Melting driven by rotating Rayleigh-Bénard convection

Abstract:

We study the melting of a horizontal layer of a pure solid above a convecting layer of its
fluid rotating about the vertical axis using numerical methods. In the rapidly rotating regime, and for the Rayleigh numbers
of order $10^7$ considered here, convection takes the form of columnar vortices. Since these vortices
transport heat from the bottom surface to the upper boundary, the melt pattern reflects the number and
size of the columnar vortices, which in turn depend on the Prandtl, Reynolds, Rossby and Stefan numbers
of the system, and on whether we treat periodic or confined horizontal geometries. The phase
boundary can be highly ramified, reflecting the nature and number of heat transporting
vortices. Whereas the number of vortices and the melt regions they produce increase
with Reynolds number, the average area of each vortex decreases and hence so too
does the average melt rate. In addition to the Stefan number, the overall melt rate also
depends on the velocity boundary condition on the lower boundary. For large values of
the latent heat of fusion, a quasi-steady geostrophic convective state is reached in which
the net vertical heat flux, or Nusselt number, reaches nearly constant maximal values
over long time intervals, so that the constant heat supplied at the base balances the melt
rate. Commensurate with this, we find that the interfacial roughness is also maximal,
independent of the flow parameters. The confluence of processes responsible for the range
of phase boundary geometries found should influence the treatment of moving boundary
problems in mathematical models, particularly those in astrophysical and geophysical
problems where rotational effects are important.

Preprint: arXiv:2007.12751