Buoyant rise of anorthosite from a layered basic complex triggered by Rayleigh-Taylor instability: Insights from a numerical modeling study

2020 ◽  
Vol 105 (4) ◽  
pp. 437-446 ◽  
Author(s):  
Amal Bikash Mukherjee ◽  
Subhasish Das ◽  
Dhrubajyoti Sen ◽  
Bikramjit Bhattacharya

Abstract A major unsolved problem of the Proterozoic is the genesis and tectonic evolution of the massif type anorthosites. The idea of large-scale floating of plagioclase crystals in a basaltic magma chamber eventually generating massif type anorthosite diapirs from the floatation cumulates is not supported by observations of the major layered basic complexes of Proterozoic to Eocene age. In this paper, we test and propose a new genetic process of anorthosite diapirism through Rayleigh-Taylor instability. We have carried out a numerical modeling study of parallel, horizontal, multiple layers of norite and anorthosite, in a model layered basic complex, behaving like Newtonian or non-Newtonian power law fluids in a jelly sandwich model of the continental lithosphere. We have shown that in this pressure-temperature-rheology configuration the model lithosphere generates Rayleigh-Taylor instability, which triggers diapirism of the anorthosite. In our model, the anorthosite diapirs buoyantly rise through stages of simple, symmetrical upwelling and pronounced bulbous growth to a full-blown mushroom-like form. This is the growth path of diapirs in nearly all analog and numerical previous studies on diapirism. Our anorthosite diapirs fully conform to this path. Furthermore, we demonstrate that the progressive diapirism brings in striking internal changes within the diapir itself. In the process, the lowermost anorthosite layer rises displacing the upper norite and anorthosite layers as progressively stretched and isolated segments driven to the margin of the rising diapir—a feature commonly seen in natural anorthosite massifs. We propose that a large plume-generated basaltic magma chamber may be ponded at the viscous lower crust or ductile-plastic upper mantle or further down in the weaker mantle of the jelly sandwich type continental lithosphere. The magma may cool and crystallize very slowly and resolve into a thick-layered basic complex with anorthosite layers. Rheologically behaving like Newtonian or non-Newtonian power law fluids, the layers of the basic complex with built-in density inversions would generate RT (Rayleigh-Taylor) instability. The RT instability would trigger a buoyant rise of the unstable anorthosite from the layered complex. The upward driven anorthosite, accumulated as anorthosite plutons, would gradually ascend across the lower and middle crust as anorthosite diapirs.

1980 ◽  
Vol 58 ◽  
pp. 571-577
Author(s):  
J. Robert Buchler ◽  
Mario Livio ◽  
Stirling A. Colgate

AbstractA two dimensional hydrodynamic study indicates that convectively unstable gradients which develop during core collapse and bounce give rise to large scale core overturn. It is also shown that the concomitant release of neutrini can deposit large amounts of energy and momentum in the infalling envelope and give rise to a powerful supernova explosion.


2019 ◽  
Vol 61 (3) ◽  
pp. 286-304 ◽  
Author(s):  
S. J. WALTERS ◽  
L. K. FORBES

Rayleigh–Taylor instability occurs when a heavier fluid overlies a lighter fluid, and the two seek to exchange positions under the effect of gravity. We present a linearized theory for arbitrary three-dimensional (3D) initial disturbances that grow in time, and calculate the evolution of the interface for early times. A new spectral method is introduced for the fully 3D nonlinear problem in a Boussinesq fluid, where the interface between the light and heavy fluids is approximated with a smooth but rapid density change in the fluid. The results of large-scale numerical calculation are presented in fully 3D geometry, and compared and contrasted with the early-time linearized theory.


2013 ◽  
Vol 735 ◽  
pp. 29-60 ◽  
Author(s):  
Pascal Noble ◽  
Jean-Paul Vila

AbstractIn this paper we derive consistent shallow-water equations for the flow of thin films of power-law fluids down an incline. These models account for the streamwise diffusion of momentum, which is important to describe accurately the full dynamics of thin-film flows when instabilities such as roll waves arise. These models are validated through a comparison with the Orr–Sommerfeld equations for large-scale perturbations. We consider only laminar flow for which the boundary layer issued from the interaction of the flow with the bottom surface has an influence all over the transverse direction to the flow. In this case the concept itself of a thin film and its relation with long-wave asymptotics leads naturally to flow conditions around a uniform free-surface Poiseuille flow. The apparent viscosity diverges at the free surface, which, in turn, introduces a singularity in the formulation of the Orr–Sommerfeld equations and in the derivation of shallow-water models. We remove this singularity by introducing a weaker formulation of the Cauchy momentum equations. No regularization procedure is needed, nor any distinction between shear thinning and thickening cases. Our analysis, though, is only valid when the flow behaviour index $n$ is larger than $1/ 2$, and strongly suggests that the Cauchy momentum equations are ill-posed if $n\leq 1/ 2$.


2019 ◽  
Vol 61 ◽  
pp. 286-304
Author(s):  
Stephen John Walters ◽  
Lawrence K. Forbes

Rayleigh–Taylor instability occurs when a heavier fluid overlies a lighter fluid, and the two seek to exchange positions under the effect of gravity. We present a linearized theory for arbitrary three-dimensional (3D) initial disturbances that grow in time, and calculate the evolution of the interface for early times. A new spectral method is introduced for the fully 3D nonlinear problem in a Boussinesq fluid, where the interface between the light and heavy fluids is approximated with a smooth but rapid density change in the fluid. The results of large-scale numerical calculation are presented in fully 3D geometry, and compared and contrasted with the early-time linearized theory. doi:10.1017/S1446181119000087


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