Transition to chaos and implications for time-scales of magma hybridization during mixing processes in magma chambers

In this contribution numerical simulations of magma mixing are carried out with the aim of understanding the physico-chemical conditions that trigger the development of chaotic mixing dynamics. In detail, the mixing process is simulated in a magma chamber where a less evolved magma underplates a more evolved magma. The ‘chaoticity’ of this system is quantitatively estimated via computed finite time Lyapunov exponents. It is shown that magma chamber dynamics are strongly controlled by the Rayleigh number (Ra), whereas other parameters, such as buoyancy ratio and viscosity ratio, play a subordinate role. Results indicate that magma chambers with Ra of the order of 106 are dominated by non-chaotic behaviour. Increasing Ra shifts the system towards an increasing chaotic state and, in particular, above Ra = 107 chaotic dynamics are fully developed in the magma chamber. Estimates of possible time-scales of hybridization of magmas during chaotic mixing suggest, for example, that a blob of mafic magma with an initial diameter of 100 m within a magma chamber with a width of 1000 m is stretched to a filament-like structure with a thickness of 15 m after 320 years and, after 1900 years its thickness is reduced to 4.0 mm. Using typical chemical diffusion coefficients for magmas (of the order of 10−14 m2/s) it can be calculated that a 4.0 mm-thick filament would homogenize by diffusion in ~ 10 years. Such homogenization time-scales are orders of magnitude lower that typical life-times estimated for magma chambers, even in the volcanic environment, indicating that fast hybridization of magmas can be rapidly achieved when chaotic dynamics govern the evolution of the magmatic system.