Open Access

Janik Dohmen, Harro Schmeling

• 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 controls whether a diapir or a porosity wave will emerge. 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 to 100 times the compaction length. If the perturbation is much larger than a regular solitary wave, its Stokes velocity is large and therefore faster than the segregating melt. Consequently, the fluid is not able to form a porosity wave and a diapir emerges. For small perturbations solitary waves emerge, either with a positive or negative vertical matrix velocity inside. In between the diapir and solitary wave regimes we observe a third regime of solitary wave induced focusing of melt. In these cases, diapirism is dominant but the fluid is still fast enough to locally build up small solitary waves which rise slightly faster than the diapir and form finger like structures at the front of the diapir. In our numerical simulations the width of these fingers is controlled by the compaction length or the grid size, whichever is larger. In cases where the compaction length becomes similar to or smaller than the grid size the finger-like leading solitary porosity waves are no more properly resolved, and too big and too fast waves may be the result. Therefore, one should be careful in large scale two-phase flow modelling with melt focusing especially when compaction length and grid size are of similar order.