Modons, or dipolar vortices, are common and long-lived features of the upper ocean, consisting of a pair of counter-rotating monopolar vortices moving through self-advection. Such structures remain stable over long times and may be important for fluid transport over large distances. Here, we present a semi-analytical method for finding fully nonlinear modon solutions in a multi-layer quasi-geostrophic model with arbitrarily many layers. Our approach is to reduce the problem to a multi-parameter linear eigenvalue problem which can be solved using numerical techniques from linear algebra. The method is shown to replicate previous results for one- and two-layer models and is applied to a three-layer model to find a solution describing a mid-depth propagating, topographic vortex.

Interest in hydrotalcite-like compounds has grown due to their role in controlling the mobility of aqueous metals in the environment as well as their use as catalysts, catalyst precursors and specialty chemicals. Although these materials have been studied in a number of contexts, little is known of their thermodynamic properties. High-temperature oxide melt solution calorimetry was used to measure the standard enthalpy of formation for compounds M(II)1−xAlx(OH)2(CO3)x/2·mH2O (0.2 < x < 0.4, M(II) = Mg, Co, Ni and Zn). The enthalpy of formation of these compounds from the relevant single cation phases was also determined. The formation of HTLCs results in a 5–20 kJ/mol enthalpy stabilization from the single cation hydroxides and carbonates and water. The data are correlated to two variables: the ratio of divalent to trivalent cation in the solid (M(II)/Al) and the identity of the divalent cation. It was observed that the M(II)/Al ratio exerts a minor influence on the enthalpy of formation from single-cation phases, while greater differences in stabilization resulted from changes in the chemical nature of the divalent cation. However, the data do not support any statistically significant correlation between the composition of HTLCs and their heats of formation. Equilibrium geochemical calculations based upon the thermodynamic data illustrate the effect of HTLCs on the speciation of metals in natural waters. These calculations show that, in many cases, HTLCs form even in waters that are undersaturated with respect to the individual divalent metal hydroxides and carbonates. Phase diagrams and stability diagrams involving Ni-bearing HTLCs and the single-cation components are presented. The Ni(II) concentration as a function of pH as well as the stability diagram for the equilibrium among minerals in the CaO-NiO-Al2O3-SiO2-CO2-H2O system at 298 K are plotted.

This work discusses modons, or dipolar vortices, propagating along sloping topography. Two different regimes exist, which are studied separately using the surface quasi-geostrophic equations. First, when the modon propagates in the direction opposite to topographic Rossby waves, steady solutions exist and a semi-analytical method is presented for calculating these solutions. Second, when the modon propagates in the same direction as the Rossby waves, a wave wake is generated. This wake removes energy from the modon, causing it to decay slowly. Asymptotic predictions are presented for this decay and found to agree closely with numerical simulations. Over long times, decaying vortices are found to break down due to an asymmetry resulting from the generation of waves inside the vortex. A monopolar vortex moving along a wall is shown to behave in a similar way to a dipole, though the presence of the wall is found to stabilise the vortex and prevent the long-time breakdown. The problem is equivalent mathematically to a dipolar vortex moving along a density front, hence our results apply directly to this case.

