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.
Characteristics and Stability Analyses of Transient One-Dimensional Two-Phase Flow Equations and Their Finite Difference Approximations
