Mathematical modeling of solidification process near the inner core boundary of the Earth / Alexandrov D. V.,Malygin A. P. // APPLIED MATHEMATICAL MODELLING. - 2013. - V. 37, l. 22. - P. 9368-9378.

ISSN/EISSN:

0307-904X / 1872-8480

Type:

Article

Abstract:

Radially symmetric analytic solutions of the heat and mass transfer equations governing convection in the Earth's fluid core are found in terms of deviations from the adiabatic reference state. We demonstrate that an increase of the convective velocity leads to a decrease of the light constituent mass fraction and specific entropy. Where fluid is rising/descending, convective motions decrease/increase the mass fraction and entropy at the inner core boundary (ICB). The influence of convective motions on the thermal fluxes at the core mantle boundary is studied. On the basis of exact solutions we demonstrate that the liquid is supercooled near the ICB. An important point is that an increase in the convective velocity directed to the ICB increases the constitutional supercooling. We show that the anelastic model (AM) can be used only at small supercoolings near the ICB. The most probable solidification scenario ``constitutional supercooling and morphological instability{''} should be described by a mushy layer theory near the ICB and by the AM in the rest region of the fluid outer core. On the basis of dendritic theory and selection mechanisms of crystal growth the dendrite tip radius and interdendritic spacing in the mushy layer at the ICB are determined in the presence of convection. (C) 2013 Elsevier Inc. All rights reserved.

Author keywords:

Mathematical modeling; Solidification; Mushy layer; Inner core boundary; Dendrites OUTER CORE; DENDRITIC GROWTH; DIRECTIONAL SOLIDIFICATION; ANELASTIC APPROXIMATION; THERMAL-CONVECTION; NATURAL-CONVECTION; PATTERN SELECTION; CHIMNEY FORMATION; 2-PHASE ZONE; MUSHY LAYER

DOI:

10.1016/j.apm.2013.04.032

Web of Science ID:

ISI:000328522500021

Соавторы в МНС:

Другие поля

Поле	Значение
Month	NOV 15
Publisher	ELSEVIER SCIENCE INC
Address	360 PARK AVE SOUTH, NEW YORK, NY 10010-1710 USA
Language	English
EISSN	1872-8480
Keywords-Plus	OUTER CORE; DENDRITIC GROWTH; DIRECTIONAL SOLIDIFICATION; ANELASTIC APPROXIMATION; THERMAL-CONVECTION; NATURAL-CONVECTION; PATTERN SELECTION; CHIMNEY FORMATION; 2-PHASE ZONE; MUSHY LAYER
Research-Areas	Engineering; Mathematics; Mechanics
Web-of-Science-Categories	Engineering, Multidisciplinary; Mathematics, Interdisciplinary Applications; Mechanics
Author-Email	Dmitri.Alexandrov@usu.ru
ResearcherID-Numbers	Alexandrov, Dmitri/D-2516-2016
ORCID-Numbers	Alexandrov, Dmitri/0000-0002-6628-745X
Funding-Acknowledgement	Federal Target Program ``Scientific and Academic - Teaching Staff of Innovative Russia{''}; Russian Foundation for Basic Research {[}11-01-00137]
Funding-Text	We are grateful for partial support from the Federal Target Program ``Scientific and Academic - Teaching Staff of Innovative Russia{''} in 2009-2013 and the Russian Foundation for Basic Research (Project No. 11-01-00137).
Number-of-Cited-References	48
Usage-Count-Since-2013	10
Journal-ISO	Appl. Math. Model.
Doc-Delivery-Number	273GE