Free Drift Research Articles

Ice and ocean velocity in the Arctic marginal ice zone: Ice roughness and momentum transfer

The interplay between sea ice concentration, sea ice roughness, ocean stratification, and momentum transfer to the ice and ocean is subject to seasonal and decadal variations that are crucial to understanding the present and future air-ice-ocean system in the Arctic. In this study, continuous observations in the Canada Basin from March through December 2014 were used to investigate spatial differences and temporal changes in under-ice roughness and momentum transfer as the ice cover evolved seasonally. Observations of wind, ice, and ocean properties from four clusters of drifting instrument systems were complemented by direct drill-hole measurements and instrumented overhead flights by NASA operation IceBridge in March, as well as satellite remote sensing imagery about the instrument clusters. Spatially, directly estimated ice-ocean drag coefficients varied by a factor of three with rougher ice associated with smaller multi-year ice floe sizes embedded within the first-year-ice/multi-year-ice conglomerate. Temporal differences in the ice-ocean drag coefficient of 20–30% were observed prior to the mixed layer shoaling in summer and were associated with ice concentrations falling below 100%. The ice-ocean drag coefficient parameterization was found to be invalid in September with low ice concentrations and small ice floe sizes. Maximum momentum transfer to the ice occurred for moderate ice concentrations, and transfer to the ocean for the lowest ice concentrations and shallowest stratification. Wind work and ocean work on the ice were the dominant terms in the kinetic energy budget of the ice throughout the melt season, consistent with free drift conditions. Overall, ice topography, ice concentration, and the shallow summer mixed layer all influenced mixed layer currents and the transfer of momentum within the air-ice-ocean system. The observed changes in momentum transfer show that care must be taken to determine appropriate parameterizations of momentum transfer, and imply that the future Arctic system could become increasingly seasonal.

The Statistical Properties of Sea Ice Velocity Fields

By arguing that the surface pressure field over the Arctic Ocean can be treated as an isotropic, stationary, homogeneous, Gaussian random field, Thorndike estimated a number of covariance functions from two years of data (1979 and 1980). Given the active interest in changes of general circulation quantities and indices in the polar regions during the recent few decades, the spatial correlations in sea ice velocity fields are of particular interest. It is thus natural to ask, “How persistent are these correlations?” To this end, a multifractal stochastic treatment is developed to analyze observed Arctic sea ice velocity fields from satellites and buoys for the period 1978–2015. Since it was previously found that the Arctic equivalent ice extent (EIE) has a white noise structure on annual to biannual time scales, the connection between EIE and ice motion is assessed. The long-term stationarity of the spatial correlation structure of the velocity fields and the robustness of their white noise structure on multiple time scales is demonstrated; these factors (i) combine to explain the white noise characteristics of the EIE on annual to biannual time scales and (ii) explain why the fluctuations in the ice velocity are proportional to fluctuations in the geostrophic winds on time scales of days to months. Moreover, it is shown that the statistical structure of these two quantities is commensurate from days to years, which may be related to the increasing prevalence of free drift in the ice pack.

Simulation of EAST vertical displacement events by tokamak simulation code

Vertical instability is a potentially serious hazard for elongated plasma. In this paper, the tokamak simulation code (TSC) is used to simulate vertical displacement events (VDE) on the experimental advanced superconducting tokamak (EAST). Key parameters from simulations, including plasma current, plasma shape and position, flux contours and magnetic measurements match experimental data well. The growth rates simulated by TSC are in good agreement with TokSys results. In addition to modeling the free drift, an EAST fast vertical control model enables TSC to simulate the course of VDE recovery. The trajectories of the plasma current center and control currents on internal coils (IC) fit experimental data well.

Exploring electrical resistance: a novel kinesthetic model helps to resolve some misconceptions

A simple ‘hands on’ physical model is described which displays analogous behaviour to some aspects of the free electron theory of metals. Using it students can get a real feel for what is going on inside a metallic conductor. Ohms Law, the temperature dependence of resistivity, the dependence of resistance on geometry, how the conduction electrons respond to a potential difference and the concepts of mean free path and drift speed of the conduction electrons can all be explored. Some quantitative results obtained by using the model are compared with the predictions of Drude’s free electron theory of electrical conduction.

