It is commonly asserted that there are two distinct classes of glacier surges: slow, long-duration ‘Svalbard-type’ surges, triggered by a transition from cold- to warm-based conditions (thermal switching), and fast, shorter-duration ‘Alaska-type’ surges triggered by a reorganisation of the basal drainage system (hydraulic switching). This classification, however, reflects neither the diversity of surges in Svalbard and Alaska (and other regions), nor the fundamental dynamic processes underlying all surges. We argue that enthalpy balance theory offers a framework for understanding the spectrum of glacier surging behaviours while emphasising their essential dynamic unity. In this paper, we summarise enthalpy balance theory, illustrate its potential to explain so-called ‘Svalbard-type’ and ‘Alaska-type’ surges using a single set of principles, and show examples of a much wider range of glacier surge behaviour than previously observed. We then identify some future directions for research, including strategies for testing predictions of the theory against field and remote sensing data, and priorities for numerical model development.

A reduced model is presented for the dynamics of a slender sheet of a viscoelastic fluid. Starting with the Oldroyd-B constitutive model and exploiting an asymptotic analysis in the small aspect ratio of the sheet, equations are derived for the evolution of a ‘visco-elastica’. These depend on an elastic modulus, a creep viscosity and a solvent viscosity. They resemble standard equations for an elastica or a viscida, to which they reduce under the appropriate limits. The model is used to explore the effects of viscoelasticity on the dynamics of a curling ribbon, a drooping cantilever, buckling sheets, snap-through and a falling catenary. We then incorporate a yield stress, for a fluid that deforms by creep only above a critical stress, revisiting the curling and cantilever problems. This model generalises a number of previous theories for viscoelastic and viscoplastic ribbons.

Analysis of a recent surge of Morsnevbreen, Svalbard, is used to test predictions of the enthalpy balance theory of surging. High-resolution time series of velocities, ice thickness and crevasse distribution allow key elements of the enthalpy (internal energy) budget to be quantified for different stages of the surge cycle. During quiescence (1936–1990), velocities were very low, and geothermal heat slowly built-up enthalpy at the bed. Measurable mass transfer and frictional heating began in 1990–2010, then positive frictional heating-velocity feedbacks caused gradual acceleration from 2010 to 2015. Rapid acceleration occurred in summer 2016, when extensive crevassing and positive air temperatures allowed significant surface to bed drainage. The surge front reached the terminus in October 2016, coincident with a drop in velocities. Ice plumes in the fjord are interpreted as discharge of large volumes of supercooled water from the bed. Surge termination was prolonged, however, indicating persistence of an inefficient drainage system. The observations closely match predictions of the theory, particularly build-up of enthalpy from geothermal and frictional heat, and surface meltwater, and the concomitant changes in ice-surface elevation and velocity. Additional characteristics of the surge reflect spatial processes not represented in the model, but can be explained with respect to enthalpy gradients.

The flow of ice sheets and glaciers dissipates significant amounts of heat, which can result in the formation of ‘temperate ice’, a binary mixture of ice and small amounts of melt water that exists at the melting point. Many ice masses are polythermal, in the sense that they contain cold ice, below the melting point, as well as temperate ice. Temperature and melt water (or moisture) content conversely affect the flow of these ice masses through their effect on ice viscosity and sliding behaviour. Ice flow models therefore require a component that can solve for temperature and moisture content, and determine the free boundary between the cold and temperate subdomains. We present such a model, based on the theory of compacting partial melts. By contrast with other models, we describe gravity- and pressure-gradient-driven drainage of moisture, while maintaining a divergence-free ice flow at leading order. We also derive the relevant boundary conditions at the free cold–temperate boundary, and find that the boundary behaves differently depending on whether ice enters or exits the temperate region. The paper also describes a number of test cases used to compare with a numerical solution, and investigates asymptotic solutions applicable to the limit of small compaction pressure gradients in the temperate ice regions. A simplified enthalpy-gradient model is finally proposed, which captures most of the behaviour of the full model in this limit.

