Prof. Dr. Ulrich Hansen
Corrensstraße 24 48149 Münster
Tel.: +49 251 83-33590
Fax: +49 251 83-36100


 Generation and Evolution of Plumes in

Mantle-relevant scenarios


U. Hansen & J. Schmalzl

Westfälische Wilhelms Universität Münster


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The Onset of Convection

Convection sets in at critical value of the Rayleighnumber RA. Atvalues, less tham the critical RAc, heat is transported by conduction, the flow velocity is zero. At Rac a bifurcation takes place, giving rise to two new states (clock- and counterclockwise rotatinf rolls). The old conductive solution further exits, is however unstable and can not be realized,



Basics of Convection

The structure of a convection cell is characterized by 2 regions: (a) the convective interior and (b) the thermal boundary layers (Fig.2). The interior is well mixed by the flow – within the boundary layers vertical heat transport takes place by conduction, such that steep temperature gradients exist. Stationary flows can be found (Fig.3), However typically convection at high Rayleighnumber is time dependent. View movie (Fig.4),  displaying convection heated from below in a 3D box. The material has constant properties at convection operates at an infinite Prandtl number, as beeing characteristic for mantle convection



 Convection at high Rayleigh -and infinite Prandtl number


Ra1e7 Vol-k 

Fig. 4

Convection in internally heated system.

The Earth‘s mantle is likely to be heated, at least partially, from within by  radioactive elements. The following animation (Fig.5) demonstrates the effect on the dynamics. The System is entirely heated by sources, which are distributed homogeneously throughout the fluid. Clearly , upwelling plumes have disappeared. This is a well-known effect in internally heated convection, i.e. Downward transport takes place via plume-like downwellings; upward transport takes place via diffuse upwellings.

The effect of internal heating- entirely heated from within


Click to view the following animations

Figs.6-8 show typical features of a starting plume. The plume has been started by applying an appropriate initial perturbation. Fig.6 displays a temperature iso-surface, in Fig.7 the evolution of a tracer cloud, initial put at the bottom is visualized. Vector-arrows show in Fig.8 the structure , as imposed by the plume at the bottom.

Formation of a Starting Plume


Fig. 6

The evolution of a tracer cloud


Fig. 7

Pattern-formation at the bottom


Fig. 8

The effect of temperature-dependent viscosity on plume dynamics

The viscosity of Earth’s mantle material and also magmas varies strongly with temperature (several orders of magnitude). The following animations demonstrate the effect. Fig.9 displays a scenario in which an initially cold system is heated from the bottom at a constant rate. Hot material is 104 times less viscous than cold material. Initially, the bottom boundary layer gets unstable, followed by an eruption of a hit blob. The blob establishes a channel of low viscosity, facilitating the rise of further blobs. Altogether  this leads to episodic plume behavior. Fig.10 displays the evolution of an initial stratification by such a plume

 Strongly temperature dependent viscosity - pulsed Plumes


Effect of Plumes on initial stratification


Fig. 10


The animations in Figs.11-13 show the plume dynamics in material with strongly temperature-dependent viscosity in full 3D geometry. Fig.11 and 12 display iso-surface of the temperature, Fig.13 displays the evolution of a carpet of tracer particles, initially distributed over the bottom of the domain. Clearly visible the pulse, traveling through the previously established channel.

The effect of temperature - dependent viscosity


Fig. 11

The episodic charakter of plumes


Fig. 12


Fig. 13

The Episodic character of Plumes

The  expected decrease of the thermal expansion coefficient and an increase of viscosity with pressure, both lead to a decrease of convective vigor with depth. Both effects lead to a concentration of the available buoyancy into a few strong upwellings. The resulting dynamics is displayed in Fig. 14 and 15. In Fig.15 initially a multiplume condition has been used in order to demonstrate the concentration of buoyancs into a few plumes. The mechanism is explained in Fig.16. Existing, strong plumes create a drag motin within the lower boundary layer, thus preventing the nucleation of other plumes.


From Plume to Superplume

The effect of thermal expansivity, decreasing with depth and motion of plumes at lower boundary layer


Fig. 14

The effect of pressure on expansivity and viscosity:


Fig. 15




Formation of a Superplume


In Fig.17 the formation of a Superplume is demonstrated, for a viscosity increasing with pressure. Initially a structure with many up-and downwellings evolves, finally giving rise to a flow pattern which is dominated by one strong plume. The evoluiton is visualized by volume rendering. Fig. 18 shows a detailed picture of the resulting superplume. If an additional temperature- dependent viscosity is accounted for, the plumes typically change to a plume-cluster structure (Fig.19)


  Fig. 17

Pressure-dependent viscosity in 3D-convection


Fig. 18


Plume-cluster at temperature- and pressure dependent viscosity



Fig. 19


Plumes are critical phenomena evolving from thermal boundary layers of high
Prandtl number fluids
Internal heating acts to weaken concentrated upflows. i.e. it destroys plumes
In fluids with strongly temperature-dependent viscosity plumes exhibit pulse-like
A decrease of convective vigor with depth (increasing viscosity and/or decreasing
Coefficient of thermal expansion leads to an accumulation of buoyancy and to the
formation of  Strong (Super) Plumes. Such Plumes show a strong thermal signal in the
lower mantle while they have relatively low temperatures in the upper mantle.
The Combination of temperature- and pressure dependent viscosity leads to the

Formation of Plume-clusters.

 see "Hotspots Unplugged", Scientific American, January, 2008 for a general discussion of hotspot motion (http://www.sciam.com)


Impressum | © 2008 Institut für Geophysik
Prof. Dr. Ulrich Hansen
Corrensstraße 24
· 48149 Münster
Tel.: +49 251 83-33590 · Fax: +49 251 83-36100