Thin-Shell Magnetohydrodynamic Equations for the Solar Tachocline

We present a new system of equations designed to study global-scale dynamics in the stably-stratified portion of the solar tachocline. This system is derived from the 3D equations of magnetohydrodynamics in a rotating spherical shell under the assumption that the shell is thin and stably-stratified (subadiabatic). The resulting thin-shell model can be regarded as a magnetic generalization of the hydrostatic primitive equations often used in meteorology. It is simpler in form than the more general anelastic or Boussinesq equations, making it more amenable to analysis and interpretation and more computationally efficient. However, the thin-shell system is still three-dimensional and as such represents an important extension to previous 2D and shallow-water approaches. In this paper we derive the governing equations for our thin-shell model and discuss its underlying assumptions, its context relative to other models, and its application to the solar tachocline. We also demonstrate that the dissipationless thin-shell system conserves energy, angular momentum and magnetic helicity.     

The rotation of Janus and Epimetheus

Epimetheus, a small moon of Saturn, has a rotational libration (an oscillation about synchronous rotation) of 5.9°±1.2°, placing Epimetheus in the company of Earth’s Moon and Mars’ Phobos as the only natural satellites for which forced rotational libration has been detected. The forced libration is caused by the satellite’s slightly eccentric orbit and non-spherical shape.Detection of a moon’s forced libration allows us to probe its interior by comparing the measured amplitude to that predicted by a shape model assuming constant density. A discrepancy between the two would indicate internal density asymmetries. For Epimetheus, the uncertainties in the shape model are large enough to account for the measured libration amplitude. For Janus, on the other hand, although we cannot rule out synchronous rotation, a permanent offset of several degrees between Janus’ minimum moment of inertia (long axis) and the equilibrium sub-Saturn point may indicate that Janus does have modest internal density asymmetries.The rotation states of Janus and Epimetheus experience a perturbation every 4 years, as the two moons “swap” orbits. The sudden change in the orbital periods produces a free libration about synchronous rotation that is subsequently damped by internal friction. We calculate that this free libration is small in amplitude (<0.1°) and decays quickly (a few weeks, at most), and is thus below the current limits for detection using Cassini images.     

The topography of Iapetus' leading side

We have used Cassini stereo images to study the topography of Iapetus' leading side. A terrain model derived at resolutions of 4-8 km reveals that Iapetus has substantial topography with heights in the range of −10 km to +13 km, much more than observed on the other middle-sized satellites of Saturn so far. Most of the topography is older than 4 Ga [Neukum, G., Wagner, R., Denk, T., Porco, C.C., 2005. Lunar Planet. Sci. XXXVI. Abstract 2034] which implies that Iapetus must have had a thick lithosphere early in its history to support this topography. Models of lithospheric deflection by topographic loads provide an estimate of the required elastic thickness in the range of 50-100 km. Iapetus' prominent equatorial ridge [Porco, C.C., and 34 colleagues, 2005. Science 307, 1237-1242] reaches widths of 70 km and heights of up to 13 km from their base within the modeled area. The morphology of the ridge suggests an endogenous origin rather than a formation by collisional accretion of a ring remnant [Ip, W.-H., 2006. Geophys. Res. Lett. 33, doi:10.1029/2005GL025386. L16203]. The transition from simple to complex central peak craters on Iapetus occurs at diameters of 11±3 km. The central peaks have pronounced conical shapes with flanking slopes of typically 11° and heights that can rise above the surrounding plains. Crater depths seem to be systematically lower on Iapetus than on similarly sized Rhea, which if true, may be related to more pronounced crater-wall slumping (which widens the craters) on Iapetus than on Rhea. There are seven large impact basins with complex morphologies including central peak massifs and terraced walls, the largest one reaches 800 km in diameter and has rim topography of up to 10 km. Generally, no rings are observed with the basins consistent with a thick lithosphere but still thin enough to allow for viscous relaxation of the basin floors, which is inferred from crater depth-to-diameter measurements. In particular, a 400-km basin shows up-domed floor topography which is suggestive of viscous relaxation. A model of complex crater formation with a viscoplastic (Bingham) rheology [Melosh, H.J., 1989. Impact Cratering. Oxford Univ. Press, New York] of the impact-shocked icy material provides an estimate of the effective cohesion/viscosity at . The local distribution of bright and dark material on the surface of Iapetus is largely controlled by topography and consistent with the dark material being a sublimation lag deposit originating from a bright icy substrate mixed with the dark components, but frost deposits are possible as well.     

