329 research outputs found
Data and software for article: Taylor-West, J. J., Balmforth, N. J., and Hogg, A. J. (2024) Lava delta formation: Mathematical modelling and laboratory experiments
No full textExperimental and numerical data and scripts required to reproduce the results of Taylor-West, Balmforth, & Hogg 2024 "Lava delta formation: Mathematical modelling and laboratory experiments". Accepted to JGR: Earth Surfaces. doi:10.1029/2023JF00750
Data and software for article: Taylor-West, J. J., Balmforth, N. J., and Hogg, A. J. (2023) Lava delta formation: Mathematical modelling and laboratory experiments
No full textExperimental and numerical data and scripts required to reproduce the results of Taylor-West, Balmforth, & Hogg 2023 "Lava delta formation: Mathematical modelling and laboratory experiments". Submitted to JGR: Earth Surfaces
Dam-breaking seiches
No full textExperimental and theoretical models are used to explore the break of a
moraine dam by catastrophic erosional incision initiated by an
overtopping wave. The experiments are conducted in a rectangular tank
with an erodible barrier made from sand and grit. Theory combines
shallow-water hydrodynamics with an empirical model of erosion. The
models confirm that dams can be broken by a catastrophic incision.
However, the displacement wave does not break the dam in its first
passage but excites a long-lived seiche that repeatedly washes over the
dam. The Cumulative erosion of the downstream face by the overtopping
seiches eventually allows an incipient channel to form, and catastrophic
incision follows. Estimates are presented of the strength of the initial
disturbance required to break the dam, the maximum discharge and the
duration of the runaway incision
Dam breaking by wave-induced erosional incision
No full textWe present an experimental and theoretical study of whether a large
displacement wave can lead to catastrophic erosional incision of a
moraine damming a glacial lake. The laboratory experiments consist of
reservoirs held by barriers of granular materials in a glass tank; the
theoretical model combines the Saint-Venant equations of hydraulic
engineering with an empirical prescription for erosion. The results of
both the laboratory experiments and the numerical simulations indicate
that a single wave is generally unable to break the dam, but a
sufficiently large disturbance in an almost-filled reservoir creates a
seiche that can repeatedly overtop the dam. In such a case, the combined
effect of the multiple erosion events ultimately breaks the dam
A shocking display of synchrony
No full textThis article explores the Kuramoto model describing the synchronization of a population of coupled oscillators. Two versions of this model are considered: a discrete version suitable for a population with a finite number of oscillators, and a continuum model found in the limit of an infinite population. When the strength of the coupling between the oscillators exceeds a threshold, the oscillators partially synchronize. We explore the transition in the continuum model, which takes the form of a bifurcation of a discrete mode from a continuous spectrum. We use numerical methods and perturbation theory to study the patterns of synchronization that form beyond transition, and compare with the synchronization predicted by the discrete model. There are similarities with instabilities in ideal plasmas and inviscid fluids, but these are superficial
Turbulent mixing at a stable density interface : the variation of the buoyancy flux–gradient relation
No full textExperiments conducted on mixing across a stable density interface in a turbulent Taylor–Couette flow show, for the first time, experimental evidence of an increase in mixing efficiency at large Richardson numbers. With increasing buoyancy gradient the buoyancy flux first passes a maximum, then decreases and at large values of the buoyancy gradient the flux increases again. Thus, the curve of buoyancy flux versus buoyancy gradient tends to be N-shaped (rather than simply bell shaped), a behaviour suggested by the model of Balmforth et al. (J. Fluid Mech. vol. 428, 1998, p. 349). The increase in mixing efficiency at large Richardson numbers is attributed to a scale separation of the eddies active in mixing at the interface; when the buoyancy gradient is large mean kinetic energy is injected at scales much smaller than the eddy size fixed by the gap width, thus decreasing the eddy turnover time. Observations show that there is no noticeable change in interface thickness when the mixing efficiency increases; it is the mixing mechanism that changes. The curves of buoyancy flux versus buoyancy gradient also show a large variability for identical experimental conditions. These variations occur at time scales one to two orders of magnitude larger than the eddy turnover time scale
A hierarchy of coupled maps
No full textA large number of logistic maps are coupled together as a mathematical metaphor for complex natural systems with hierarchical organization. The elementary maps are first collected into globally coupled lattices. These lattices are then coupled together in a hierarchical way to form a system with many degrees of freedom. We summarize the behavior of the individual blocks, and then explore the dynamics of the hierarchy. We offer some ideas that guide our understanding of this type of system
Shallow viscoplastic flow on an inclined plane
No full textEvolving viscoplastic flows upon slopes are an important idealization of many flows in a variety of geophysical situations where yield stress is thought to play a role. For such models, asymptotic expansions suitable for slowly moving shallow fluid layers (lubrication theory) reduce the governing equations to a simpler problem in terms of the fluid thickness. We consider the version of the theory for fluids described by the Herschel-Bulkley constitutive law, and provide a variety of solutions to the reduced equation, both numerical and analytical. For extruded inclined domes, we derive the characteristic temporal behavior of measures of the dome's dimensions
Viscoplastic flow over an inclined surface
No full textWe review viscoplastic flow over inclined surfaces, focusing on constant-flux extrusions from small vents and the slumping of a fixed volume of material. Lubrication theory is used for shallow and slow flows to reduce the governing equations to a nonlinear diffusion-type equation for the local fluid depth; this model is used as the basis for exploration of the problem. Theory is compared to experiments. A number of complications and additional physical effects are discussed that enrich real situations
Dynamics of cooling viscoplastic domes
No full textA variety of problems in engineering and geology involve spreading cooling non-Newtonian fluids. If the fluid is relatively shallow and spreads slowly, lubrication-style asymptotic approximations can be used to build reduced models for the spreading dynamics. The centrepiece of such models is a nonlinear diffusion equation for the local fluid thickness, and ideally this should become coupled to a correspondingly simple equation determining the local temperature field. However, when heat diffuses relatively slowly as the fluid flows, we cannot usefully reduce the temperature equation, and the asymptotic reduction couples the local thickness equation to an advection diffusion equation that crucially involves diffusion in the vertical. We present an efficient computational algorithm for numerically solving this more complicated type of lubrication model, and describe a suite of solutions that illustrate the dynamics captured by the model in the case of an expanding Bingham fluid with a temperature-dependent viscosity. Based on these solutions, we evaluate two simpler models that further approximate the temperature equation: a vertically isothermal theory, and a ‘skin theory’. The latter is based on the integral-balance method of heat-transfe
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