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What is a plume?

Don L. Anderson

Seismological Laboratory, California Institute of Technology, Pasadena, CA 91125

dla@gps.caltech.edu

The term plume in the Earth sciences is not always consistently used or precisely defined. What a geophysicist means by a plume is not always understood to be the case by a geochemist or a geologist. Nevertheless, the term has been precisely defined in classical fluid dynamics, and it is probably best to provide at least that one description of a plume in the framework of geophysics as an entrée to the many contributions that treat them on this website.

Melting anomalies can result from concentrated hot regions of the shallow mantle – hotspots – or from upwelling jets – plumes. They can also result from fertile patches or regions of shallow mantle with low melting point. Focusing, edge effects (see also EDGE convection page), ponding and interactions of surface features with a partially molten asthenosphere can also create melting anomalies at the surface. Adiabatic decompression melting can be caused by passive upwellings, changes in thickness of the lithosphere, or by recycling of basaltic material with a low melting temperature. The usual explanation for melting anomalies is that they result from active hot upwellings from a deep thermal boundary layer. In the laboratory, upwellings thought to be analogous to these are often created by the injection of hot fluids, not by the free circulation of a fluid (click for more on this).

Upwelling and downwelling features in a fluid that are maintained by thermal buoyancy are called plumes. This standard fluid dynamical definition of a plume does not exclude types of circulation that might occur in the Earth’s mantle, or other types of convection and upwelling. However, the mantle is not the ideal homogeneous fluid heated entirely from below – or cooled from above – that is usually envisaged in textbooks on fluid dynamics. Normal convection in a fluid with the properties of the mantle occurs on a very large scale, comparable to the lateral scales of plates and the thicknesses of mantle layers. In geophysics, plumes are a special form of small-scale convection originating in a thin, lower, thermal boundary layer (TBL) heated from below; in this sense not all upwellings, even those driven by their own buoyancy, are plumes (click for more on this). Narrow downwellings in the Earth are called slabs. The dimension of a plume is controlled by the thickness of the lower boundary layer or the diameter of the hypodermic needle used in the injection experiment. There is likely to be a thermal boundary layer at the core-mantle boundary (CMB), and there is one at the Earth's surface. There is no reason to believe that these are the only ones, however. In the Earth, boundary layers tend to collect the buoyant products of mantle differentiation at the surface one (continents, crust, harzburgite) and the dense dregs at the lower one. Because of these complications, and the scales of TBLs, it is difficult for seismic techniques alone to detect the high temperature gradient that is the signature of a thermal boundary layer. Nevertheless, Earth scientists are confident that substantial TBLs exist at the surface and at the CMB. Upwelling plumes should spread out and pond beneath internal boundary layers. Large scale low-velocity zones at 650 km or 1000 km, for example, would be good evidence both for the existence of boundary layers at these depths and of upwelling plumes.

Convecting systems that are chemically stratified or involve endothermic phase changes (e.g. with negative Clapeyron slopes) develop internal thermal boundary layers. Because of their small density contrasts, chemical interfaces are predicted to have large relief. This, plus the low sensitivity of seismic velocity to temperature at high pressure, further complicates the seismic detection of deep TBL. On the other hand, the presence of deep TBLs does not require that they form narrow upwelling instabilities that rise to the Earth’s surface. A TBL is a necessary condition for the formation of a plume – as it is understood in the geophysics and geochemistry literature – but is not a sufficient condition. Likewise, the formation of a melting anomaly at the surface, or a buoyant upwelling, does not require a deep TBL.

Internal and lower thermal boundary layers in the mantle need not have the same dimensions and time constants as the upper one. Plate tectonics and mantle convection can be maintained by cooling of plates, sinking of slabs and secular cooling, without any need for a lower thermal boundary layer, – particularly one with the same time constants as the upper one. Buoyant decompression upwellings can also be generated without a lower thermal boundary layer. Because of internal heating and the effects of pressure, the upper and lower thermal boundary layers are neither symmetric nor equivalent.

Upwellings in the mantle can be triggered by spreading, by dehydration and melting of slabs, by phase changes and by displacement by sinking materials. Cooling of the surface boundary layer creates dense slabs. These are all plumes in the strict fluid dynamic sense but in geophysics the term is restricted to narrow hot upwellings rooted in a deep thermal boundary layer, and having a much smaller scale than normal mantle convection and the lateral dimensions of plates. Sometimes geophysical plumes are considered to be “the way the core gets rid of its heat”.

If the mantle is homogeneous and convects as a unit, from top to bottom, it will have a Rayleigh number of > 107. Convection withhigh Rayleigh number (> 107) is time-dependent, and should contain length scales that vary between the thickness of the boundary layer to many times the depth of the layer. If pressure did not increase with depth, a physically impossible circumstance, we would expect to see convective features throughout the mantle with scales from 50 to 10,000 km. There is good evidence that the mantle is not homogeneous; some slabs become horizontal at depths near ~ 650 km and there is a drastic change in the characteristics of mantle structure at this depth.

If the mantle is chemically stratified and the effects of pressure on physical properties are taken into account, the effective Rayleigh number of the mantle may be orders of magnitude less than 107. Deep boundary layers must be much thicker and more sluggish than the surface boundary layer. Lower mantle thermal features – because of pressure effects – must be orders of magnitude larger than the thicknesses of slabs and surface plates, and orders of magnitude older.

The view that the mantle has high Rayleigh number (click for more on this) and relatively symmetric upper and lower boundary layers is the conventional wisdom of most geophysicists who have worked on mantle convection. High Rayleigh numbers imply time-dependent and intermittent convection, small-scale features, and rapid mixing. A fully self-consistent thermal-dynamic treatment (non-Boussinesq, and including deformable boundaries, non-uniform internal heating and secular cooling) has yet to be done and much of the fluid dynamic intuition regarding plumes is based on unrealistic laboratory experiments (low Prandtl number) involving either heating from below or the injection of hot fluids. A homogeneous mantle with constant melting point, well below the solidus, is the usual starting point in mantle convection simulations. A plume, in the geophysical sense, requires heating from below. Upwellings in internally heated fluids, or secularly cooled fluids, are broad and non-stationary. Other kinds of upwellings such as at ridges, and island arcs, or which result from heating and melting of slabs or the displacement by sinking slabs, are alternatives to thermal plumes of the type discussed by Morgan in 1971. Regions of excess magmatism or low seismic velocity can be confidently attributed to plumes only if they can be shown to originate in a lower thermal boundary layer. Cracks and dikes the upper boundary layer can also generate melting anomalies. Low velocity zones can be due to composition or the presence of small amounts of grain boundary fluids; they do not have to result from deeper upwellings.

More on laboratory plumes:

Strictly speaking, geophysical plume theory is motivated by experiments that inject narrow streams of hot fluid into a stationary tank of low viscosity fluid. These are not the same as the natural instabilities that form at the base of a fluid heated from below. Computer simulations often mimic the laboratory experiments by inserting a hot sphere at the base of the fluid and watching it evolve with time during the period that it rises to the surface. These are not cyclical or steady-state convection experiments.

More on the Boussinesq approximation:

The Boussinesq approximation is widely used in fluid dynamics. It simply means that all physical properties are assumed to be independent of depth and pressure and, except for density, independent of temperature. This is not a good approximation for the deep mantle. High Prandtl number essentially means high viscosity, a characteristic of the mantle but not of laboratory fluids.

For more information or for definitions search Google, for example for “Prandtl mantleplumes"   or "melting anomaly mantleplumes”.
last updated 27th September, 2004
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