Pitted terrains on (1) Ceres and implications for shallow subsurface volatile distribution.

Prior to the arrival of the Dawn spacecraft at Ceres, the dwarf planet was anticipated to be ice-rich. Searches for morphological features related to ice have been ongoing during Dawn's mission at Ceres. Here we report the identification of pitted terrains associated with fresh Cerean impact craters. The Cerean pitted terrains exhibit strong morphological similarities to pitted materials previously identified on Mars (where ice is implicated in pit development) and Vesta (where the presence of ice is debated). We employ numerical models to investigate the formation of pitted materials on Ceres and discuss the relative importance of water ice and other volatiles in pit development there. We conclude that water ice likely plays an important role in pit development on Ceres. Similar pitted terrains may be common in the asteroid belt and may be of interest to future missions motivated by both astrobiology and in situ resource utilization.

Extensive water ice within Ceres' aqueously altered regolith: Evidence from nuclear spectroscopy.

The surface elemental composition of dwarf planet Ceres constrains its regolith ice content, aqueous alteration processes, and interior evolution. Using nuclear spectroscopy data acquired by NASA's Dawn mission, we determined the concentrations of elemental hydrogen, iron, and potassium on Ceres. The data show that surface materials were processed by the action of water within the interior. The non-icy portion of Ceres' carbon-bearing regolith contains similar amounts of hydrogen to those present in aqueously altered carbonaceous chondrites; however, the concentration of iron on Ceres is lower than in the aforementioned chondrites. This allows for the possibility that Ceres experienced modest ice-rock fractionation, resulting in differences between surface and bulk composition. At mid-to-high latitudes, the regolith contains high concentrations of hydrogen, consistent with broad expanses of water ice, confirming theoretical predictions that ice can survive for billions of years just beneath the surface.

The geomorphology of Ceres.

Analysis of Dawn spacecraft Framing Camera image data allows evaluation of the topography and geomorphology of features on the surface of Ceres. The dwarf planet is dominated by numerous craters, but other features are also common. Linear structures include both those associated with impact craters and those that do not appear to have any correlation to an impact event. Abundant lobate flows are identified, and numerous domical features are found at a range of scales. Features suggestive of near-surface ice, cryomagmatism, and cryovolcanism have been identified. Although spectroscopic analysis has currently detected surface water ice at only one location on Ceres, the identification of these potentially ice-related features suggests that there may be at least some ice in localized regions in the crust.

Basins of attraction on random topography.

We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to the curvature of the contour line divided by the local slope. Consequently, rivers tend to lie in locations of high curvature and flat slopes. Gaussian surfaces are introduced as a model of random topography. For Gaussian surfaces the relation between convergence and slope is obtained analytically. The convergence of flow lines correlates positively with drainage area, so that lower slopes are associated with larger basins. As a consequence, we explain the observed relation between the local slope of a landscape and the area of the drainage basin geometrically. To some extent, the slope-area relation comes about not because of fluvial erosion of the landscape, but because of the way rivers choose their path. Our results are supported by numerically generated surfaces as well as by real landscapes.

Universality of probability distributions among two-dimensional turbulent flows

We study statistical properties of two-dimensional turbulent flows. Three systems are considered: the Navier-Stokes equation, surface quasigeostrophic flow, and a model equation for thermal convection in the Earth's mantle. Direct numerical simulations are used to determine one-point fluctuation properties. Comparative study shows universality of probability density functions (PDFs) across different types of flow. For instance, the PDFs for derivatives of the advected quantity are the same for the three flows, once normalized by the average size of fluctuations. The single-point statistics is surprisingly robust with respect to the nature of the nonlinearity.

Energy spectra of steady two-dimensional turbulent flows

The power spectrum is measured in direct numerical simulations of the two-dimensional Navier-Stokes equation and other two-dimensional flows with white-in-time forcing at large scales. For the Navier-Stokes equation the energy spectrum in the inertial range approaches k(-3) with increasing Reynolds number, with possible logarithmic corrections. A family of two-dimensional flows, including the surface quasigeostrophic equation, allows us to vary the locality of the "enstrophy" transfer, where enstrophy is the mean square of the convected quantity. Dimensional analysis based on the enstrophy dissipation correctly predicts the energy spectrum, whenever the enstrophy transfer can be assumed to be spectrally local. Otherwise, the enstrophy spectrum is steeper than would be expected on the basis of local transfer. In this case the data suggest a k(-1) passive scalar spectrum.

Front formation in an active scalar equation.

We study the formation of thermal fronts in an active scalar equation that is similar to the Euler equation. For a particular initial condition, an earlier candidate for finite-time blowup, the front forms in a generalized self-similar way with constant hyperbolicity at the center. The behavior belongs to a class of scenarios for which finite-time blowup is impossible. A systematic exploration of many different initial conditions reveals no evidence of singular solutions.