124 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
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
Tidal Conversion by Supercritical Topography
No full textCalculations are presented of the rate of energy conversion of the barotropic tide into internal gravity waves above topography on the ocean floor. The ocean is treated as infinitely deep, and the topography consists of periodic obstructions; a Green function method is used to construct the scattered wavefield. The calculations extend the previous results of Balmforth et al. for subcritical topography (wherein waves propagate along rays whose slopes exceed that of the topography everywhere), by allowing the obstacles to be arbitrarily steep or supercritical (so waves propagate at shallower angles than the topographic slopes and are scattered both up and down). A complicated pattern is found for the dependence of energy conversion on , the ratio of maximum topographic slope to wave slope, and the ratio of obstacle amplitude and separation. This results from a sequence of constructive and destructive interferences between scattered waves that has implications for computing tidal conversion rates for the global ocean.National Science Foundation (Award 0645529)United States. Office of Naval Research (Grant N00014-0501-0575
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
Damping of surface waves by a floating dissipative plate
No full textThis thesis explores the damping and cessation of surface waves in an inviscid layer, particularly under the influence of a floating, dissipative plate. Experimental results [39, 40, 70] indicate that when a floating particle layer is present, surface waves will come to rest in a finite time. In particular, the cessation process experiences a transition from exponential decay to finite-time decay in a power-law manner when wave amplitudes are sufficiently small. This pattern potentially resembles a jamming effect [70].
To theoretically elucidate the cessation time of surface waves and the shift in wave attenuation laws, we construct a two-layer model. The model combines inviscid shallow water theory with plate theory under the long-wavelength limit. The top layer is treated as a plate, as we establish that it has constant thickness. For plate theory, this model characterizes the top plate using a range of models. This includes a viscoplastic plate modeled following the Herschel-Bulkley constitutive law. An exploration of the en- ergetics captured by the model suggests that waves decay to rest in a finite time. This result is confirmed using a combination of approximate, numer- ical, and asymptotic solutions to the model equations. In the limit that the plate behaves like a perfectly plastic material, the sloshing motions take the form of triangular waves with bending restricted to narrow viscoplastic hinges. Additionally, alternative models are considered for a more accurate explanation of the decaying pattern observed experimentally [39, 40, 70]. These alternatives include One-Way Bingham (OWB) models, a two-phase model, and Boyer et al.’s model [11]. OWB models address the impact of particle dilation and compaction on Bingham plate bending by modulating the yield stress and viscous force. For the two-phase model, we illustrate that scaling consistency is ensured when the difference between the total plate density and the fluid phase density is small. In addition, Boyer et al.’s model is incorporated into the two-phase scheme for further insights.Science, Faculty ofMathematics, Department ofGraduat
A study of the Saffman-Taylor instability in viscoplastic fluids
No full textThis thesis aims to explore and understand the Saffman-Taylor instability at the interface of a Hershel-Bulkley fluid and air. We describe the flow in a Hele-Shaw cell theoretically and experimentally. For our theoretical analysis, we follow the usual Hele-Shaw approximations for incompressible flows with a Herschel-Bulkley constitutive law. We extend this model by allowing the fluid to slip on the smooth walls of the cell. We conduct a linear stability analysis for both planar and circular geometries and predict that effective slip stabilizes the interface. We also use numerical computations to examine the non-linear regime of a single finger in the planar geometry. We find that slip generates wider fingers and makes the plugged-up area at the roots of the fingers smaller and appear at later times. We conduct experiments using corn syrup as a control case and aqueous suspensions of Carbopol as a model Herschel-Bulkley fluid. The fluids are pumped into a Hele-Shaw cell through a circular vent, forming an initial disk in the cell. Then, we either pump air into the center of the disk, creating an expanding annulus, or we withdraw the disk through the vent. In both cases, the interface is in an unstable Saffman-Taylor configuration causing fingers to appear. We look at the effect of the type of cell wall, the gap size, the flux and the size of the initial disk. The instability and the observed patterns are very different between a cell with smooth or rough walls, confirming our theoretical prediction on the influence of effective slip. The trends with the other parameter variations are in reasonable agreement with the theoretical predictions.Science, Faculty ofMathematics, Department ofGraduat
2004 program of study : tides
No full textThe summer of 2004 saw the GFD program tackle “Tides”. Myrl Hendershott (Scripps
Institution of Oceanography) gave a fabulous introduction to the subject in the first week
of the course, laying the foundations from astronomy and classical geophysical
fluid dynamics. In the second week, Chris Garrett (University of Victoria) admirably followed
up with recent developments on the subject, including the recent observations from satellite
altimetry, their implications to mixing and circulation, and even a memorable lecture on
the noble theme of how we might solve the world's energy crisis. The principal lectures
proved unusually popular this summer, and the seminar room at Walsh often overflowed in the
first two weeks.
