A one dimensional convection model application to an internally heated two-phase mantle
R. P. Lowell, Gunnar Bödvarsson · 1973
We simplify the well known Rayleigh convection model by neglecting horizontal heat conduction, using an average flow velocity, and assuming the cell size on physical grounds.For a homogeneous Newtonian fluid layer, the resultlng one dimensional 'strip-model' yields results similar to those obtained by the classical lineariiation method.Ry applying the strip model in the case of an internally heated fluid with two phases, we obtain a new critical Rayleigh number which ls a function of the transition parameters, the physical properties of the fluid, and the depth °f the fluid layer.We treat both normal and abnormal transitions, that is transitions with either a positive or negative slope Clapeyron curves respectively.For the olivine-spinel and spinel-oxides transitions which are thought to occur in the upper mantle, the new critical number deviates little from the critical number for a homogeneous fluid.Hence the known phase transitions appear to be of minor importance with regard to the existence of mantle convection.The one dimensional model can also be applied in the study of convection phenomena tnvolving other complex geophysical systems.