Ambient Changes in Tracer Concentrations from a Multilevel Monitoring System in Basalt

Starting in 2008, a 4‐year tracer study was conducted to evaluate ambient changes in groundwater concentrations of a 1,3,6‐naphthalene trisulfonate tracer that was added to drill water. Samples were collected under open borehole conditions and after installing a multilevel groundwater monitoring system completed with 11 discrete monitoring zones within dense and fractured basalt and sediment layers in the eastern Snake River aquifer. The study was done in cooperation with the U.S. Department of Energy to test whether ambient fracture flow conditions were sufficient to remove the effects of injected drill water prior to sample collection. Results from thief samples indicated that the tracer was present in minor concentrations 28 days after coring, but was not present 6 months after coring or 7 days after reaming the borehole. Results from sampling the multilevel monitoring system indicated that small concentrations of the tracer remained in 5 of 10 zones during some period after installation. All concentrations were several orders of magnitude lower than the initial concentrations in the drill water. The ports that had remnant concentrations of the tracer were either located near sediment layers or were located in dense basalt, which suggests limited groundwater flow near these ports. The ports completed in well‐fractured and vesicular basalt had no detectable concentrations.     

A Lee wave cloud climatology for pincher creek,Alberta

Abstract

The annual, monthly and diurnal frequencies and durations of wave clouds are summarized from twelve years of observations at Pincher Creek, Alberta. Wave clouds occur on an average of 141 days annually. There is a distinct winter maximum anda summer minimum of occurrence. Wave clouds occur on 50% or more of the days during October and February, the most active months. Wave clouds persist for longer periods in the cooler half of the year. There appears to be a marked diurnal variation in wave cloudfrequency with maxima in the afternoon, however, this may be due to decreased visibility at sunrise and sunset.     

An evolutionary algorithm for multicriteria path optimization problems

For many years researchers and decision makers (DMs) faced with multicriteria shortest path problems (MSPPs) have resorted to reductions to the classical shortest path problem (SPP) by means of weighted linear combinations of the criteria. Algorithmic and approximation schemes are available to solve MSPPs but these approaches often display complexities prohibitive to their implementation on real‐world applications. This paper describes the development of an Evolutionary Algorithm (EA) approach to MSPPs on networks with multiple independent criteria. The EA approach is shown to sufficiently explore the underlying network space, generate large candidate path sets, and evolve high quality approximations to the optimal MSPP solution(s). Opportunities for early termination of the EA in time‐critical applications are also offered. Among the issues for further work is the integration of the EA as a tool within a GIS for path optimization.     

Reconstruction of contaminant trends in a salt wedge estuary with sediment cores dated using a multiple proxy approach

The Taunton River is a partially mixed tidal estuary in southeastern Massachusetts (USA) which has received significant contaminant inputs, yet little information exists on the history of discharge and the subsequent fate of these contaminants. Three sediment cores taken along a transect were analyzed, reconstructing the spatial and temporal trends of pollution in the estuary. A combination of radiometric dating, contaminant markers, and storm layers from major hurricanes were used to establish age models and sedimentation rates. Age estimates obtained from the different dating methods compared well, establishing an accurate history of contaminant release to the estuary. Polycyclic aromatic hydrocarbons (PAHs) were present in one core at depths corresponding to the early 1860s, earlier than previously established dates of introduction. Temporal and spatial trends of Cr, Cu, Hg and Pb indicated multiple sources of varying input to the river. Polychlorinated biphenyls (PCBs) were present in each of the cores from the 1930s onward, with elevated levels still present in surficial sediments at several sites. A unique organic compound, Topanol, which was produced locally was used as a tracer to track contaminant transport in the river. Tracer data indicates that contaminants are still being transported and deposited to surficial sediments at high concentrations well after their discharge. This reconstruction demonstrates the utility of using multiple dating proxies where often the sole use of radiometric dating techniques is not an option and provides insights into the fate of contaminants discharged decades ago but continue to represent environmental risks.     

Phytoplankton biomass and size fractions in surface waters of the Australian sector of the southern ocean

We collected surface water along the 142nd E meridian from Tasmania to Antarctica in December 1999. We measured temperature, salinity and total chlorophyll a; additionally, we collected suspended particle size fractions and used fluorometric analysis to determine the quantity of chlorophyll a in each of four cell size classes: picoplankton (<3 μm), two nanoplankton fractions (3–10 μm and 10–20 μm) and microplankton (> 20 μm). Changes in temperature and salinity show that we crossed 6 water masses separated by 5 fronts. We found low abundance (<0.2 mg m⁻³) of chlorophyll in all size classes, with the exception of higher values near the continent (0.2 to 0.4 mg m⁻³). Lowest chlorophyll values (<0.1 mg m⁻³) were found in the Polar Frontal Zone (51° to 54°S). Microplankton made up the largest portion of total chlorophyll throughout most of the region. We conclude that biomass of all phytoplankton fractions, especially pico-and nanoplankton, was constrained by limiting factors, most probably iron, throughout the region and that ecosystem dynamics within a zone are not circumpolar but are regionalized within sectors.