Geophysical and Astrophysical Fluid Dynamics

Abstract:

The regions of Saturn’s cloud-covered atmosphere polewards of 60^o latitude are dominated in each hemisphere near the cloud tops by an intense, cyclonic polar vortex surrounded by a strong, high latitude eastward zonal jet. In the north, this high latitude jet takes the form of a remarkably regular zonal wavenumber m=6 hexagonal pattern that has been present at least since the Voyager spacecraft encounters with Saturn in 1980-81, and probably much longer. The origin of this feature, and the absence of a similar feature in the south, has remained poorly understood since its discovery. In this work, we present some new analyses of horizontal wind measurements at Saturn’s cloud tops polewards of 60 degrees in both the northern and southern hemispheres, previously published by Antuñano et al. (2015) using images from the Cassini mission, in which we compute kinetic energy spectra and the transfer rates of kinetic energy (KE) and enstrophy between different scales. 2D KE spectra are consistent with a zonostrophic regime, with a steep (~n^-5) spectrum for the mean zonal flow (n is the total wavenumber) and a shallower Kolmogorov-like KE spectrum (~n^-5/3) for the residual (eddy) flow, much as previously found for Jupiter’s atmosphere (Galperin et al. 2014; Young & Read 2017). Three different methods are used to compute the energy and enstrophy transfers, (a) as latitude-dependent zonal spectral fluxes, (b) as latitude-dependent structure functions and (c) as spatially filtered energy fluxes. The results of all three methods are largely in agreement in indicating a direct (forward) enstrophy cascade across most scales, averaged across the whole domain, an inverse kinetic energy cascade to large scales and a weak direct KE cascade at the smallest scales. The pattern of transfers has a more complex dependence on latitude, however. But it is clear that the m=6 North Polar Hexagon (NPH) wave was transferring KE into its zonal jet at 78^o N (planetographic) at a rate of ∏_E ≈ 1.8 x 10^-4 W kg^-1 at the time the Cassini images were acquired. This implies that the NPH was not maintained by a barotropic instability at this time, but may have been driven via a baroclinic instability or possibly from deep convection. Further implications of these results will be discussed.

 

References

Antuñano, A., T. del Río-Gaztelurrutia, A. Sánchez-Lavega, and R. Hueso (2015), Dynamics of Saturn’s polar regions, J. Geophys. Res. Planets, 120, 155–176, doi:10.1002/2014JE004709.

Galperin, B., R. M.B. Young, S. Sukoriansky, N. Dikovskaya, P. L. Read, A. J. Lancaster & D. Armstrong (2014) Cassini observations reveal a regime of zonostrophic macroturbulence on Jupiter, Icarus, 229, 295–320.doi: 10.1016/j.icarus.2013.08.030

Young, R. M. B. & Read, P. L. (2017) Forward and inverse kinetic energy cascades in Jupiter’s turbulent weather layer, Nature Phys., 13, 1135-1140. Doi:10.1038/NPHYS4227

Abstract:

Abstract:

The tectonic regime of rocky planets fundamentally influences their long-term evolution and cycling of volatiles between interior and atmosphere. Earth is the only known planet with active plate tectonics, but observations of exoplanets may deliver insights into the diversity of tectonic regimes beyond the solar system. Observations of the thermal phase curve of super-Earth LHS 3844b reveal a solid surface and lack of a substantial atmosphere, with a temperature contrast between the substellar and antistellar point of around 1000 K. Here, we use these constraints on the planet's surface to constrain the interior dynamics and tectonic regimes of LHS 3844b using numerical models of interior flow. We investigate the style of interior convection by assessing how upwellings and downwellings are organized and how tectonic regimes manifest. We discover three viable convective regimes with a mobile surface: (1) spatially uniform distribution of upwellings and downwellings, (2) prominent downwelling on the dayside and upwellings on the nightside, and (3) prominent downwelling on the nightside and upwellings on the dayside. Hemispheric tectonics is observed for regimes (2) and (3) as a direct consequence of the day-to-night temperature contrast. Such a tectonic mode is absent in the present-day solar system and has never been inferred from astrophysical observations of exoplanets. Our models offer distinct predictions for volcanism and outgassing linked to the tectonic regime, which may explain secondary features in phase curves and allow future observations to constrain the diversity of super-Earth interiors.

Abstract:

All the studies of the interaction between tides and a convective flow assume that the large scale tides can be described as a mean shear flow which is damped by small scale fluctuating convective eddies. The convective Reynolds stress is calculated using mixing length theory, accounting for a sharp suppression of dissipation when the turnover timescale is larger than the tidal period. This yields tidal dissipation rates several orders of magnitude too small to account for the circularization periods of late–type binaries or the tidal dissipation factor of giant planets. Here, we argue that the above description is inconsistent, because fluctuations and mean flow should be identified based on the timescale, not on the spatial scale, on which they vary. Therefore, the standard picture should be reversed, with the fluctuations being the tidal oscillations and the mean shear flow provided by the largest convective eddies. We assume that energy is locally transferred from the tides to the convective flow. Using this assumption, we obtain values for the tidal Q factor of Jupiter and Saturn and for the circularization periods of PMS binaries in good agreement with observations. The timescales obtained with the equilibrium tide approximation are however still 40 times too large to account for the circularization periods of late–type binaries. For these systems, shear in the tachocline or at the base of the convective zone may be the main cause of tidal dissipation.