References
- Almgren, A.S., Bell, J.B., Rendleman, C.A. and Zingale, M., Low Mach number modeling of type Ia supernovae. I. Hydrodynamics. Astrophys. J. 2006a, 637, 922–936.
- Almgren, A.S., Bell, J.B., Rendleman, C.A. and Zingale, M., Low Mach number modeling of type Ia supernovae. II. Energy evolution. Astrophys. J. 2006b, 649, 927–938.
- Almgren, A.S., Bell, J.B., Nonaka, A. and Zingale, M., Low Mach number modeling of stratified flows. In Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, edited by J. Fuhrmann, M. Ohlberger and C. Rohde, Vol. 77, pp. 3–15, 2014 (Springer: Berlin).
- Batchelor, G., The conditions for dynamical similarity of motions of a frictionless perfect-gas atmosphere. Q. J. Roy. Meteor. Soc. 1953, 79, 224–235.
- Bell, J.B., Day, M.S., Rendleman, C.A., Woosley, S.E. and Zingale, M.A., Adaptive low Mach number simulations of nuclear flame microphysics. J. Comput. Phys. 2004, 195, 677–694.
- Berkoff, N., Kersalé, E. and Tobias, S., Comparison of the anelastic approximation with fully compressible equations for linear magnetoconvection and magnetic buoyancy. Geophys. Astrophys. Fluid Dyn. 2010, 104, 545–563.
- Braginsky, S. and Roberts, P., Equations governing convection in Earth’s core and the geodynamo. Geophys. Astrophys. Fluid Dyn. 1995, 79, 1–97.
- Calkins, M.A., Julien, K. and Marti, P., Onset of rotating and non-rotating convection in compressible and anelastic ideal gases. Geophys. Astrophys. Fluid Dyn. 2015a, 109, 422–449.
- Calkins, M.A., Julien, K. and Marti, P., The breakdown of the anelastic approximation in rotating compressible convection: Implications for astrophysical systems. Proc. R. Soc. A 2015b, 471, 20140689.
- Christensen-Dalsgaard, J., Däppen, W., Ajukov, S.V., Anderson, E.R., Antia, H.M., Basu, S., Baturin, V.A., Berthomieu, G., Chaboyer, B., Chitre, S.M., Cox, A.N., Demarque, P., Donatowicz, J., Dziembowski, W.A., Gabriel, M., Gough, D.O., Guenther, D.B., Guzik, J.A., Harvey, J.W., Hill, F., Houdek, G., Iglesias, C.A., Kosovichev, A.G., Leibacher, J.W., Morel, P., Proffitt, C.R., Provost, J., Reiter, J., Rhodes, Jr., E.J., Rogers, F.J., Roxburgh, I.W., Thompson, M.J. and Ulrich, R.K., The current state of solar modeling. Science 1996, 272, 1286–1292.
- Clayton, D.D., Principles of Stellar Evolution and Nucleosynthesis, 1968 (Chicago: University of Chicago Press).
- Drew, S., Jones, C. and Zhang, K., Onset of convection in a rapidly rotating compressible fluid spherical shell. Geophys. Astrophys. Fluid Dyn. 1995, 80, 241–254.
- Durran, D.R., Improving the anelastic approximation. J. Atmos. Sci. 1989, 46, 1453–1461.
- Durran, D.R., A physically motivated approach for filtering acoustic waves from the equations governing compressible stratified flow. J. Fluid Mech. 2008, 601, 365–379.
- Favier, B., Silvers, L. and Proctor, M., Inverse cascade and symmetry breaking in rapidly rotating Boussinesq convection. Phys. Fluids 2014, 26, 096605.
- Gastine, T., Heimpel, M. and Wicht, J., Zonal flow scaling in rapidly-rotating compressible convection. Phys. Earth Planet. In. 2014, 232, 36–50.
- Gilman, P.A., Non-linear dynamics of Boussinesq convection in a deep rotating spherical shell. Geophys. Astrophys. Fluid Dyn. 1977, 8, 93–135.
