Charles R. Carrigan

Biot number and thermos bottle effect: Implications for magma-chamber convection

Thermal boundary conditions model the coupling between a convecting magmatic body and its host. Such conditions need to be considered in models of igneous systems that involve thermal histories, crystallization and fractionation of melt, formation of aureoles by contact metamorphism, and any other processes in which transport of heat plays a role. Usually, investigations of magmatic systems have tended to emphasize modeling the interior convective regime relative to treatment of the thermal coupling. Yet it is found that the thermal nature of an intrusion is likely to be influenced more by coupling to its host than by the details of internal convective flows. Evaluation of a parameter having the form of a Biot number ( Bi ) provides a basis for estimating which boundary conditions are most appropriate. It is found that Bi ≤0.1 (constant heat-flux limit) for models of several caldera systems. For such values of the Biot number, the host regime behaves somewhat like a thermos bottle by limiting the flow of heat through the magma-host system so that convective stirring of magma has little effect on the cooling rate of the intrusion. Because of this insulating effect, boundary temperatures assumed in convection models should approach magmatic values even if an active hydrothermal system is present. However, high boundary temperatures do not imply that melting and assimilation of host rock by magma must occur. Despite the thermos bottle effect, magmatic convection can still be quite vigorous.

A two-phase hydrothermal cooling model for shallow intrusions

Abstract An approximate model for shallow, magma—groundwater interaction is developed. The model assumes a compressible, two-phase hydrothermal zone separated from hot mobile magma by a zone of cooler magma having a more plastic rheology and vanishing permeability (Fig. 1). With the model it is shown that the compressibility of vapor causes increases in the cooling rates of shallow intrusions with increasing depth of intrusion. Furthermore, hydrothermal infiltration, i.e., motion of the liquid/vapor groundwater zones toward the magma, is shown to occur if the rate at which heat is removed by the hydrothermal zone exceeds the rate of heat transfer by conduction across the impermeable plastic zone. Maximum infiltration rates of several meters per year are predicted by a one-dimensional infiltration model. Other calculations show that the environment exterior to convecting magma, which includes the hydrothermal regime, is typically far more resistive to heat flow than the convecting magma itself. As a result, the environment, not magma convection, determines the cooling rate of typical intrusions as well as the temperature gradients within those intrusions.

Convection in an internally heated high Prandtl number fluid: a laboratory study

Abstract The stability regimes for convection in an internally heated, high Prandtl number, glycerin-based solution have been investigated for the first time by inducing particular planforms under controlled conditions. Down hexagons were found to be stable to about 40 Rac having wavenumbers which are in reasonable agreement with both linear and finite amplitude calculations. Beyond this value of the Rayleigh number, the cells were observed to undergo a transition from flow down to flow up at the center. Most of these new cells are not completely closed and bear some similarity to distorted rolls. They were also found to be time dependent and their horizontal scale did not differ substantially from that associated with the hexagonal planform at lower Rayleigh numbers. However, at about 125 Rac , the onset of two-scale flow was observed—a phenomenon which may be associated with the finite thermal conductivity of the upper boundary.

A heat pipe model for vertical, magma-filled conduits☆

Abstract A 5-m radius magma-filled conduit will solidify in much less than one year if heat losses to the conduit wall are not offset by some form of forced or free convection of magma from some source body through the conduit. If the forced convection of magma from a source through the conduit is either too weak or is prevented by closure of the conduit at the end nearest the surface, only free convective circulations between the source chamber and conduit are available to balance the wall heat loss. Using an integral approach, the efficiency of free convection is investigated for conduits emplaced in both conductive and hydrothermally convective host rock environments. The results of the model strongly suggest that free circulations within conduits of large aspect ratio provide an efficient mechanism for offsetting heat losses to the conduit wall. The model provides a possible explanation for the occurrence of periodic eruptions from a conduit when the periodicity greatly exceeds the time scale for the cooling of a quiescent conduit by heat loss through the wall.

Multiple-Scale Convection in the Earth's Mantle: A Three-Dimensional Study

Laboratory experiments suggest that a convective regime characterized by two length scales of motion is a reasonable model for circulations in the earths upper mantle. The flows of largest horizontal scale represent a likely plate-driving mechanism, required by some theories of plate tectonics. It is also suggested that the small-scale circulations could influence the chemical evolution of the mantle by extracting primitive mantle material that is otherwise entrained in the large-scale flow.

Heat Transfer in Magma in situ

Heat transfer rates in a basaltic magma were measured under typical magma chamber conditions and a numerical model of the experiment was used to estimate magma viscosity. The results are of value for assessing methods of thermal energy extraction from magma bodies in the upper crust as well as for modeling the evolutionary track of these systems.

The Viscoscity of Synthetic and Natural Silicate Melts and Glasses at High Temperatures and 1 Bar (105 Pascals) Pressure and at Higher Pressures, U.S. Geol. Surv. Bull. 1764

Over the past decade, I have routinely collected papers dealing with the physical properties of rocks and other materials. Their dog-eared and coffee-stained appearance is just one indication of their continuing value to me. Focusing on viscosity of silicate melts, Michael Ryan and James Blevins have considerably extended and formalized this collection process, resulting in the publication of a massive report containing viscosity data on an extensive variety of melt compositions. According to the authors, this report represents an initial step in establishing a comprehensive U.S. Geological Survey (USGS) data base for the properties of multicomponent silicate melts.