We study a simplified model of ice–ocean interaction beneath a floating ice shelf, and investigate the possibility for channels to form in the ice shelf base due to spatial variations in conditions at the grounding line. The model combines an extensional thin-film description of viscous ice flow in the shelf, with melting at its base driven by a turbulent ocean plume. Small transverse perturbations to the one-dimensional steady state are considered, driven either by ice thickness or subglacial discharge variations across the grounding line. Either forcing leads to the growth of channels downstream, with melting driven by locally enhanced ocean velocities, and thus heat transfer. Narrow channels are smoothed out due to turbulent mixing in the ocean plume, leading to a preferred wavelength for channel growth. In the absence of perturbations at the grounding line, linear stability analysis suggests that the one-dimensional state is stable to initial perturbations, chiefly due to the background ice advection.

The Murchison Widefield Array is a new low-frequency interferometric radio telescope built in Western Australia at one of the locations of the future Square Kilometre Array. We describe the automated radio-frequency interference detection strategy implemented for the Murchison Widefield Array, which is based on the aoflagger platform, and present 72–231 MHz radio-frequency interference statistics from 10 observing nights. Radio-frequency interference detection removes 1.1% of the data. Radio-frequency interference from digital TV is observed 3% of the time due to occasional ionospheric or atmospheric propagation. After radio-frequency interference detection and excision, almost all data can be calibrated and imaged without further radio-frequency interference mitigation efforts, including observations within the FM and digital TV bands. The results are compared to a previously published Low-Frequency Array radio-frequency interference survey. The remote location of the Murchison Widefield Array results in a substantially cleaner radio-frequency interference environment compared to Low-Frequency Array’s radio environment, but adequate detection of radio-frequency interference is still required before data can be analysed. We include specific recommendations designed to make the Square Kilometre Array more robust to radio-frequency interference, including: the availability of sufficient computing power for radio-frequency interference detection; accounting for radio-frequency interference in the receiver design; a smooth band-pass response; and the capability of radio-frequency interference detection at high time and frequency resolution (second and kHz-scale respectively).

We consider a nonlinear diffusion equation describing the planar spreading of a viscous fluid injected between an elastic sheet and an underlying rigid plane. The dynamics depends sensitively on the physical conditions at the contact line where the sheet is lifted off the plane by the fluid. We explore two possibilities for these conditions (or “regularisations”): a pre-wetted film and a constant-pressure fluid lag (a gas-filled gap between the fluid edge and the contact line). For both flat and inclined planes, we compare numerical and asymptotic solutions, identifying the distinct stages of evolution and the corresponding characteristic rates of spreading.

We present a new model of subglacial drainage incorporating flow in a network of channels and a porous sheet, with water exchange between the two determined by pressure gradients. The sheet represents the average effect of many linked cavities, whilst the channels emerge from individual cavities that enlarge due to dissipation-induced melting. The model distinguishes cases when the water pressure drops to zero, in which case it allows for the drainage space to be only partially filled with water (free surface flow), and when the pressure reaches the ice overburden pressure, in which case it allows for uplift of the ice to whatever extent is needed to accommodate the water (flotation). Numerical solutions are found for a one-dimensional flow-line version of the model. The results capture typically observed or inferred features of subglacial drainage systems, including open channel flow at the ice margin, seasonal channel evolution, and high water pressures and uplift of the ice surface driven by rapid changes in water supply.

We investigate the dynamics of an object towed over the surface of an initially flat, deformable layer. Using a combination of simple laboratory experiments and a theoretical model, we demonstrate that an inclined plate, pivoted so as to move up and down, may be towed steadily over a substrate at low speed, but become unstable to vertical oscillations above a threshold speed. That threshold depends upon the weight of the plate and the physical properties of the substrate, but arises whether the substrate is a viscous fluid, a viscoplastic fluid, or a granular medium. For the latter two materials, the unstable oscillations imprint a permanent rippled pattern on the layer, suggesting that the phenomenon of the ‘washboard road’ can arise from the passage of a single vehicle (i.e. the absolute instability of a flat bed). We argue that the mechanism behind the instability originates from the mound of material that is pushed forward ahead of the object: the extent of the mound determines the resultant force, whereas its growth is controlled by the object’s height relative to the undisturbed surface, allowing for an unstable coupling between the vertical motion and the substrate deformation.

