An asymptotic and numerical study of slow, steady ascent in a Newtonian fluid with temperature-dependent viscosity

Vynnycky, Michael; O'Brien, Michael

doi:10.1016/j.amc.2012.09.049

Cited by 4 publications

(3 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With reference to equation (51), an increase appears to be plausible, since (1 − T ∞ ) increases with t, whereas Pe * 1/2 decreases. For comparison, we have also included the regime D expression for Nu; in line with the findings of Vynnycky and O'Brien (2012), it proves much more difficult to reproduce Nu asymptotically than it is to reproduce V, although there are signs that the computed curve tends towards the regime D curve. Nevertheless, this illustrates the need for numerical computations, rather than relying on asymptotical results alone.…”

Section: Resultsmentioning

confidence: 68%

“…On the other hand, a more expedient alternative is via numerical computations of the full non-isothermal axisymmetric equations, as carried out already by Vynnycky and O'Brien (2012) forn = 1; those were found not only to reproduce the asymptotic regimes, but were also able to account for the transition regimes.…”

Section: It Is Perhaps Not Immediately Obvious Whethermentioning

confidence: 98%

“…an absolute tolerance of 1×10 −6 and a relative tolerance of 1×10 −3 . The PDEs were solved using the finite-element-based software Comsol Multiphysics, as detailed by Vynnycky and O'Brien (2012). All computations were performed on a computer with a 2 GHz Intel Pentium Dual-Core processor and 4 GB RAM.…”

Section: Numerical Implementationmentioning

confidence: 99%

See 2 more Smart Citations

A quasi-asymptotic model for the ascent of magmatic diapirs

Vynnycky¹,

O'Brien²

2013

Geophysical & Astrophysical Fluid Dynamics

Self Cite

View full text Add to dashboard Cite

Recent asymptotic analysis for the slow, steady ascent of a zero-traction sphere in a power-law fluid with temperature-dependent viscosity is applied to the derivation of a model for magmatic diapirism in the Earth's mantle and continental crust. As an example, the model is applied to the case of a mantle diapir rising through country rock that is treated as a strongly shear-thinning fluid. It is found that, within the geologically relevant timescale of 10 5 years, the diapir would only encounter two of the four possible asymptotic regimes that the earlier analysis uncovered, before stalling at a considerably greater depth below the Earth's surface than was predicted by an earlier model. The implications of this result for the modelling of magmatic diapirism are discussed.

show abstract

Section: Resultsmentioning

confidence: 68%

Section: It Is Perhaps Not Immediately Obvious Whethermentioning

confidence: 98%