An analytical model for wind-driven Arctic summer sea ice drift

Abstract. The authors present an analytical model for wind-driven free drift of sea ice that allows for an arbitrary mixture of ice and open water. The model includes an ice–ocean boundary layer with an Ekman spiral, forced by transfers of wind-input momentum both through the sea ice and directly into the open water between the ice floes. The analytical tractability of this model allows efficient calculation of the ice velocity provided that the surface wind field is known and that the ocean geostrophic velocity is relatively weak. The model predicts that variations in the ice thickness or concentration should substantially modify the rotation of the velocity between the 10 m winds, the sea ice, and the ocean. Compared to recent observational data from the first ice-tethered profiler with a velocity sensor (ITP-V), the model is able to capture the dependencies of the ice speed and the wind/ice/ocean turning angles on the wind speed. The model is used to derive responses to intensified southerlies on Arctic summer sea ice concentration, and the results are shown to compare closely with satellite observations.

Methods for the correction of second-order aberrations in laser time-of-flight analyzers with axial-symmetric fields

A rigorous way is described to increase the resolution of laser time-of-flight (TOF) mass spectrometers with an axially symmetric electrostatic analyzer by more than one order of magnitude. The inventive method consists in the introduction of a reflector into the ion optics of the mass spectrometer, which generates a second-order temporal aberration with an opposite polarity with respect to the aberration occurring in the free plasma drift space because of the compensation of time aberrations by energy of the second order, optimization of the ion-optical scheme of a laser time-of-flight mass spectrometer, and taking into account the partial compensation of the third-order aberrations, the resolution of the mass spectrometer is increased to (1–2) × 104. Theoretical calculations justifying the proposed method are presented.

Treating electrostatics with Wolf summation in combined quantum mechanical and molecular mechanical simulations.

The Wolf summation approach [D. Wolf et al., J. Chem. Phys. 110, 8254 (1999)], in the damped shifted force (DSF) formalism [C. J. Fennell and J. D. Gezelter, J. Chem. Phys. 124, 234104 (2006)], is extended for treating electrostatics in combined quantum mechanical and molecular mechanical (QM/MM) molecular dynamics simulations. In this development, we split the QM/MM electrostatic potential energy function into the conventional Coulomb r(-1) term and a term that contains the DSF contribution. The former is handled by the standard machinery of cutoff-based QM/MM simulations whereas the latter is incorporated into the QM/MM interaction Hamiltonian as a Fock matrix correction. We tested the resulting QM/MM-DSF method for two solution-phase reactions, i.e., the association of ammonium and chloride ions and a symmetric SN2 reaction in which a methyl group is exchanged between two chloride ions. The performance of the QM/MM-DSF method was assessed by comparing the potential of mean force (PMF) profiles with those from the QM/MM-Ewald and QM/MM-isotropic periodic sum (IPS) methods, both of which include long-range electrostatics explicitly. For ion association, the QM/MM-DSF method successfully eliminates the artificial free energy drift observed in the QM/MM-Cutoff simulations, in a remarkable agreement with the two long-range-containing methods. For the SN2 reaction, the free energy of activation obtained by the QM/MM-DSF method agrees well with both the QM/MM-Ewald and QM/MM-IPS results. The latter, however, requires a greater cutoff distance than QM/MM-DSF for a proper convergence of the PMF. Avoiding time-consuming lattice summation, the QM/MM-DSF method yields a 55% reduction in computational cost compared with the QM/MM-Ewald method. These results suggest that, in addition to QM/MM-IPS, the QM/MM-DSF method may serve as another efficient and accurate alternative to QM/MM-Ewald for treating electrostatics in condensed-phase simulations of chemical reactions.

Kinetics of fluoride removal from spent pot liner leachate (SPLL) contaminated groundwater

Groundwater contaminated with spent pot liner leachate (SPLL) was treated with calcite (CaCO3) and CO2 in a series of free drift batch reactor kinetic experiments with the aim of optimizing fluoride removal. In order to better understand the reaction kinetics for SPLL, the pseudo-second order (PSO), four and five parameter Hill (Hill 4 & Hill 5) models were applied to observed fluoride removal as a function of CO2 partial pressure and stirring rate. To account for differences in the number of model parameters, model fitting was compared using the Akaike information criterion (AIC), the Schwartz Bayesian information criterion (BIC) and the statistical F-test. In every case, the best fitting model order was found to be Hill 5>Hill 4>PSO due to the ability of the Hill models to accommodate sigmoidal kinetics. Removal of fluoride from SPLL under atmospheric CO2 conditions was found to be inhibited with no removal occurring for the first 3000min with the inhibition times, based on the reaction half-life, reducing with increased CO2 partial pressure and stirring rate. X-ray diffraction (XRD) analysis revealed that the residual solid filtrate consisted of trona (Na3(CO3)(HCO3)·2H2O) a potentially valuable mineral kogarkoite (Na3SO4F) and fluorite (CaF2) accounting for fluoride removal, and unreacted calcite (CaCO3).

