The transition between solitary wave and diapir emergence from a high porosity disturbance in two-phase flow

Many processes in the earth involve the melting of rocks and the percolation of the produced melt through the residuum. These processes have been extensively studied but there is still much left what is not completely understood. In this work we focus on the emergence of solitary porosity waves, which can emerge from disturbances in regions where melt is allowed to percolate relatively to the matrix. These waves are regions of higher melt fractions that ascend with a constant velocity while not changing their shape during this ascending process. The size of these waves depends on the compaction length, which depends on just poorly known parameters such as the permeability and the viscosity of the matrix. As they can vary over several orders of magnitudes it might have a strong influence on porosity waves and their emergence from local disturbances with higher porosities than the background.

In this work we start with a 2D Gaussian-bell shaped disturbance with a certain porosity amplitude and vary the initial radius which is non-dimensionized by the characteristic compaction length. For some cases this disturbance results in an ascending solitary wave and for others it rises upwards as a diapir. For a few cases a kind of fingering can be observed which  looks like a small emerging porosity wave which is just slightly faster than the following melt of the initial larger disturbance. This leads to a melt ascent with a strongly focused front.

Comparison of porosity wave dispersion curves with analytical ascent rates of a Stokes sphere helps explaining this transition of diapirs to solitary waves via a melt ascent with a strongly focused front.