A moving-mesh finite element method and its application to the numerical solution of phase-change problems

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a generalization of the original algorithm presented in Applied Numerical Mathematics, 54:450--469 (2005). Having described the details of the generalized algorithm it is validated on two test cases from the original paper and is then applied to one-phase and, for the first time, two-phase Stefan problems in one and two space dimensions, paying particular attention to the implementation of the interface boundary conditions. Results are presented to demonstrate the accuracy and the effectiveness of the method, including comparisons against analytical solutions where available.

Space weather driven changes in lower atmosphere phenomena

During a period of heliospheric disturbance in 2007-9 associated with a co-rotating interaction region (CIR), a characteristic periodic variation becomes apparent in neutron monitor data. This variation is phase locked to periodic heliospheric current sheet crossings. Phase-locked electrical variations are also seen in the terrestrial lower atmosphere in the southern UK, including an increase in the vertical conduction current density of fair weather atmospheric electricity during increases in the neutron monitor count rate and energetic proton count rates measured by spacecraft. At the same time as the conduction current increases, changes in the cloud microphysical properties lead to an increase in the detected height of the cloud base at Lerwick Observatory, Shetland, with associated changes in surface meteorological quantities. As electrification is expected at the base of layer clouds, which can influence droplet properties, these observations of phase-locked thermodynamic, cloud, atmospheric electricity and solar sector changes are not inconsistent with a heliospheric disturbance driving lower troposphere changes.

Comprehensive ground-based and in situ observations of substorm expansion phase onset

In this paper, we present comprehensive ground-based and space-based in situ geosynchronous observations of a substorm expansion phase onset on 1 October 2005. The Double Star TC-2 and GOES-12 spacecraft were both located within the substorm current wedge during the substorm expansion phase onset, which occurred over the Canadian sector. We find that an onset of ULF waves in space was observed after onset on the ground by extending the AWESOME timing algorithm into space. Furthermore, a population of low-energy field-aligned electrons was detected by the TC-2 PEACE instrument contemporaneous with the ULF waves in space. These electrons appear to be associated with an enhancement of field-aligned Poynting flux into the ionosphere which is large enough to power visible auroral displays. The observations are most consistent with a near-Earth initiation of substorm expansion phase onset, such as the Near-Geosynchronous Onset (NGO) substorm scenario. A lack of data from further downtail, however, means other mechanisms cannot be ruled out.

Timing and localization of ionospheric signatures associated with substorm expansion phase onset

In this paper, we present case studies of the optical and magnetic signatures of the characteristics of the first minute of substorm expansion phase onset observed in the ionosphere. We find that for two isolated substorms, the onset of magnetic pulsations in the 24–96 s period wavelet band are colocated in time and space with the formation and development of small-scale optical undulations along the most equatorward preexisting auroral arc prior to auroral breakup. These undulations undergo an inverse spatial cascade into vortices prior to the release of the westward traveling surge. We also present a case study of a multiple activation substorm, whereby discrete onsets of ULF wave power above a predetermined quiet time threshold are shown to be associated with specific optical intensifications and brightenings. Moreover, in the multiple activation substorm event, we show that neither the formation of the small-scale undulations nor the formation of similar structures along a north–south aligned arc is sufficient to produce auroral breakup associated with expansion phase onset. It is only ∼10 min after these two disparate activation regions initiate that auroral breakup and the subsequent formation of a westward traveling surge occur. We discuss the implications of these results in terms of the triggering mechanisms likely to be occurring during these specific events.

On wave action and phase in the non-canonical Hamiltonian formulation

The long time–evolution of disturbances to slowly–varying solutions of partial differential equations is subject to the adiabatic invariance of the wave action. Generally, this approximate conservation law is obtained under the assumption that the partial differential equations are derived from a variational principle or have a canonical Hamiltonian structure. Here, the wave action conservation is examined for equations that possess a non–canonical (Poisson) Hamiltonian structure. The linear evolution of disturbances in the form of slowly varying wavetrains is studied using a WKB expansion. The properties of the original Hamiltonian system strongly constrain the linear equations that are derived, and this is shown to lead to the adiabatic invariance of a wave action. The connection between this (approximate) invariance and the (exact) conservation laws of pseudo–energy and pseudomomentum that exist when the basic solution is exactly time and space independent is discussed. An evolution equation for the slowly varying phase of the wavetrain is also derived and related to Berry's phase.

A mixed-phase bulk orographic precipitation model with embedded convection

A novel analytical model for mixed-phase, unblocked and unseeded orographic precipitation with embedded convection is developed and evaluated. The model takes an idealised background flow and terrain geometry, and calculates the area-averaged precipitation rate and other microphysical quantities. The results provide insight into key physical processes, including cloud condensation, vapour deposition, evaporation, sublimation, as well as precipitation formation and sedimentation (fallout). To account for embedded convection in nominally stratiform clouds, diagnostics for purely convective and purely stratiform clouds are calculated independently and combined using weighting functions based on relevant dynamical and microphysical time scales. An in-depth description of the model is presented, as well as a quantitative assessment of its performance against idealised, convection-permitting numerical simulations with a sophisticated microphysics parameterisation. The model is found to accurately reproduce the simulation diagnostics over most of the parameter space considered.

Automated determination of auroral breakup during the substorm expansion phase using all sky imager data

This technique paper describes a novel method for quantitatively and routinely identifying auroral breakup following substorm onset using the Time History of Events and Macroscale Interactions During Substorms (THEMIS) all-sky imagers (ASIs). Substorm onset is characterised by a brightening of the aurora that is followed by auroral poleward expansion and auroral breakup. This breakup can be identified by a sharp increase in the auroral intensity i(t) and the time derivative of auroral intensity i'(t). Utilising both i(t) and i'(t) we have developed an algorithm for identifying the time interval and spatial location of auroral breakup during the substorm expansion phase within the field of view of ASI data based solely on quantifiable characteristics of the optical auroral emissions. We compare the time interval determined by the algorithm to independently identified auroral onset times from three previously published studies. In each case the time interval determined by the algorithm is within error of the onset independently identified by the prior studies. We further show the utility of the algorithm by comparing the breakup intervals determined using the automated algorithm to an independent list of substorm onset times. We demonstrate that up to 50% of the breakup intervals characterised by the algorithm are within the uncertainty of the times identified in the independent list. The quantitative description and routine identification of an interval of auroral brightening during the substorm expansion phase provides a foundation for unbiased statistical analysis of the aurora to probe the physics of the auroral substorm as a new scientific tool for aiding the identification of the processes leading to auroral substorm onset.

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Exhibition investigating the role of different methods of drawing in the visualization of architectural space