Planar multi-body model of iceberg free drift and towing in broken ice

There are no full-scale data on iceberg towing in ice. However, there is a great interest in such an operation. Simulating the interaction between icebergs and surrounding ice floes during towing may help with choosing iceberg management strategies and design criteria for icebreakers and tug vessels. Broken ice has a discontinuous nature; therefore, it is proposed to model the interaction using a discrete element method (DEM) and known approximations of wind and water drag, wave, and Coriolis forces. The DEM is used to simulate the contacts between rigid, polygon-shaped ice floes. The floes are prevented from interpenetration by applying contact impulses tending to separate the bodies. Depending on the relative velocity of the contacting bodies, the contacts can be classified into two categories: collisions at non-zero relative velocity and resting contacts where the contacting bodies have the same velocity. Converting the calculated impulses into contact forces is straightforward for resting contacts but not for collisions. First, the applied impulses for collisions depend on the choice of restitution coefficient. Second, the collision duration must be estimated in order to convert collision impulses into forces. This paper discusses the choice of the restitution coefficient for ice and proposes an approach to estimate the collision force using the collision duration, which appears to be roughly proportional to the square root of the reduced mass. Additionally, the paper presents an innovative method to generate the ice field through which the iceberg is towed. The field is represented by a domain filled with randomly shaped rigid ice floes. The algorithm is capable of creating an ice field of given concentration and size distribution of the ice floes. The power law size distribution, obtained from aerial and satellite image analysis, is reproduced with high accuracy. The new approach to estimate the collision forces is subjected to a simple test on isolated floe impacts showing a good agreement with experimental and full-scale data. Finally, the simulation of iceberg towing is demonstrated and compared to experimental data. The results of the simulation were found to be in satisfactory agreement with the experiment.

Plasma vertical stabilisation in ITER

This paper describes the progress in analysis of the ITER plasma vertical stabilisation (VS) system since its design review in 2007–2008. Two indices characterising plasma VS were studied. These are (1) the maximum value of plasma vertical displacement due to free drift that can be stopped by the VS system and (2) the maximum root mean square value of low frequency noise in the dZ/dt measurement signal used in the VS feedback loop. The first VS index was calculated using the PET code for 15 MA plasmas with the nominal position and shape. The second VS index was studied with the DINA code in the most demanding simulations for plasma magnetic control of 15 MA scenarios with the fastest plasma current ramp-up and early X-point formation, the fastest plasma current ramp-down in a divertor configuration, and an H to L mode transition at the current flattop. The studies performed demonstrate that the VS in-vessel coils, adopted recently in the baseline design, significantly increase the range of plasma controllability in comparison with the stabilising systems VS1 and VS2, providing operating margins sufficient to achieve ITER's goals specified in the project requirements. Additionally two sets of the DINA code simulations were performed with the goal of assessment of the capability of the PF system with the VS in-vessel coils: (i) to control the position of runaway electrons generated during disruptions in 15 MA scenarios and (ii) to trigger ELMs in H-mode plasmas of 7.5 MA/2.65 T scenarios planned for the early phase of ITER operation. It was also shown that ferromagnetic structures of the vacuum vessel (ferromagnetic inserts) and test blanket modules insignificantly affect the plasma VS.

On the Smoothing Effect in the Kinematic Dynamo Equations in Critical Spaces

We study the smoothing effects of diffusion in a 3D vector system of linear advection-diffusion PDEs known as the kinematic dynamo equations. We examine the case where both the divergence free drift velocity \({\mathbf{u}(x,t)}\) and the mild solution \({\mathbf{B}(x,t)}\) to the PDE obey the natural scaling of the equation. We consider initial data \({\mathbf{B}_0(x) \in L^3(\mathbb{R}^3)}\) and demonstrate how the regularization effects of diffusion are influenced by the profile of \({\mathbf{u}(x,t)}\).

