Dynamic mixing in magma bodies: Theory, simulations, and implications
Authors: Oldenburg Curtis M. , Spera Frank J. , Yuen David A. , Sewell Granville 
Published: February 2008

Considerable geochemical and petrographic evidence suggests that magma mixing phenomena are important in producing the chemical heterogeneity commonly observed in plutonic and volcanic rocks on a variety of scales in both space and time. Simulations of time‐dependent, variable viscosity, double‐diffusive convection have been carried out to quantitatively investigate the mixing dynamics of magma in melt‐dominated magma bodies. Two distinct measures of the “goodness of mixing” are used to quantify magma mixing: (1) the linear scale of segregation (L) which corresponds to the length scale of a typical compositional anomaly; and, (2) the intensity of segregation (I) which is a measure of the deviation of compositional anomalies from the mean. Nondimensionalization of the governing conservation equations shows that the style and time scale of mixing depend on the flux Rayleigh number (Rq = αgqd4/kκνm), the buoyancy ratio (Rr = βΔCk/αqd), the Lewis number (Le = κ/D), the silicic to mafic melt viscosity ratio (νr = νS/νm), and the aspect ratio (A = w/d) of the chamber. Simulations of magma mixing were carried out by solving the conservation equations for parameter ranges 105 < Rq < 3 × 105, 0 < Rr < 1.1, 100 < Le < 600, 1 < νr < 20, 0.3 < A < 3 by a Galerkin finite element method over a two‐dimensional domain with various geologically relevant boundary conditions. The mixing time (tmix) is defined as the time required for the intensity of segregation to decay to a certain value. Magma mixing occurs by complex time‐dependent flows with numerous flow reversals associated with local unmixing events superimposed on a larger time scale process in which the intensity of segregation decays to zero. For parameters within the ranges investigated, tmix is roughly proportional to νr1/2Le1/2Rr2Rq−1 for the heating from below scenario. For values of νr, Le, Rr, and Rq appropriate to natural systems, this relationship gives a range of mixing times from about one tenth to 10 times d2/κ, implying that both well‐mixed and heterogeneous magmas will be commonly observed in nature. Mixing times are at a minimum for equant bodies, while for silllike bodies, mixing is inhibited by the formation of multiple cells of different composition in the horizontal. Assimilation and fractional crystallization geochemical models that assume “well‐mixed” magma bodies may be grossly misleading. A viscous (i.e., crystal laden), large (d∼5 km) magma body heated weakly from below and initially strongly chemically stratified will remain unmixed for several Ma. A large‐volume, thermally well‐connected basaltic body will mix rapidly (103–104 years). Because flow reversals may occur in dynamic mixing (Rr>0), crystal distributions within convecting magma bodies will be different from those predicted assuming steady state velocity fields. Flow reversals cause significant temporal variation in the heat supplied to the roof of the chamber; these may be important in explaining episodic phases of hydrothermal alteration. In sill‐like magma bodies (A>2), multiple cells of distinct composition may persist for geologically significant time periods. Finally, our simulations show that the dynamics of double‐diffusive convection can impart complex patterns of composition through time and space in magma bodies.