A lava lake is modelled as a layer of molten basalt deep with a top-to-bottom…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Convection, rotation and geophysical flows

Fluid Dynamics, Ch Thermal convection and the Rayleigh-Benard problem

Problem

A lava lake is modelled as a layer of molten basalt

5.0\,\mathrm{m}

deep with a top-to-bottom temperature difference of

20\,\mathrm{K}

. Take

\alpha_T = 3.0\times10^{-5}\,\mathrm{K^{-1}}

, dynamic viscosity

\mu = 100\,\mathrm{Pa\,s}

, density

\rho = 2700\,\mathrm{kg\,m^{-3}}

, thermal diffusivity

\kappa = 1.0\times10^{-6}\,\mathrm{m^2\,s^{-1}}

and

g = 9.8\,\mathrm{m\,s^{-2}}

. ((a)) Find the kinematic viscosity of the melt. ((b)) Find the Rayleigh number of the lake. ((c)) Find the Prandtl number, and say what regime (in the sense of the mantle example) this places the lake in.

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