Evidence for the Presence of Quaternary Loess-Derived Soils in the Burren Karstic Area, Western Ireland

Quaternary loess-derived soils are found in many mid-latitude countries. Extensive loess deposits have not been described from Ireland except in unpublished reports of possible loessic soils (“stone-free drift”) on karstic terrain in die Burren, Co. Clare. The objective of this study is to verify or discount the presence of loess-derived soils in the Burren. Data on particle size, mineralogy and bulk geochemistry are presented for 14 soil samples from 12 sites, including 6 from areas which unpublished studies had identified (in map form) as covered by stone free drift. Most samples comprise silly clay soils (up to 58% sill) with low carbonate contents and low organic carbon contents. With regard to the carbonate-poor samples, XRD and XRF analyses enabled two groups to be distinguished. Group A soils show characteristics consistent with weathered till, while Group B soils show characteristics consistent with weathered loess. All sites falling within areas mapped as possible loess in previous studies provided samples which were assigned to group B. while group A soils were mapped as till or rendzina. Samples from two sites previously mapped as loess, which are relatively rich in silica and sill-sized particles, are the strongest candidates for being largely of loessic origin. These findings strongly support the view that scattered, weathered, aeolian deposits are found in upland karstic sites within the Burren. but further work is needed to confirm their extent.

Ice ridge keel geometry and shape derived from one year of upward looking sonar data in the Fram Strait

Ice ridge keel geometry was studied by analyzing one year of upward looking sonar data collected in the Transpolar drift stream at 79°N, 6.5°W in 2008/2009. Ridges were identified using the Rayleigh criterion with a threshold value of 2.5m and a minimum draft of 5m. The keel shape was studied after the identification of ridges from temporal data. On average ridge keels were symmetric both with respect to the centroid of the keel and the keel crest location. By quantifying the ratio between observed keel area and the keel area of an assumed triangular keel shape (often assumed for first year ridges) we observed that in 79% of the cases the ridge cross sectional area would be underestimated by a triangular keel shape. Because keel loads on ships and structures increase with keel draft and keel area it is important that an assumed keel shape maintains the observed keel area. Thus we suggest that a better generalization of the shape of first year ridges is a trapezoidal keel shape rather than triangular. Based on the observations the mean trapezoidal keel, representing both first year ridges and old ridges, has a keel bottom-width which on average is 17% of the keel width. For the deepest keels (>15m) the mean keel bottom width was 12% of the keel width. The mean keel draft was 7.3m and the deepest ridge was 25m. The temporal data was converted to spatial data based on an ice drift speed estimate which assumed free drift. From the spatial data we found that the mean keel width was 28m and the mean keel cross sectional area was 164m2.

Partition coefficient of Ra in witherite

The heterogeneous partition coefficient (λ) for Ra in BaCO3 (witherite) was determined by coprecipitation using the free drift method. Initially, CO2 (100 %) was bubbled through a solution equilibrated with witherite. After a small amount of Ra was added into the solution, coprecipitation was induced by a slow increase in pH, caused by degassing CO2(g) from the solution. Kinetically controlled precipitation was restricted to be slow because of the slow degassing of CO2(g). The observed low precipitation rate allowed for the equilibrium partitioning of elements during coprecipitation of witherite. The value of λ derived for Ra was (1.3 ± 0.7) × 10−1, a value similar to that obtained from the coprecipitation of Ra in CaCO3 (calcite). The obtained results indicated that partitioning of Ra in carbonate-based minerals was not dependent on the similarity of its ionic radius with that of the metal in the host carbonate.

Hölder Continuity of Solutions to the Kinematic Dynamo Equations

We study the propagation of regularity of solutions to a three dimensional system of linear parabolic PDE known as the kinematic dynamo equations. The divergence free drift velocity is assumed to be at the critical regularity level with respect to the natural scaling of the equations.

Experimental investigation of Ca isotopic fractionation during abiotic gypsum precipitation

