Search for: All records

Abstract Foraminifera are unicellular organisms that inhabit the oceans. They play an important role in the global carbon cycle and record valuable paleoclimate information through the uptake of trace elements such as strontium into their calcitic shells. Understanding how foraminifera control their internal fluid composition to make calcite is important for predicting their response to ocean acidification and for reliably interpreting the chemical and isotopic compositions of their shells. Here, we model foraminiferal calcification and strontium partitioning in the benthic foraminiferaCibicides wuellerstorfiandCibicidoides mundulusbased on insights from inorganic calcite experiments. The numerical model reconciles inter-ocean and taxonomic differences in benthic foraminifer strontium partitioning relationships and enables us to reconstruct the composition of the calcifying fluid. We find that strontium partitioning and mineral growth rates of foraminiferal calcite are not strongly affected by changes in external seawater pH (within 7.8–8.1) and dissolved inorganic carbon (DIC, within 2100–2300 μmol/kg) due to a regulated calcite saturation state at the site of shell formation. 

Bedload particle hops are defined as successive motions of a particle from start to stop, characterizing one of the most fundamental processes of bedload sediment transport in rivers. Although two transport regimes have been recently identified for short and long hops, respectively, there is still the lack of a theory explaining the mean hop distance–travel time scaling for particles performing short hops, which dominate the transport and may cover over 80 % of the total hop events. In this paper, we propose a velocity-variation-based formulation, the governing equation of which is intrinsically identical to that of Taylor dispersion for solute transport within shear flows. The key parameter, namely the diffusion coefficient, can be determined by hop distances and travel times, which are easier to measure and more accurate than particle accelerations. For the first time, we obtain an analytical solution for the mean hop distance–travel time relation valid for the entire range of travel times, which agrees well with the measured data. Regarding travel times, we identify three distinct regimes in terms of different scaling exponents: respectively, $$\sim$$ 1.5 for the initial regime and $$\sim$$ 5/3 for the transition regime, which define the short hops, and 1 for the Taylor dispersion regime defining long hops. The corresponding distribution of the hop distance is analytically obtained and experimentally verified. We also show that the conventionally used exponential distribution, as proposed by Einstein, is solely for long hops. Further validation of the present formulation is provided by comparing the simulated accelerations with measurements. 

Abstract Accounting for the burial of tracer particles during bedload transport is an important component in the formulation of tracer dispersal in rivers. Herein we propose a modified active layer formulation, which accounts for the effect of burial and admits analytical solutions, enabling insightful exploration of the phenomenon of superdiffusion of bedload tracers at the intermediate timescale. This phenomenon has been observed in recent numerical results using the 2‐D Exner‐Based Master Equation. By assuming that tracers in the active layer can exchange with nontracer particles in the substrate layer to preserve mass, and that tracers entering the substrate layer get permanently trapped during the timescale of analysis, we are able to deduce governing equations for the tracer concentration in both layers. The active layer tracer concentration is shown to be governed by an advection‐diffusion equation with a sink term, and the increase of tracers in the substrate layer is driven by a corresponding source term. The solution for the variance of tracer population is analytically determined and can be approximated by the sum of a diffusion‐induced scaling (∝t¹) and an advection‐induced scaling (∝t³) terms at the intermediate timescale, which explains the phenomenon of superdiffusion. The proposed formulation is shown to be able to capture the key characteristics of tracer transport as inferred by comparison with available results of numerical simulations.