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.

中文翻译：

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孤立孔隙度波向底辟作用过渡区的岩浆上升机制

在地球内部的部分熔融区域，熔体浮力可能会引发固相和液相的上涌，即底辟作用。如果允许熔体相对于基体单独移动，熔体扰动可能演变成孤立的孔隙度波。虽然底辟可能形成的尺度范围很广，但孔隙度波的大小仅限于压实长度的几倍。因此，就压实长度而言，部分熔融扰动的大小控制着材料主要是由孔隙度波还是由底辟作用输送。我们通过求解二维质量守恒和动量守恒的两相流动方程，研究从底辟上升到孤立孔隙度波的转变，其中具有孔隙度相关的基质粘度。我们系统地改变孔隙度扰动的初始大小，从 1 开始。8 到 120 倍的压实长度。如果扰动是几个压实长度的数量级，则会出现单个孤立波，具有正或负的垂直矩阵通量。如果不允许熔体单独移动到基质中，就会出现底辟。在这些端部成员之间，我们观察到一种状态，部分熔融的扰动将分裂成许多孤立波，其相速度与斯托克斯速度相比非常低，以至于整个波群将作为底辟共同上升，只是由于到更高振幅的主要孤立波。只有当不允许熔体单独移动到基体时，才不会建立孤立波，但一旦启用两相流，孤立波就会最终出现。