Experiments investigating Ca isotopic fractionation during gypsum precipitation were undertaken in order to elucidate the mechanisms and conditions that govern isotopic fractionation during mineral precipitation. Both stirred and unstirred free drift gypsum precipitation experiments were conducted at constant initial ionic strength (0.6M) and variable initial saturation states (4.8–1.5) and Ca2+:SO42− ratios (3 and 0.33). Experimental durations varied between 0.5 and 190h, while temperature (25.9–24.0°C), pH (5.8–5.4) and ionic strength (0.6–0.5) were relatively constant. In all experiments, 20–80% of the initial dissolved Ca reservoir was precipitated. Isotopically light Ca preferentially partitioned into the precipitated gypsum; the effective isotopic fractionation factor (Δ44/40Cas–f=δ44/40Casolid−δ44/40Cafluid) of the experimental gypsum ranged from −2.25‰ to −0.82‰. The log weight-averaged, surface area normalized precipitation rates correlated with saturation state and varied between 4.6 and 2.0μmol/m2/h. The crystal size and aspect ratios, determined by SEM images, BET surface area, and particle size measurements, co-varied with precipitation rate, such that fast growth produced small (10–20μm), tabular crystals and slow growth produced larger (>1000μm), needle shaped crystals.Mass balance derived δ44Cas and Δ44Cas–f, calculated using the initial fluid δ44Ca and the mass fraction of Ca removed during precipitation (fCa) as constraints, suggest that the precipitate was not always sampled homogeneously due to the need to preserve the sample for SEM, surface area, and particle size analyses. The fractionation factor (αs–f), derived from Rayleigh model fits to the fluid and calculated bulk solid, ranged from 0.9985 to 0.9988 in stirred experiments and 0.9987 to 0.9992 in unstirred experiments. The αs–f demonstrated no clear dependence on either precipitation rate or initial saturation state in stirred reactors, but exhibited a positive dependence on rate in unstirred experiments. The differences in αs–f between stirred and unstirred reactors, as well as a general correlation between αs–f and crystal morphology, led us to hypothesize that growth on different crystal faces controls the isotopic composition of gypsum. We also explore the idea that speciation in solution explains the difference between experiments in which the only major difference was the Ca2+ to SO42− ratio in solution.The importance of understanding the environmental controls on the fractionation factor during mineral precipitation is highlighted in this study. The fractionation factor of gypsum precipitation near chemical equilibrium was found to be ∼0.9995, rather than 1, indicating that even at near equilibrium conditions, the δ44Ca of minerals are not likely to record the δ44Ca of the solution directly. However, the measurable isotopic fractionation associated with gypsum formation does suggest that a gypsum-based proxy may be useful in constraining Ca cycling in marginal environments over geologic time scales. Model examples are provided that demonstrate how such a proxy would operate.

Monetite promoting effect of citric acid on brushite cement setting kinetics

Brushite forming calcium phosphate cements receive growing interest in hard tissue scaffold applications due to their high surface area and high bioresorbability. The finer microstructure of monetite, the dehydrated form of brushite, has attracted attention for bone tissue engineering applications. The reduction in brushite content of the β-tricalcium phosphate–monocalcium phosphate monohydrate cement system by selective inhibition of growth upon addition of citric acid to excess setting liquid was investigated. The relaxation period during cement setting was monitored by pH stat titration and free drift runs. Spectrometric analysis revealed that the change in solubility of calcium phosphates upon addition of citric acid caused the inhibition of brushite formation and promotion of monetite precipitation. Dissolution of monetite crystals was insensitive to citrate adsorption despite their lower surface area compared to brushite. Overall brushite/monetite ratio decreased consistently with increasing citric acid concentration in the of 0·1–0·5M range.

On fundamental solutions for non-local parabolic equations with divergence free drift

We are concerned with non-local parabolic equations in the presence of a divergence free drift term. By using the classical Nash approach, we show the existence of fundamental solutions together with continuity estimates, under weak regularity assumptions on the kernel of the non-local term and the velocity of the drift term. As an application, we give an alternative proof of global regularity for the two-dimensional dissipative quasi-geostrophic equations in the critical case.

Experimental assessment of intact and damaged ship motions in head, beam and quartering seas

This paper presents an extensive study on the experimental prediction of motions for the well-known 5415 frigate hull in intact and damaged conditions. The experimental campaign is conducted for two geosim models, 1/100 and 1/51 scale, at zero speed in head, beam and quartering seas. All experimental results for 1/51 model are presented as 1st and 2nd order RAO, commenting on physical reasons for second order response occurrences. The results show the changes in motion responses when a ship hull is in damaged condition, they highlight the model scale effects and demonstrate the comparisons between the tests in which the model may freely drift and those in which the mean position of the model is restrained. For damaged ship in free drift tests the damage opening orientation is varied and its effect on RAO and free drift velocity is commented.

Upper bounds for fundamental solutions to non-local diffusion equations with divergence free drift

We consider some non-local diffusion equations in the presence of a divergence free drift term, where the diffusion operators are related to certain Dirichlet forms of jump type. We derive pointwise upper bounds for fundamental solutions of the equations under weak assumptions for the velocity of the drift term. Our class of the velocity includes functions with the scale-critical regularity and some growing functions at spatial infinity.