Core formation in Terrestrial planets via global Rayleigh-Taylor destabilization
Final Report Abstract
A power law relationship exists between the convective Rossby number and the density contrast such that a value C can be used to determine the behavior of a rotating convective fluid in the two dimensional equatorial plane. As the value of C decreases, the local generation of vorticity as fluid parcels move with respect to the background density stratification in the rotating disk (LVDS), becomes increasingly dominant in determining the fluid flow pattern. High values of C correspond to dipolar flow patterns, while low values of C correspond to differential flow patterns. This correlation holds for simulations with central heating or uniform heating, and for simulations with varying Prandtl number. Keeping in mind that this is an extrapolation, a body's value of C can be calculated based on estimates of its parameters to determine if the density stratification needs to be included in simulations. Giant planets are seen to lie in the region of differential flow (therefore including the density stratification is likely very important), while surprisingly the Earth's outer core also appears to lie in the differential flow region. This indicates that LVDS vorticity generation could be playing a role in forming differential rotation in the Earth's outer core and therefore in the production and maintenance of the geomagnetic field. A power law relationship also exists between the C value and the equatorial eccentricity such that a value Cm can be used to determine the behavior of the fluid convection in an elliptic object. Internal convective patterns have important ramifications for magnetic field generation both in giant planets and in their host stars as these fields then interact with each other. While the giant planets in our solar system do not experience large changes in their equatorial eccentricity, it is possible that hot jupiters or binary stars may experience large time dependent shifts from spherical geometry over the course of their orbits. For such bodies it is possible that this change in equatorial eccentricity could result in varying Cm which could result in a time dependent transition between flow regimes, or even a time dependent oscillation between flow patterns within a flow regime (such as an oscillation between three stable jets and two stable jets within the differential flow regime). Varying Cm could have interesting effects on the planet or stars' magnetic fields. To explore this further simulations would have to be conducting in three dimensions, and in two and three dimensions with time varying equatorial eccentricity.
