Compressible convection in the Earth's mantle: A comparison of different approaches

Numerical models of mantle convection using the Boussinesq, extended Bousinessq and anelastic‐liquid approximation are compared. For steady state solutions there is good quantitative agreement between the results if they are scaled in a proper way. Time‐dependent extended Boussinesq and anelastic‐liquid flows show only qualitative agreement, the main difference being a distortion of timescale. Compressibility induces an asymmetry in the structure of upper and lower boundary layers that cannot be observed in Boussinesq fluids.