Following on from the lectures, the seminar schedule of the summer covered in greater
detail the oceanographic issues with which researchers are actively grappling. We also
heard about related problems regarding atmospheric, planetary and stellar tides, together
with the usual mix of topics on GFD in general.
The summer once again featured a lecture for the general public in the Woods Hole
area. Carl Wunsch delivered a very well received lecture entitled “Climate Change Stories”,
in which he gave an impression of how scientists generally believe our climate is currently
changing, whilst simultaneously urging caution against some of the more outrageous and
exaggerated claims. The lecture was held at Lilly Auditorium, thanks to the hospitality
of the Marine Biology Laboratory. The reception following the lecture was enjoyed by
all.
Neil Balmforth and Stefan Llewellyn Smith acted as Co-Directors for the summer.
Janet Fields, Jeanne Fleming and Penny Foster provided the administrative backbone to
the Program, both during the summer and throughout the year beforehand. As always,
we were grateful to the Woods Hole Oceanographic Institution for the use of Walsh Cottage,
and Keith Bradley's solid service could not be overlooked. Shilpa Ghadge and Shreyas
Mandre are to be thanked for their part in comforting the fellows, developing the summer's
proceedings volume (available on the GFD web site) and for running the computer network.Funding was provided by the Office of Naval Research under Contract No. N00014-04-1-0157 and the National Science Foundation under Grant No. OCE-0325296
Optimal material absorption of a model oyster
No full textOysters are suspension feeders which rely on actively moving fluid into and through themselves for sustenance. This investment of energy suggests a benefit to pumping fluid and consequently presents the question: To what degree it improves filtration rates. To investigate this, we develop a simplified model of the animal where the inner boundary of an annulus represents the oyster and the outer boundary represents a wall. The fluid flow is generated by a prescribed radial velocity condition on the inner boundary and material interaction with the model animal is modulated by a matching boundary condition in concentration. We show, through analysis of the model, that the material flux into the model animal is invariant under reversing the direction of flow and particular reflections of the geometry when the flow is in steady-state. In numerical simulations, we explore both the low and high Reynolds number limits for the flow. The low Reynolds number model (Stokes flow) produces material fluxes closest to the full model and the high Reynolds number model (potential flow) shows more similar optimal configurations; including both viscosity and inertia in the flow results in the highest amount of material capture as turbulence mixes the domain more effectively. Despite their limitations, Stokes flow and potential flow facilitate an adjoint formulation. In these cases, we use gradient-based optimization using the adjoint to find the boundary conditions that maximize material capture.Science, Faculty ofMathematics, Department ofGraduat
Liquid jet impingement on a moving wall
No full textThis research studies the impingement of a free surface Newtonian liquid jet on a dry solid moving wall using theoretical, numerical and experimental methods. The study focus mainly on the parameter range of jet Reynolds numbers 100< Reⱼ <1000 and the wall-to-jet velocity ratios 0.04<uw/vⱼ <30, where the effect of surface tension is negligible, and the major impingement regimes are splash and deposition, although cases with a wider parameter range are probed through CFD or experiments to identify the limit of the proposed theory.
First, the 2D (slot or planar) jet impingement problem is explored. A regime diagram based on Reⱼ and uw/vⱼ is established using CFD, and four regimes are identified: splash, steady deposition with a heel, steady deposition with a heel with bumps, and unsteady deposition.
A semi-empirical model based on the boundary layer theory and the Karman-Pohlhausen averaging scheme is developed to describe the flow of the steady heel regime. The model provides full solutions for the interface profile, boundary layer thickness, and the velocity field for a given the parameter setting of Reⱼ and uw/vⱼ, and the model predictions agree well with CFD. A second model using the time-dependent boundary-layer equations is developed to rationalize the spreading dynamics of the shallow film, which provides explanations on why the steady state disappears when uw/vⱼ < 2 or when uw/vⱼ is too large.
Then, the study advances to the 3D (circular) jet impingement problem. Experiments are conducted using a custom apparatus with high speed imaging technique that map out the regime diagram based on Reⱼ and uw/vⱼ and measure the geometry of the impinging jet. The experiments are complemented with numerical simulations, which reveal the anatomy of the spreading film (lamella) and aid the development of a theoretical model. The model predicts the dimensions of the lamella (the length of the upstream heel and the width of the downstream lamella), and that the shape takes a universal form when scaled by one of these distances. These predictions agree well with the experiments and simulations provided that a lamella exists.Applied Science, Faculty ofMechanical Engineering, Department ofGraduat
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