Thermosolutal convection at infinite Prandtl number: initial layer and infinite Prandtl number limit

Abstract

We examine the initial layer problem and the infinite Prandtl number limit of the thermosolutal convection, which is applicable to magma chambers. We derive the effective approximating system of the Boussinesq system at large Prandtl number using two time scale approach [M. Holmes, Introduction to Perturbation Methods, Springer, New York, 1995, A. Majda, Introduction to PDEs and Waves for the Atmosphere and Ocean, Courant Lecture Notes in Mathematics, Vol. 9, New York, American Mathematical Society, Providence, RI, 2003]. We show that the effective approximating system is nothing but the infinite Prandtl number system with initial layer terms. We also show that the solutions of the Boussinesq system converge to solutions of the effective approximating system with the convergence rate of O(ϵ).

Keywords:

• thermosolutal convection
• infinite prandtl number
• effective approximating system
• initial layer

AMS Subject Classifications::

• 35Q
• 35B
• 37L
• 76D
• 76F

Acknowledgements

The work was supported by 2011 NYIT Institutional Support of Research and Creativity Grants.