Journal of Earth System Science

, Volume 114, Issue 2, pp 169–176 | Cite as

A moving boundary solution for solidification of lava lake and magma intrusion in the presence of time-varying contact temperature

  • Ajay Manglik
Article
Received:
Accepted:

Abstract

During the solidification of a lava lake heat is released convectively from the top surface as well as conductively into the country rock from the base, leading to non-uniform solidification. The upper solidified layer grows at a faster rate than the lower solidified layer. Similarly, solidification of magma intrusion within the crust is also non-uniform due to the presence of thermal gradient in the crust. Available analytical solution for solidification of a melt layer assumes only symmetric cooling about the centre of the layer. In the present work a moving boundary solution for thermal evolution and non-uniform solidification of a melt layer incorporating time-varying contact temperature conditions at both of its boundaries is developed. The solution is obtained by using the Fourier spectral approach in the space domain and a modified finite difference scheme in the time domain, and is validated with available analytical solutions for simple cases and a semi-analytical solution for the case involving temperature gradient in the country rock. This solution can be used to analyse solidification of lava lakes and magma intrusions experiencing time-dependent temperature variation at their contacts with the country rock.

Keywords

Non-uniform solidification moving boundary problem continental crust time-varying contact temperature 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Carslaw H S and Jaeger J C 1959Conduction of Heat in Solids. 2nd Edn (New York: Oxford Univ. Press) p. 510.Google Scholar
  2. Cox K G 1993 Continental magmatic underplating;Phil. Trans. R. Soc. Lond. A342 155–166.Google Scholar
  3. Delany P T 1987 Heat transfer during emplacement and cooling of mafic dykes; In:Mafic Dyke Swarms (eds) H C Halls and W F FahrigGeol. Assoc. Can. Spec. Pap. 34 31–36.Google Scholar
  4. Delany P T 1988 Fortran 77 programs for conductive cooling of dykes with temperature dependent thermal properties and heat of crystallization;Comput. Geosci. 14 181–212.CrossRefGoogle Scholar
  5. Gettings M E 1988 Variation of depth to the brittle-ductile transition due to cooling of a midcrustal intrusion;Geophys. Res. Lett. 153 213–126.Google Scholar
  6. Gliko A O and Rovensky O N 1985 A numerical study of the process of lithospheric thinning under conditions of large heat flow;Izv. Akad. Nauk. SSSR Ser. Fiz. 21 416–419.Google Scholar
  7. Griffiths R W and Fink J H 1992 Solidification and morphology of submarine lavas: A dependence on extrusion rate;J. Geophys. Res. 97 19729–19737.Google Scholar
  8. Huppert H E 1990 The fluid mechanics of solidification;J. Fluid Mech. 212 209–240.CrossRefGoogle Scholar
  9. Huppert H E and Worster M G 1992 Vigorous motions in magma chambers and lava lakes; In:Chaotic Processes in the Geological Sciences (ed.) D A Yuen (New York: Springer-Verlag) Pp. 141–185.Google Scholar
  10. Jaeger J C 1968 Cooling and solidification of igneous rocks; In:Basalts: The Poldervaart Treatise on Rocks of Basaltic Composition (eds) H H Hess and A Poldervaart (New York: Wiley-Interscience) Pp. 503–536.Google Scholar
  11. Jaupart C and Tait S 1995 Dynamics of differentiation in magma reservoirs;J. Geophys. Res. 100 17615–17636.CrossRefGoogle Scholar
  12. Karner G D, Egan S S and Weissel J K 1992 Modeling the tectonic development of the Tucano and Sergipe-Alagoas rift basin, Brazil;Tectonophys. 215 133–160.CrossRefGoogle Scholar
  13. Lightfoot N M H 1929 The solidification of molten steel;Proc. London Math. Soc. 31 97–116.CrossRefGoogle Scholar
  14. Lister J R 1995 Fluid-mechanical models of the interaction between solidification and flow in dykes; In:Physics and chemistry of dykes (eds) Baer and Heimann, Balkema and Rotterdam, Pp. 115–124.Google Scholar
  15. Lister J R and Kerr R C 1991 Fluid-mechanical models of crack propagation and their application to magma transport in dykes;J. Geophys. Res. 96 10049–10077.Google Scholar
  16. Manglik A and Singh R N 1995 Postintrusive thermal evolution of continental crust: A moving boundary approach;J. Geophys. Res. 100 18031–18043.CrossRefGoogle Scholar
  17. Manglik A, Ramana D V, Gliko A O and Singh R N 1992 Application of the Fourier method to the numerical solution of moving boundary problem in heat conduction;Proc. Ind. Acad. Sci. (EPS) 101 77–88.Google Scholar
  18. Malamed V G 1958 Reducing Stefan's problem to a system of ordinary differential equation;Izv. Akad. Nauk. SSSR Ser. Geofis. 7 843–869.Google Scholar
  19. Turcotte D L and Schubert G 1982Geodynamics: Applications of Continuum Physics to Geological Problems (New York: John Wiley) p. 450.Google Scholar
  20. White R S 1992 Magmatism during and after continental break-up; In:Magmatism and the Causes of Continental Break-up (eds) B C Storey, T Alabaster and R J PankhurstGeol. Soc. Spec. Publ. 68 1–16.Google Scholar
  21. Watson S and McKenzie D 1991 Melt generation by plumes: A study of Hawaiian volcanism;J. Petrol. 32 501–537.Google Scholar
  22. White R S 1993 Melt production rates in mantle plumes;Phil. Trans. R. Soc. Lond. A342 137–153.CrossRefGoogle Scholar
  23. White R S and McKenzie D 1989 Magmatism at rift-zones: The generation of volcanic continental margins and flood basalts;J. Geophys. Res. 94 7685–7729.CrossRefGoogle Scholar
  24. Worster M G, Huppert H E and Sparks R S J 1993 The crystallization of lava lakes;J. Geophys. Res. 98 15891–15901.Google Scholar

Copyright information

© Indian Academy of Sciences 2005

Authors and Affiliations

  • Ajay Manglik
    • 1
  1. 1.National Geophysical Research InstituteHyderabadIndia

Personalised recommendations