On Convective Style and Vigor in Sheet-like Magma Chambers |
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| Authors: | MARSH BRUCE D |
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| Institution: | Department of Earth and Planetary Sciences, The Johns Hopkins University Baltimore Maryland 21218 |
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| Abstract: | The well known absence of magrnatic superheat is held here tobe a direct reflection of the ease and efficiency of large Rayleighnumber (Ra) convection in evacuating all convectable heat fromthe magma. Magmatic temperature is thus continually bufferedat or below the convective liquidus where the temperature differencedriving convection is vanishingly small and the governing Rais also always small regardless of body size. It is furtherheld here that for bodies where side wall cooling is of lesserimportance, the more common perception of magma chambers isof cooling from above and below where both the initial, isothermal(i.e. isodensity), and final (solid) states are dynamicallystable and that convection is necessarily a transient processconnecting these states. Extensive theoretical and experimentalstudies of cooling from above show that regardless of boundaryconditions transient, small Ra convection is independent oflayer thickness. Instead, convection is driven by formationof a thin, cool, and dense sublayer along the top boundary,and the characteristic length scale of the governing Rayleighnumber, which is time-dependent, is the sublayer thickness (d<<L).All dynamic features of the flow, including heat transfer relyon this length scale and not body thickness; virtually any sheet-likemagmatic body appears infinitely thick to such convection. BecauseRa is small, this transient stage persists for most, if notall, of the period of solidification to mush, whence the bodyis dynamically dead. Under conditions of strongly variable viscosity, only the leadingpart of d (i.e. d'), forward of a critical rheological front,is unstable. Convection itself is restricted to a region whereviscosity changes by no more than a factor of about 3 to 10.Most of the cool, dense sublayer is rigid, immobile crust, unableto participate in convection and cool the body. Rapid advanceof this crust due to cooling inhibits convection by consuminginstabilities before maturation to finite amplitude. Inclusionof solidification in the stability analysis changes the lengthscale in the governing Rayleigh number (Rav) to K/V (thermaldiffusivity/advance velocity). Ra is subcritical for large V0(early times) and only with time becomes supcrcritical. Thisis in striking contrast to the usual RaL, which is initiallythe largest it will ever be. Because of continual collapse ofthe unstable sublayer, convection may remain near the criticalRav. Convection is thus initially weak and, because the heatflux from the system monotonically decreases with time due tothe thickening conductive crust and cooling, it is preventedfrom becoming indefinitely strong and instead slowly diminisheswith time. Conduction through the advancing crust is balanced by latentheat of crystallization at the crystallization front and convectionoccurs in response to this cooling. Because convection is confinedto the nearly isoviscous, nonsuperheated magma, crust growthis unaffected by convection, even when it is artificially forcedat unnatural rates. The crusts of Hawaiian lava lakes reflectthis in growing at the same rate regardless of lake thicknessand, in numerical convective modeling, imposed Rayleigh number.Overall cooling is well approximated by that of a stagnant,purely conducting layer whose central temperature is constantuntil arrival of the slowly moving cooling front In fact, therate of change of a body's central temperature is a direct measureof the total rate of heat transfer (i.e. Nusselt number, Nu)from that region. This is shown to be very nearly zero for Hawaiianlava lakes, precluding all but the weakest of convective heattransfer within the magma itself. The maximum heat transfer in terms of Nusselt number of anyunheated body within a conductive medium and always kept perfectlywell mixed thermally, relative to the same stagnant body, isshown to be Nu=2 regardless of shape and size. This thermalevolution is closely followed by previous calculations thatassume a large Rayleigh number based on layer thickness. Thermal convection in unheated, sheetlike magma chambers isa transient, sluggish process governed by solidification andsmall scale, small Rayleigh number instabilities; thermallydriven convective turbulence, in the usual sense, is out ofthe question. |
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