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:

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.

Abstract:

The data comprise two 2-dimensional gridded maps of horizontal wind measurements covering the north and south polar regions of Saturn, as previously published by Antuñano et al. (2015). As fully described in that paper, these measurements were derived from sets of Cassini Orbiter Imaging Sub-System (ISS) Wide Angle Camera (WAC) and Narrow Angle Camera (NAC) images using the continuum band CB2 and CB3 filters, acquired for the northern hemisphere in June 2013 and for the southern hemisphere using WAC CB2 and CB3 images taken in October 2006 and December 2008. Additional NAC images using the CB2 and red filters taken in July 2008 were also used to analyse the southern polar vortex. The WAC images covered a region extending from a planetocentric latitude of around 60-65 degrees to each pole (apart from a segment in longitude between around 35 - 110 degrees W) with a horizontal resolution equivalent to around 0.05 degrees latitude (around 50km) per pixel, while NAC images were mostly used for the polar vortices, with a resolution equivalent to around 0.01 degrees latitude (around 10 km) per pixel. Horizontal velocities were obtained using semi-automated image correlation methods between pairs of images separated in time by intervals of approximately 1-10 hours. The correlation algorithm used pixel box sizes of 23 x 23 (in the north) or 25 x 25 (in the south), leading to a spatial resolution of the velocity vectors equivalent to around 1 degree latitude or 1000 km outside the polar vortices, reducing to around 0.2 degrees or 200 km within the polar vortices themselves. The automatically generated velocity vectors were supplemented by a small number (around 1% of the total) of vectors obtained manually from the motion of visually identified cloud tracers. The estimated measurement uncertainty on each vector was around 5-10 m/s. The original velocity vectors from Antuñano et al. (2015) were interpolated onto a regular latitude-longitude grid using convex hulls and Delauney triangulation via the QHULL routine of the Interactive Data Language (IDL). The final datasets are held on a regular grid separated by 3-4 degrees in longitude and 0.23 degrees in latitude. Data are stored as two text files, tabulating the latitude and (west) longitude of each point and the eastward and northward velocity components respectively in units of m/s. Reference: Antuñano,A., del Río-Gaztelurrutia,T., Sánchez-Lavega,A., & Hueso, R. (2015). Dynamics of Saturn’s polar regions. J. Geophys. Res.: Planets, 120, 155–176. doi: 10.1002/2014JE004709