Magma ascent mechanisms in the transition regime from solitary porosity waves to diapirism

Abstract

Abstract. In partially molten regions inside the Earth, melt buoyancy may trigger upwelling of both solid and fluid phases, i.e., diapirism. If the melt is allowed to move separately with respect to the matrix, melt perturbations may evolve into solitary porosity waves. While diapirs may form on a wide range of scales, porosity waves are restricted to sizes of a few times the compaction length. Thus, the size of a partially molten perturbation in terms of compaction length controls whether material is dominantly transported by porosity waves or by diapirism. We study the transition from diapiric rise to solitary porosity waves by solving the two-phase flow equations of conservation of mass and momentum in 2D with porosity-dependent matrix viscosity. We systematically vary the initial size of a porosity perturbation from 1.8 to 120 times the compaction length. If the perturbation is of the order of a few compaction lengths, a single solitary wave will emerge, either with a positive or negative vertical matrix flux. If melt is not allowed to move separately to the matrix a diapir will emerge. In between these end members we observe a regime where the partially molten perturbation will split up into numerous solitary waves, whose phase velocity is so low compared to the Stokes velocity that the whole swarm of waves will ascend jointly as a diapir, just slowly elongating due to a higher amplitude main solitary wave. Only if the melt is not allowed to move separately to the matrix will no solitary waves build up, but as soon as two-phase flow is enabled solitary waves will eventually emerge. The required time to build them up increases nonlinearly with the perturbation radius in terms of compaction length and might be too long to allow for them in nature in many cases.

A unified numerical model for two-phase porous, mush and suspension flow dynamics in magmatic systems

“…The breakup of a 1D Gaussian or 1D solitary wave into approximately 2D spherical waves was also previously observed in Scott & Stevenson (1986); Dohmen & Schmeling (2021). While we observe a similar evolution, we note that the emergent wave is not stable over time -it is not a true soliton with a fixed amplitude traveling at a fixed speed.…”

“…At high liquid fraction, the small segregation-compaction length δ s 0 on the solid grain scale suggests that mixture convection should dominate dynamics in real magmatic systems on the meter to kilometer scale (Keller & Suckale, 2019;Dohmen & Schmeling, 2021). The 1D simulations above are useful for studying phase segregation dynamics; however, to observe mixture convection, we require simulations in 2D to account for shear stresses.…”

Melt Migration and Chemical Differentiation by Reactive Porosity Waves

“…From a physical point of view, the rise of large coherent magma bodies in a viscous solid can be described by diapiric flow (e.g., Cruden, 1988;Dohmen & Schmeling, 2021;Miller & Paterson, 1999;Weinberg & Podladchikov, 1994). However, the physical process of melt extraction and migration in partially molten viscous rock is commonly described by two-phase flow models whereby the melt, representing the fluid phase, flows through the pore space of the viscous rock, representing the solid phase (e.g., McKenzie, 1984;Schmeling et al, 2019).…”

“…These spatial scales must be chosen in such way that the considered compaction-driven melt migration can be numerically resolved. We consider initial spatial distributions of porosity and/or total concentration of SiO 2 that have the form of a Gaussian with a standard deviation, or width w, which is 10 times larger than the compaction length, w = 10⋅L c , so that the applied distribution can initiate a significant compaction-driven melt migration (e.g., Dohmen & Schmeling, 2021). If w ≪ L c then the distributions of porosity and/or total concentration of SiO 2 will not initiate a significant compaction-driven melt flow by porosity waves (e.g., Dohmen & Schmeling, 2021).…”

Viscosity of crystal-mushes and implications for compaction-driven fluid flow

“…Taking the Linear-Weakening formulation as representative of the low-porosity steady-state porosity-wave solution to the compaction equations, wave velocities are O(10) 𝐴𝐴 𝐴𝐴0 (Connolly & Podladchikov, 2015), where 𝐴𝐴 𝐴𝐴0 is the Darcyian velocity (q f /ϕ 0 , Equation 21) of the melt through the unperturbed matrix. For such velocities, wavelengths are O(10)δ 0 , that is, < O(10)m. Two implications of these scales are: that in the porosity-wave regime, melt transport is accomplished by numerous, spatially small, albeit potentially large amplitude, waves; and that such short viscous compaction lengths may promote melt transport by magmatic diapirs (Dohmen & Schmeling, 2021). Although small waves would increase the rate of melt expulsion relative to uniform melt flow, and are capable of carrying geochemical signatures (Jordan et al, 2018), they would be indistinguishable from homogeneous flow by geophysical methods except, perhaps, as seismic tremors (Skarbek & Rempel, 2016).…”