Creeping axisymmetric plumes with strongly temperature-dependent viscosity

The structure of a steady axisymmetric thermal plume rising through a very viscous fluid with strongly temperature-dependent viscosity of the form $\mu \propto \exp (-\gamma T)$ is investigated. An analytic asymptotic solution is derived for the fast-flowing core of the plume, which predicts that the excess centreline temperature decays exponentially as $\exp \{ - 12 \pi \kappa z/(\gamma A) \}$, where $\kappa $ is the thermal diffusivity, $z$ the height and $A$ the vertical heat flux. This rate of decay, which is found to be in good agreement with numerical simulations of the boundary-layer equations, is three times faster than that predicted by the oft-quoted model of Olson, Schubert and Anderson (J. Geophys. Res., vol. 98 (B4), 1993, pp. 6829–6844).