Publications
354 results found
Balmforth NJ, Craster RV, 2001, Geophysical aspects of non-Newtonian fluid mechanics, Gran Combin Summer School on Geomorphological Fluid Mechanics, Publisher: SPRINGER-VERLAG BERLIN, Pages: 34-51, ISSN: 0075-8450
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- Citations: 25
Balmforth NJ, Burbidge AS, Craster RV, 2001, Shallow lava theory, Gran Combin Summer School on Geomorphological Fluid Mechanics, Publisher: SPRINGER-VERLAG BERLIN, Pages: 164-187, ISSN: 0075-8450
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- Citations: 14
Balmforth NJ, Craster RV, 2000, Dynamics of cooling domes of viscoplastic fluid, JOURNAL OF FLUID MECHANICS, Vol: 422, Pages: 225-248, ISSN: 0022-1120
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- Citations: 40
Craster RV, Williams DP, 2000, A reciprocity relation for fluid-loaded elastic plates that contain rigid defects, JOURNAL OF SOUND AND VIBRATION, Vol: 235, Pages: 655-670, ISSN: 0022-460X
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- Citations: 3
Williams DP, Craster RV, 2000, Cagniard-de Hoop path perturbations with applications to nongeometric wave arrivals, JOURNAL OF ENGINEERING MATHEMATICS, Vol: 37, Pages: 253-272, ISSN: 0022-0833
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- Citations: 4
Balmforth N, Burbidge AS, Craster RV, et al., 2000, Visco-plastic models of isothermal lava domes, JOURNAL OF FLUID MECHANICS, Vol: 403, Pages: 37-65, ISSN: 0022-1120
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- Citations: 92
Balmforth NJ, Craster RV, Kevrekidis PG, 2000, Being stable and discrete, PHYSICA D, Vol: 135, Pages: 212-232, ISSN: 0167-2789
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- Citations: 28
Craster RV, Matar OK, 2000, The role of dynamic modulation in the stability of viscoelastic flow down an inclined plane, Journal of Fluid Mechanics, Vol: 425, Pages: 213-233, ISSN: 0022-1120
In this study we have theoretically investigated the effect of parallel superposition of modulation on the stability of single-layer Newtonian and viscoelastic flows down an inclined plane. Specifically, a specifically, a spectrally based numerical technique in conjunction with Floquet theory has been used to investigate the linear stability of this class of flows. Based on these analyses we have demonstrated that parallel superposition of modulation can be used to stabilize or destabilize flow of Newtonian and viscoelastic fluids down an inclined plane. In general at low Reynolds number Re (i.e. O(1)) and in the limit of long and O(1) waves the effect of dynamic modulation on the stability of viscoelastic flows is much more pronounced; however, relatively large modulation amplitudes are required to achieve significant stabilization/destabilization. In addition, the dependence of the most dominant modulation frequencies on Re and the Weissenberg number We have been identified. Specifically, it has been shown that for Newtonian flows low-frequency modulations are destabilizing and the most dominant modulation frequency scales with 1/Re. On the other hand, for viscoelastic flows in the absence of fluid inertia low-frequency modulations are stabilizing and the most dominant modulation frequency scales with 1/We. In finite-Re viscoelastic flows the most dominant destabilizing modulation frequency scales with 1/Re while the most stabilizing modulation frequency scales with 1/WeRe. Finally, it has been demonstrated that the mechanism of both purely elastic and inertial instabilities in flows down an inclined plane is unchanged in the presence of dynamic modulation.