- Gilman, P.A. and Glatzmaier, G.A., Compressible convection in a rotating spherical shell I. Anelastic equations. Astrophys. J. Suppl. S. 1981, 45, 335–349.
- Glatzmaier, G.A., Numerical simulations of stellar convective dynamos. I. The model and method. J. Comput. Phys. 1984, 55, 461–484.
- Glatzmaier, G.A., Introduction to Modeling Convection in Planets and Stars. Magnetic Field, Density Stratification, Rotation, 2014 ( Princeton Series in Astrophysics. Princeton and Oxford: Princeton University Press).
- Glatzmaier, G.A. and Gilman, P.A., Compressible convection in a rotating spherical shell II. A linear anelastic model. Astrophys. J. Suppl. S. 1981a, 45, 351–380.
- Glatzmaier, G.A. and Gilman, P.A., Compressible convection in a rotating spherical shell IV. Effects of viscosity, conductivity, boundary conditions, and zone depth. Astrophys. J. Suppl. S. 1981b, 47, 103–115.
- Gough, D.O., The anelastic approximation for thermal convection. J. Atmos. Sci. 1969, 26, 448–456.
- Guervilly, C., Hughes, D.W. and Jones, C.A., Large-scale vortices in rapidly rotating Rayleigh--Bénard convection. J. Fluid Mech. 2014, 758, 407–435.
- Heimpel, M., Gastine, T. and Wicht, J., Simulation of deep-seated zonal jets and shallow vortices in gas giant atmospheres. Nat. Geosci. 2015, 9, 19–24.
- Jones, C., Kuzanyan, K. and Mitchell, R., Linear theory of compressible convection in rapidly rotating spherical shells, using the anelastic approximation. J. Fluid Mech. 2009, 634, 291–319.
- Klein, R. and Pauluis, O., Thermodynamic consistency of a pseudoincompressible approximation for general equations of state. J. Atmos. Sci. 2012, 69, 961–968.
- Lantz, S. and Fan, Y., Anelastic magnetohydrodynamic equations for modeling solar and stellar convection zones. Astrophys. J. Suppl. S. 1999, 121, 247–264.
- Lecoanet, D., Brown, B.P., Zweibel, E.G., Burns, K.J., Oishi, J.S. and Vasil, G.M., Conduction in low Mach number flows. I. Linear and weakly nonlinear regimes. Astrophys. J. 2014, 797, 16.
- Majda, A. and Sethian, J., The derivation and numerical solution of the equations for zero Mach number combustion. Combust. Sci. Technol. 1985, 42, 185–205.
- Ogura, Y. and Phillips, N., Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci. 1962, 19, 173–179.
- Rubio, A.M., Julien, K., Knobloch, E. and Weiss, J.B., Upscale energy transfer in three-dimensional rapidly rotating turbulent convection. Phys. Rev. Lett. 2014, 112, 144501.
- Stellmach, S., Lischper, M., Julien, K., Vasil, G., Cheng, J., Ribeiro, A., King, E. and Aurnou, J., Approaching the asymptotic regime of rapidly rotating convection: Boundary layers versus interior dynamics. Phys. Rev. Lett. 2014, 113, 254501.
- Vasil, G.M., Lecoanet, D., Brown, B.P., Wood, T.S. and Zweibel, E.G., Energy conservation and gravity waves in sound-proof treatments of stellar interiors. II. Lagrangian constrained analysis. Astrophys. J. 2013, 773, 23.
- Verhoeven, J. and Stellmach, S., The compressional beta effect: A source of zonal winds in planets? Icarus 2014, 237, 143–158.
- Verhoeven, J., Wiesehöfer, T. and Stellmach, S., Anelastic versus fully compressible turbulent Rayleigh--Bénard convection. Astrophys. J. 2015, 805, 14.
- Wood, T.S. and Bushby, P.J., Oscillatory convection and limitations of the Boussinesq approximation. J. Fluid Mech. 2016, 803, 502–515.