Using a combination of theoretical modelling and experiments, seiches in a reservoir are shown to become linearly unstable due to the coupling with flow under a dam that opens and closes in response to the upstream water pressure. The phenomenon is related to the mechanism commonly attributed to generate sound in musical instruments like the clarinet. Shallow water theory is used to model waves in the reservoir, and these are coupled, by an outflow condition, to a nonlinear oscillator equation for the dam opening. In general, several modes of oscillation are predicted to be unstable, and the frequency of the most unstable mode compares well with the dominant frequencies observed in the experiments. The experiments also show a systematic variation of the amplitude and spatial structure of the oscillations with the weight of the dam, reflecting the nonlinear coupling between the unstable modes of the system.

Experiments are conducted to study the planing and skipping of a rectangular paddle on the surface of a shallow stream. The paddle is allowed to move freely up and down by attaching it to a pivoted arm. A steady planing state, in which the lift force from the water balances the weight on the paddle, is found to be stable for small stream velocities but to become unstable above a certain threshold velocity which depends upon the weight and the angle of attack. Above this threshold, the paddle oscillates in the water and can take off into a continual bouncing, or skipping, motion, with a well-defined amplitude and frequency. The transition is sometimes bistable so that both a steady planing state and a regular skipping state are possible for the same experimental parameters. Shallow-water theory is used to construct simple models that explain the qualitative features of the planing and skipping states in the experiments. It is found that a simple parameterisation of the lift force on the paddle proportional to the depth of entry is not sufficient to explain the observations, and it is concluded that the rise of water ahead of the paddle, in particular the way this varies over time, is responsible for causing the planing state to become unstable and for enabling a continual skipping state.

On June 1, 1984 we conducted a seven station 18-cm VLBI observation of the 2016+112 gravitational lens system. Preliminary brightness distributions for A and B have been obtained via model fitting. Weak correlated flux density was detected in the C component region.

Gravitational interactions allow one to investigate the nature of matter in the universe independent of the properties that make it luminous. Much as studies of the dynamics of galaxies and clusters of galaxies have indicated the presence of dark matter, gravitational lensing provides an independent probe of the large scale distribution of dark matter in the universe.

Gravitational lens surveys are of cosmological interest because they provide a way to measure the gravitational field of both luminous and dark matter. Many of the other methods used to detect the presence of dark matter, such as studies of galaxy rotation curves and cluster dynamics, require that there be luminous objects in the gravitational field that act as tracers of the mass. This may introduce a selection effect. In constrast, in studies of gravitational lenses, the beacon we observe can be far (at distances of order one thousand Mpc) from the gravitational field. In this paper we describe a VLA survey designed to detect gravitational lensing on sub-arc second and arc second scales. We also present a preliminary result of the radio data: we find that the density of matter in the form of a uniform, comoving number density of 1011 to 1012M⊙ compact objects, luminous or dark, must be substantially less than the critical density.

For the diffusion branching process, we consider a method of inference that is essentially sequential in nature. The method allows us to simplify the natural sufficient statistics involved, and we are able to get their distributions quite easily by translating our problem into a standard problem in Brownian motion. Under certain circumstances, we are left with a complete sufficient statistic whose distribution belongs to an exponential family, and can therefore derive minimum variance unbiased estimators, etc.

We investigate the large-sample behaviour of maximum likelihood estimates (MLE's) of the parameters of a diffusion process, which is observed throughout continuous time. The results (limit normal distribution for the MLE and an asymptotic chi-squared likelihood ratio test) correspond exactly to classical asymptotic likelihood results, and follow easily from a central limit theorem for stochastic integrals.