Balmforth N, Burbidge AS, Craster RV, 2000, Extrusion of isothermal and non-isothermal viscoplastic materials - evolving lava domes, XIIIth International Congress on Rheology, Pages: 4-4
Craster RV, Matar OK, 2000, Surfactant transport on mucus films, Journal of Fluid Mechanics, Vol: 425, Pages: 235-258
Craster RV, 2000, On effective resistivity and related parameters for periodic checkerboard composites, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, Vol: 456, Pages: 2741-2754, ISSN: 1364-5021
Craster RV, Smith SGL, 1999, A class of expansion functions for finite elastic plates in structural acoustics, JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, Vol: 106, Pages: 3128-3134, ISSN: 0001-4966
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- Citations: 3
Balmforth NJ, Craster RV, 1999, A consistent thin-layer theory for Bingham plastics, JOURNAL OF NON-NEWTONIAN FLUID MECHANICS, Vol: 84, Pages: 65-81, ISSN: 0377-0257
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- Citations: 150
Smith SGL, Craster RV, 1999, Numerical and asymptotic approaches to scattering problems involving finite elastic plates in structural acoustics, WAVE MOTION, Vol: 30, Pages: 17-41, ISSN: 0165-2125
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- Citations: 9
Craster RV, 1999, A class of Fuchsian differential equations, Centenary conference in honour of P. Ya Polubarinova-Kochina, Pages: 38-39
Balmforth NJ, Craster RV, Malham SJA, 1999, Unsteady fronts in an autocatalytic system, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, Vol: 455, Pages: 1401-1433, ISSN: 1364-5021
Balmforth NJ, Craster RV, 1999, Ocean waves and ice sheets, Journal of Fluid Mechanics, Vol: 395, Pages: 89-124, ISSN: 0022-1120
Williams DP, Craster RV, 1998, Scattering by small defects in the neighbourhood of a fluid-solid interface, IMA JOURNAL OF APPLIED MATHEMATICS, Vol: 61, Pages: 155-177, ISSN: 0272-4960
Craster RV, Hoang VH, 1998, Applications of Fuchsian differential equations to free boundary problems, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 454, Pages: 1241-1252, ISSN: 1364-5021
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- Citations: 18
Craster RV, 1998, Scattering by cracks beneath fluid-solid interfaces, JOURNAL OF SOUND AND VIBRATION, Vol: 209, Pages: 343-372, ISSN: 0022-460X
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- Citations: 6
Craster RV, 1997, The light fluid loading limit for fluid/solid interactions, EUROPEAN JOURNAL OF APPLIED MATHEMATICS, Vol: 8, Pages: 485-505, ISSN: 0956-7925
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- Citations: 2
Craster RV, 1997, The solution of a class of free boundary problems, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, Vol: 453, Pages: 607-630, ISSN: 1364-5021
Craster RV, Balmforth NJ, 1997, Synchronizing Moore and Spiegel, Chaos, Vol: 7, Pages: 738-752
Craster RV, 1997, The light fluid loading limit for fluid/solid interactions, European Journal of Applied Mathematics, Vol: 7, Pages: 485-506
Craster RV, Balmforth NJ, 1997, Stability of vorticity defects in viscoelastic shear flow, Journal of Non-Newtonian Fluid Mechanics, Vol: 72, Pages: 281-304
Craster RV, Atkinson C, 1996, On finite-length cracks and inclusions in poroelasticity, Quarterly Journal of Mechanics and Applied Mathematics, Vol: 49, Pages: 310-332, ISSN: 0033-5614
A procedure is devised for the asymptotic solution of finite-length crack and inclusion problems under arbitrary time-dependent stress, pore pressure or pressure gradient loadings in porous elastic materials. The stress-intensity factors are identified explicitly as an expansion in real time for model problems involving uniformly loaded cracks. In the most general case this involves matched asymptotic expansions and rescalings that take advantage of the singular perturbation nature of the governing equations. The problems are written in terms of coupled Cauchy singular integral equations containing a small parameter; these can be combined to form a single subsidiary integral equation. This approach is used to split the problems into pieces driven by elastic, or pore-pressure, dominated solutions. Outer solutions that are driven by elastic solutions and eigensolutions are identified; these are matched to inner problems. The inner problems require the solution of a system of coupled integral equations; these are formulated in terms of functional equations. Fortunately the system uncouples and allows the inner solutions to be found explicitly. The pore-pressure driven pieces are deduced, to leading order, by a direct rescaling.
