The gravitational stability of lenses in magma mushes: confined Rayleigh-Taylor instabilities

In the current paradigm, magma primarily exists in the crust as a crystalline mush containing distributed melt lenses. If a melt-rich (or fluid) lens is less dense than the overlying mush, then Rayleigh-Taylor (RT) instabilities will develop and could evolve into spheroids of ascending melt. Due to contrasting melt-mush rheologies, the theoretical RT instability wavelength can be orders of magnitude larger than the magmatic system. We explored how this confinement affects the gravitational stability of melt lenses through laboratory experiments with pairs of liquids with one layer much thinner and up to 2.2·10⁵ times less viscous than the other; we extended the viscosity ratio to 10⁶ with linear stability analysis. We found the growth rate of a bounded RT instability is approximately (Formula presented.), where Δρ is the difference in density between the fluids, g is gravity, D is the container diameter, and μ₂ is the viscosity of the thicker viscous layer. This differs from the unbounded case, where the growth rate also depends on the thickness and viscosity of the thin, low-viscosity layer. Applying the results to melt lenses in magmatic mushes, we find that for the ranges of expected rheologies, the timescales for development of the instability, and the volumes of packets of rising melt generated span very wide ranges. They are comparable with the frequencies and sizes of volcanic eruptions and episodes of unrest and so suggest that RT instabilities in mush systems can cause episodic volcanism.