ON CONVECTIVE STYLE AND VIGOR IN SHEET-LIKE MAGMA CHAMBERS

Abstract

The well known absence of magrnatic superheat is held here to be a direct reflection of the ease and efficiency of large Rayleigh number (Ra) convection in evacuating all convectable heat from the magma. Magmatic temperature is thus continually buffered at or below the convective liquidus where the temperature difference driving convection is vanishingly small and the governing Ra is also always small regardless of body size. It is further held here that for bodies where side wall cooling is of lesser importance, the more common perception of magma chambers is of cooling from above and below where both the initial, isothermal (i.e. isodensity), and final (solid) states are dynamically stable and that convection is necessarily a transient process connecting these states. Extensive theoretical and experimental studies of cooling from above show that regardless of boundary conditions transient, small Ra convection is independent of layer thickness. Instead, convection is driven by formation of a thin, cool, and dense sublayer along the top boundary, and the characteristic length scale of the governing Rayleigh number, which is time-dependent, is the sublayer thickness (d<<L). All dynamic features of the flow, including heat transfer rely on this length scale and not body thickness; virtually any sheet-like magmatic body appears infinitely thick to such convection. Because Ra is small, this transient stage persists for most, if not all, of the period of solidification to mush, whence the body is dynamically dead.Under conditions of strongly variable viscosity, only the leading part of d (i.e. d'), forward of a critical rheological front, is unstable. Convection itself is restricted to a region where viscosity changes by no more than a factor of about 3 to 10. Most of the cool, dense sublayer is rigid, immobile crust, unable to participate in convection and cool the body. Rapid advance of this crust due to cooling inhibits convection by consuming instabilities before maturation to finite amplitude. Inclusion of solidification in the stability analysis changes the length scale in the governing Rayleigh number (Ra v) to K/V (thermal diffusivity/advance velocity). Ra is subcritical for large V 0 (early times) and only with time becomes supcrcritical. This is in striking contrast to the usual Ra L, which is initially the largest it will ever be. Because of continual collapse of the unstable sublayer, convection may remain near the critical Ra v. Convection is thus initially weak and, because the heat flux from the system monotonically decreases with time due to the thickening conductive crust and cooling, it is prevented from becoming indefinitely strong and instead slowly diminishes with time.Conduction through the advancing crust is balanced by latent heat of crystallization at the crystallization front and convection occurs in response to this cooling. Because convection is confined to the nearly isoviscous, nonsuperheated magma, crust growth is unaffected by convection, even when it is artificially forced at unnatural rates. The crusts of Hawaiian lava lakes reflect this in growing at the same rate regardless of lake thickness and, in numerical convective modeling, imposed Rayleigh number. Overall cooling is well approximated by that of a stagnant, purely conducting layer whose central temperature is constant until arrival of the slowly moving cooling front In fact, the rate of change of a body's central temperature is a direct measure of the total rate of heat transfer (i.e. Nusselt number, Nu) from that region. This is shown to be very nearly zero for Hawaiian lava lakes, precluding all but the weakest of convective heat transfer within the magma itself.The maximum heat transfer in terms of Nusselt number of any unheated body within a conductive medium and always kept perfectly well mixed thermally, relative to the same stagnant body, is shown to be Nu=2 regardless of shape and size. This thermal evolution is closely followed by previous calculations that assume a large Rayleigh number based on layer thickness.Thermal convection in unheated, sheetlike magma chambers is a transient, sluggish process governed by solidification and small scale, small Rayleigh number instabilities; thermally driven convective turbulence, in the usual sense, is out of the question.