Refine
Document Type
- Article (2)
- Doctoral Thesis (1)
Language
- English (3)
Has Fulltext
- yes (3)
Is part of the Bibliography
- no (3)
Keywords
Institute
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.
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.
Melting inside earth is a common phenomenon and can be observed in many different regions where melt travels through the mantle and crust to eventually reach the surface where it crystallizes to build large volcanic provinces, whole stratigraphic layers of flood basalts, or even the oceanic crust. Often, melt reaching the surface is a good source of information. It can be used to achieve a better understanding about processes taking place in deeper regions inside the mantle and it is therefore essential to fundamentally understand melting and melt percolation processes. In order to achieve a deeper understanding, the aim of this thesis is to investigate processes that are connected to melting by using numerical models.
The physical model used is a so called two-phase flow model which describes the ability of melt to percolate through a viscously deforming, partially molten matrix. A famous feature of two-phase flow are solitary porosity waves, which are waves of locally higher porosity ascending through a partially molten background, keeping its shape constant, driven by decompaction and compaction of the solid matrix in front and behind the wave.
The viscosity law for shear- and volume viscosity was strongly simplified in most previous studies that modeled solitary waves. Often the porosity dependency is underestimated or its influence on the volume viscosity is even neglected, leading to too high viscosities. In this work more realistic laws are used that strongly decrease for small melt fractions. Those laws are incorporated into a 2D Finite Difference mantle convection code with two-phase flow to study the ascent of solitary porosity waves.
The model results show that an initial Gaussian-shaped wave rapidly evolves into a solitary wave with a certain amplitude, traveling upwards with constant velocity. Even though strongly weaker viscosities are used, the effect on dispersion curves and wave shape are only minor as long as the background porosity is rather small. The results are still in agreement to semi-analytical solutions which neglect shear stresses in the melt segregation equation. Higher background porosities and wave amplitudes lead to significant decrease in phase velocity and wave width, as the viscosity is strongly effected. However, the models show that solitary waves are still a possible mechanism for more realistic matrix viscosities.
While the ascending of porosity waves are mostly described by the movement of fluid melt, partially molten regions inside Earth trigger upwelling of both, solid and fluid phases, which can be called diapirism. While diapirs can have a wide variety of wavelengths, porosity waves are restricted to a few times the compaction length. The size of a melt perturbation in terms of compaction length therefore describes whether material is transported by diapirism or porosity waves. In this thesis we study the transition from diapiric rise to solitary porosity waves by systematically changing the size of a porosity perturbation from 1.8 to 120 times the compaction length. In case of a perturbation of the size of a few times the compaction length a single porosity wave will emerge, either with a positive or negative vertical matrix flux and if melt is not allowed to move relative to the matrix a diapir will emerge. In between these physical end members a regime can be observed where the partially molten perturbation will split up into numerous solitary waves, whose phase velocity is low compared to the Stokes velocity and the swarm of solitary waves will ascend jointly as a diapir, slowly elongating due to a higher amplitude main solitary wave.
Solitary waves will always emerge from a melt perturbation as long as two-phase flow is enabled, but the time for a solitary wave to emerge increases non-linearly with the perturbation radius in terms of compaction length. In nature, in many cases this time might be too long for solitary waves to emerge.
Another important feature when it comes to two-phase flow is the transport of trace elements in melt. Incompatible elements prefer to go into the melt, which eventually enriches the area where it crystallizes again. In order to model this redistribution, the code FDCON was extended to allow for fully consistent transport of elements in melt, including melting, freezing and re-equilibration with time. A 2D model, a simple representation of a volcanic back arc, is set up to investigate the behavior of trace elements. The influence of retention number and re-equilibration time is examined. Lava-lamp like convection can be observed in the lower part of the model, producing melt, that eventually leads to enrichment in trace elements in the upper high-viscous layer. The total enrichment in this layer approaches an asymptotic value and a 0D model is introduced to recreate this behavior.