ogawa, Schubert & Zebib 1991;Hansen & Yuen 1993;Davaille & Jaupart 1994;Solomatov 1995;Tackley 1996;Kameyama & Ogawa 2000). While numerical simulations and laboratory experiments consider the Rayleigh-Bénard system in a rectangular box, naturally, the spherical shell convection is treated by means of numerical simulations only for constant viscosity (Baumgardner 1985;Bercovici, Schubert & Glatzmaier 1989a;Bercovici et al 1989b;Bercovici, Schubert & Glatzmaier 1991, 1992Schubert, Glatzmaier & Travis 1993) and for varying viscosity (Ratcliff, Schubert & Zebib 1996;Kellogg & King 1997;Ratcliff et al 1997;Zhong et al 2000 …”

Section: Thermally Driven Flow In Liquids Of Temperature-dependent VImentioning

confidence: 99%

Sheet-like and plume-like thermal flow in a spherical convection experiment performed under microgravity

et al. 2013

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We introduce, in spherical geometry, experiments on electro-hydrodynamic driven Rayleigh-Bénard convection that have been performed for both temperatureindependent ('GeoFlow I') and temperature-dependent fluid viscosity properties ('GeoFlow II') with a measured viscosity contrast up to 1.5. To set up a selfgravitating force field, we use a high-voltage potential between the inner and outer boundaries and a dielectric insulating liquid; the experiments were performed under microgravity conditions on the International Space Station. We further run numerical simulations in three-dimensional spherical geometry to reproduce the results obtained in the 'GeoFlow' experiments. We use Wollaston prism shearing interferometry for flow visualization -an optical method producing fringe pattern images. The flow patterns differ between our two experiments. In 'GeoFlow I', we see a sheet-like thermal flow. In this case convection patterns have been successfully reproduced by three-dimensional numerical simulations using two different and independently developed codes. In contrast, in 'GeoFlow II', we obtain plume-like structures. Interestingly, numerical simulations do not yield this type of solution for the low viscosity contrast realized in the experiment. However, using a viscosity contrast of two orders of magnitude or higher, we can reproduce the patterns obtained in the 'GeoFlow II' experiment, from which we conclude that nonlinear effects shift the effective viscosity ratio.

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A boundary-layer analysis of Benard convection in a fluid of strongly temperature-dependent viscosity

Cited by 131 publications

References 13 publications

Three regimes of mantle convection with non‐Newtonian viscosity and stagnant lid convection on the terrestrial planets

Three regimes of mantle convection with non‐Newtonian viscosity and stagnant lid convection on the terrestrial planets

Thermal convection in the outer shell of large icy satellites

Sheet-like and plume-like thermal flow in a spherical convection experiment performed under microgravity

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