Geophysical and Astrophysical Fluid Dynamics

Abstract:

In protoplanetary discs, planetary cores must be at least 0.1 M+ at 1 au for migration to be significant; this mass rises to 1 M+ at 5 au. Planet formation models indicate that these cores form on million year timescales. We report here a study of the evolution of 0.1 M+ and 1 M+ cores, migrating from about 2 and 5 au respectively, in million year old photoevaporating discs. In such a disc, a gap opens up at around 2 au after a few million years. The inner region subsequently accrete onto the star on a smaller timescale. We find that, typically, the smallest cores form systems of non{resonant planets beyond 0.5 au with masses up to about 1.5 M+. In low mass discs, the same cores may evolve in situ. More massive cores form systems of a few earth masses planets. They migrate within the inner edge of the disc gap only in the most massive discs. Delivery of material to the inner parts of the disc ceases with opening of the gap. Interestingly, when the heavy cores do not migrate significantly, the type of systems that are produced resembles our solar system. This study suggests that low mm ux transition discs may not form systems of planets on short orbits but may instead harbour earth mass planets in the habitable zone.

Abstract:

A two-dimensional regime diagram for geostrophic turbulence in the ocean is constructed by plotting observation-based estimates of the nondimensional eddy radius and unsuppressed mixing length against a nonlinearity parameter equal to the ratio of the root-mean square eddy velocity and baroclinic Rossby phase speed. For weak nonlinearity, as found in the tropics, the mixing length mostly corresponds to the stability threshold for baroclinic instability whereas the eddy radius corresponds to the Rhines scale; it is suggested that this mismatch is indicative of the inverse energy cascade that occurs at low latitudes in the ocean and the zonal elongation of eddies. At larger values of nonlinearity, as found at mid- and high-latitudes, the eddy length scales are much shorter than the stability threshold, within a factor of 2.5 of the Rossby deformation radius.