The interaction of a plume with a rheological boundary: A comparison between two‐ and three‐dimensional models

Abstract

The discrete nature of volcanic hot spot chains, whose origin is believed to be related to mantle plumes, is suggestive that the plumes feeding them may be pulsating. A possible origin of the pulsations is the interaction of mantle plumes with a rheological interface in the transition zone. We have studied the time‐dependent, three‐dimensional interaction of an upwelling mantle plume with a rheological interface that separates a Newtonian lower mantle from a Newtonian upper mantle with a lower viscosity. Previous two‐dimensional (2‐D) work demonstrates that when a hot plume enters a non‐Newtonian layer with lower viscosity, the hot material is carried from the interface in pulsating, diapiric events. A purely Newtonian analog to this model mimics this behavior in a qualitative manner if the viscosity contrast across the interface is larger than 2 orders of magnitude. In this work, we have used this Newtonian model to make three‐dimensional (3‐D) modeling feasible. A combined spectral/finite difference code has been employed to solve the 2‐D and 3‐D convection equations in Cartesian coordinates. We have varied the Rayleigh number (scaled to the constant viscosity of the lower mantle) between 104 and 105 and the viscosity contrast of the layers between 10 and 1000. In 2‐D situations with low viscosity contrasts, a plume thins in a steady state fashion as it enters the upper layer. At moderate and higher viscosity contrasts (above 50), the plume shows a pulsating behavior. This transition from “thinning” to “pulsating” is found to be strongly dependent on viscosity contrast and only moderately dependent on Rayleigh number. The frequency of the pulsations is linearly dependent on Rayleigh number and viscosity contrast. In three dimensions, the plume thins less and is therefore less susceptible to disruption by shear and the plume moves through the upper layer in a steady state fashion. This disappearance of pulsating behavior in three dimensions indicates a case where conclusions about plume dynamics in two dimensions do not apply to 3‐D situations.