Craster RV, Atkinson C, 1996, On finite-length cracks and inclusions in poroelasticity, QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, Vol: 49, Pages: 311-335, ISSN: 0033-5614
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- Citations: 3
Craster RV, Atkinson C, 1996, On finite-length cracks and inclusions in poroelasticity, Quarterly Journal of Mechanics and Applied Mathematics, Vol: 49, Pages: 311-335, ISSN: 0033-5614
A procedure is devised for the asymptotic solution of finite-length crack and inclusion problems under arbitrary time-dependent stress, pore pressure or pressure gradient loadings in porous elastic materials. The stress-intensity factors are identified explicitly as an expansion in real time for model problems involving uniformly loaded cracks. In the most general case this involves matched asymptotic expansions and rescalings that take advantage of the singular perturbation nature of the governing equations. The problems are written in terms of coupled Cauchy singular integral equations containing a small parameter; these can be combined to form a single subsidiary integral equation. This approach is used to split the problems into pieces driven by elastic, or pore-pressure, dominated solutions. Outer solutions that are driven by elastic solutions and eigensolutions are identified; these are matched to inner problems. The inner problems require the solution of a system of coupled integral equations; these are formulated in terms of functional equations. Fortunately the system uncouples and allows the inner solutions to be found explicitly. The pore-pressure driven pieces are deduced to leading order, by a direct rescaling.
Craster RV, 1996, Wavefront expansions for pulse scattering by a surface inhomogeneity, Quarterly Journal of Mechanics and Applied Mathematics, Vol: 49, Pages: 656-674, ISSN: 0033-5614
Much recent interest has arisen in the coupled dynamics of fluid-solid interfaces, mainly with regard to the use of the acoustic microscope as a valuable technique for material characterization and the detection of surface, and subsurface, flaws; there is also interest in structural acoustics and geophysical applications. The majority of recent work has dealt with time-harmonic waves; in this paper solutions for transient disturbances are developed and analysed in detail. The resulting fluid and solid responses are found in closed form allowing specific wavefronts to be identified and explicit results are given. Wavefront expansions for the head waves and cylindrical wave in the fluid are found explicitly together with the disturbance generated by the leaky Rayleigh wave; these are the dominant fluid responses detected experimentally and such exact solutions will be of value. The limit of light fluid loading is examined separately; it is shown that the leading-order fluid-solid results are reconstructed by considering simpler problems where the fluid loading is taken to be absent. An unambiguous interpretation of the disturbance in the fluid created by the leaky Rayleigh wave is given in this light fluid-loading limit.
Craster RV, 1996, A canonical problem for fluid-solid interfacial wave coupling, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 452, Pages: 1695-1711, ISSN: 1364-5021
Wave-coupling involving defects or obstacles on fluid-solid interfaces is of recurrent interest in geophysics, transducer devices, structural acoustics, the acoustic microscope and related problems in non-destructive testing. Most theoretical analysis to date has, in effect, involved stress or pressure loadings along the interface, or scattering from surface inhomogeneities, that ultimately result in unmixed boundary value problems. A more complicated situation occurs if a displacement is prescribed over a region of the interface, and the rest of the interface is unloaded (or stress/pressure loaded); the resulting boundary value problem is mixed. This occurs if a rigid strip lies along part of the interface and will introduce several complications due to the presence of the edge. For simplicity a lubricated rigid strip is considered, i.e. it is smoothly bonded to the elastic substrate. To consider such mixed problems, e.g. the vibration of a finite rigid strip or diffraction by a finite strip, a canonical semi-infinite problem must be solved. It is the aim of this paper to solve the canonical problem associated with the vibrating strip exactly, and extract the form of the near strip edge stress, and displacement fields, and the far-field directivities associated with the radiated waves. The near strip edge results are checked using an invariant integral based upon a pseudo-energy momentum tensor and gives a useful independent check upon this piece of the analysis. The directivities will be useful in formulating a ray theory approach to finite strip problems. An asymptotic analysis of the solution, in the far field, is performed using a steepest descents approach and the far-field directivities are found explicitly. In the light fluid limit a transition analysis is required to determine uniform asymptotic solutions in an intermediate region over which the leaky Rayleigh wave will have an influence. In a similar manner to related work on the acoustic behaviour of flui
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