Paleoproterozoic massive Cu-Zn±Pb±Au±Ag sulphide deposits metamorphosed to the middle-upper amphibolite facies in central-south Colorado formed in a volcanic arc setting on the edge of the Yavapai crustal province. Previously published U-Pb ages on spatially related granitoids range from ∼1.9 to ∼1.1 Ga, while Pb isotope studies on galena from massive sulphides suggest mineralization formed at around 1.8–1.7 Ga. Some deposits in the Dawson-Green Mountain trend (DGMT) and the Gunnison belt are composed of Cu-Zn-Au-(Pb-Ag) mineralization that were overprinted by later Au-(Ag-Cu-Bi-Se-Te) mineralization. Sulphide mineralization is spatially related to amphibolite and bimodal, mafic-felsic volcanic rocks (gabbro, amphibolite, rhyolite and dacite) and granitoids, but it occurs mostly in biotite-garnet-quartz±sillimanite±cordierite schists and gneisses, spatially related to nodular sillimanite rocks, and in some locations, exhalative rocks (iron formations, gahnite-rich rocks and quartz-garnetite). The major metallic minerals of the massive sulphides include chalcopyrite, sphalerite, pyrite, pyrrhotite, and magnetite, with minor galena and gahnite. Altered rocks intimately associated with mineralization primarily consist of various amphiboles (gedrite, tremolite and hornblende), gahnite, biotite, garnet, cordierite, carbonate and rare högbomite. The Zn/Cd ratios of sphalerite (44 to 307) in deposits in the DGMT fall within the range of global volcanogenic massive sulphide (VMS) deposits but overlap with sphalerite from sedimentary exhalative (Sedex) deposits. Sulphur isotope values of sulphides (δ34S = −3.3 to +6.5) suggest sulphur was largely derived from magmatic sources, and that variations in isotopic values resulting from thermochemical sulphate reduction are due to small differences in physicochemical conditions. The preferred genetic model is for the deposits to be bimodal-mafic (Gunnison) to mafic-siliciclastic VMS deposits (Cotopaxi, Cinderella-Bon Ton, DGMT).

Geophysical mass flows such as debris flows, dense pyroclastic flows and snow avalanches can self-channelize on shallow slopes. The confinement afforded by formed levees helps to maintain the flow depth, and hence mobility, allowing self-channelized flows to run out significantly farther than unconfined, spreading flows. Levee formation and self-channelization are strongly associated with particle-size segregation, but can also occur in monodisperse flows. This paper uses the monodisperse depth-averaged theory of Rocha et al. (J. Fluid Mech., vol. 876, 2019, pp. 591–641), which incorporates a hysteretic friction law and second-order depth-averaged viscous terms. Both of these are vital for the formation of a travelling wave that progressively deposits a pair of levees just behind the front. The three-dimensional velocity field is reconstructed in a frame moving with the front assuming Bagnold flow. This enables a bidisperse particle-size segregation theory to be used to solve for the large and small particle concentrations and particle paths in three-dimensions, for the first time. The model shows that the large particles tend to segregate to the surface of the flow, forming a carapace that extends over the centre of the channel, as well as along the external sides and base of the levee walls. The small particles segregate downwards, and are concentrated in the main channel and in the inner levee walls. This supports the contention that a low-friction channel lining provides a secondary mechanism for run-out enhancement. It is also shown that the entire theory scales with particle diameter, so experiments with millimetre-sized particles provide important insights into geophysical-scale flows with boulders and smaller rock fragments. The model shows that self-channelization does not need particle-size segregation to occur, but supports the hypothesis that particle-size segregation and the associated frictional feedback can significantly enhance both the flow mobility and the levee strength.

The alpine–subalpine Loch Vale watershed (LVW) of Colorado, USA, has relatively high natural lithogenic P5+ fluxes to surface waters. For 1992–2018, the largest number of stream samples with P5+ concentrations ([P5+]) above detection limits occurred in 2008, corresponding with the highest frost-cracking intensity (FCI). Therefore, relatively cold winters and warm summers with a comparatively low mean annual temperature partly influence stream [P5+]. Sediment cores were collected from The Loch, an outlet lake of the LVW. Iron-, Al-, and Mn-oxide-bound phosphorus (adsorbed and authigenic phosphates; NP) serves as a proxy measurement for paleolake [P5+]. The highest NP in the core occurred during the cold and dry Allerød interstade. The lowest NP concentrations in the core occurred during climatically very wet periods in the Late Pleistocene and Early Holocene. Therefore, [P5+] are highest with relatively cold winters followed by relatively warm summers, relatively low mean annual temperatures, and relatively little rainfall and/or cryospheric melting. Currently the LVW is experiencing warming and melting of the permanent cryosphere with a rapidly declining FCI since 2008. This has the potential to dramatically decrease [P5+] in surface water ecosystems of the LVW, reducing biological productivity, enhancing P-limitation, and increasing ecosystem reliance on aeolian P5+.

A coastal eddy is modelled as a barotropic vortex propagating along a coastal shelf. If the vortex speed matches the phase speed of any coastal trapped shelf wave modes, a shelf wave wake is generated leading to a flux of energy from the vortex into the wave field. Using a simple shelf geometry, we determine analytic expressions for the wave wake and the leading-order flux of wave energy. By considering the balance of energy between the vortex and wave field, this energy flux is then used to make analytic predictions for the evolution of the vortex speed and radius under the assumption that the vortex structure remains self-similar. These predictions are examined in the asymptotic limit of small rotation rate and shelf slope and tested against numerical simulations. If the vortex speed does not match the phase speed of any shelf wave, steady vortex solutions are expected to exist. We present a numerical approach for finding these nonlinear solutions and examine the parameter dependence of their structure.

Hill's vortex is a classical solution of the incompressible Euler equations which consists of an axisymmetric spherical region of constant vorticity matched to an irrotational external flow. This solution has been shown to be a member of a one-parameter family of steady vortex rings and as such is commonly used as a simple analytic model for a vortex ring. Here, we model the decay of a Hill's vortex in a weakly rotating flow due to the radiation of inertial waves. We derive analytic results for the modification of the vortex structure by rotational effects and the generated wave field using an asymptotic approach where the rotation rate, or inverse Rossby number, is taken to be small. Using this model, we predict the decay of the vortex speed and radius by combining the flux of vortex energy to the wave field with the conservation of peak vorticity. We test our results against numerical simulations of the full axisymmetric Navier–Stokes equations.

A simple model is presented for the evolution of a dipolar vortex propagating horizontally in a vertical-slice model of a weakly stratified inviscid atmosphere, following the model of Flierl & Haines (Phys. Fluids, vol. 6, 1994, pp. 3487–3497) for a modon on the ${\rm beta}$-plane. The dipole is assumed to evolve to remain within the family of Lamb–Chaplygin dipoles but with varying radius and speed. The dipole loses energy and impulse through internal wave radiation. It is argued, and verified against numerical solutions of the full equations, that an appropriately defined centre vorticity for the dipole is closely conserved throughout the flow evolution. Combining conservation of centre vorticity with the requirement that the dipole energy loss balances the work done on the fluid by internal wave radiation gives a model that captures much of the observed dipole decay. Similar results are noted for a cylindrical dipole propagating along the axis of a rotating fluid when the dipole axis is perpendicular to the axis of rotation and for a spherical vortex propagating horizontally in a weakly stratified fluid. The model extends to fluids of small viscosity and so provides an estimate for the relative importance of wave drag and dissipation in dipole decay.

The net erosion-deposition rate of an avalanche is fundamental to its dynamics and in determining its growth or decay. Small-scale experiments are performed by releasing a given volume of yellow sand onto a stationary erodible red sand layer on a rough inclined plane. Depending on the erodible layer depth and the slope angle, the avalanche is found to either decay, grow, propagate steadily or rapidly shed grains to produce secondary avalanches. The use of different coloured sand with identical properties shows that a particle exchange occurs, which eventually results in a flow that is comprised entirely of particles from the stationary layer rather than the initial release. It is notoriously difficult to model the erosion and deposition processes in granular flows, but it is shown that a two-dimensional depth-averaged avalanche model, with a hysteretic basal friction law, can reproduce all of the observed behaviours. The results illustrate how a continuous exchange of particles with the substrate layer is fundamentally important to the propagation of such avalanches. An investigation into long distance propagation behaviour reveals that avalanches can reach a steady state, the size and speed of which are independent of the initially released volume. In certain conditions avalanches can grow to steady states that are significantly more massive than the flows from which they are originally formed. This paper demonstrates the importance of correctly including erosion-deposition in operational forecast models of snow avalanches and other geophysical mass flows.

Understanding place-based contributors to health requires geographically and culturally diverse study populations, but sharing location data is a significant challenge to multisite studies. Here, we describe a standardized and reproducible method to perform geospatial analyses for multisite studies. Using census tract-level information, we created software for geocoding and geospatial data linkage that was distributed to a consortium of birth cohorts located throughout the USA. Individual sites performed geospatial linkages and returned tract-level information for 8810 children to a central site for analyses. Our generalizable approach demonstrates the feasibility of geospatial analyses across study sites to promote collaborative translational research.