Publications
31 results found
Capper SD, Moore DR, 2006, On High Order MIRK Schemes and Hermite-Birkhoff Interpolants, Journal of Numerical Analysis, Industrial and Applied Mathematics, Vol: 1, Pages: 27-47
Capper SD, Cash JD, Moore DR, 2006, Lobatto - Obrechkoff Formulae for 2nd Order Two-POint Boundary Value Problems, Journal of Numerical Analysis, Industrial and Applied Mathematics, Vol: 1, Pages: 13-25
Schwartz SJ, Zane S, Wilson RJ, et al., 2005, The Gamma-Ray Giant Flare from SGR 1806-20: Evidence of Crustal Cracking via Initial Timescales, \apjl, Vol: 627, Pages: L129-L132-L129-L132
Cash JR, Moore DR, 2004, High-order interpolants for solutions of two-point boundary value problems using MIRK methods, COMPUTERS & MATHEMATICS WITH APPLICATIONS, Vol: 48, Pages: 1749-1763, ISSN: 0898-1221
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- Citations: 4
Gibbon JD, Moore DR, Stuart JT, 2003, Exact, infinite energy, blow-up solutions of the three-dimensional Euler equations, NONLINEARITY, Vol: 16, Pages: 1823-1831, ISSN: 0951-7715
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- Citations: 28
Cash JR, Moore DR, Sumarti N, et al., 2003, A highly stable deferred correction scheme with interpolant for systems of nonlinear two-point boundary value problems, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, Vol: 155, Pages: 339-358, ISSN: 0377-0427
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- Citations: 5
Cash JR, Garcia MP, Moore DR, 2002, Mono-implicit Runge-Kutta formulae for the numerical solution of second order nonlinear two-point boundary value problems, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, Vol: 143, Pages: 275-289, ISSN: 0377-0427
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- Citations: 2
Aston JAG, Chan WL, Moore DR, et al., 2000, Radiative transfer in a static model atmosphere, GEOPHYSICAL AND ASTROPHYSICAL FLUID DYNAMICS, Vol: 93, Pages: 253-287, ISSN: 0309-1929
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- Citations: 1
Moore DR, Weiss NO, 2000, Resonant interactions in thermosolutal convection, Proceedings of the Royal Society a-Mathematical Physical and Engineering Sciences, Vol: 456, Pages: 39-62, ISSN: 1364-5021
When convection occurs in a finite box, successive modes become unstable as the Rayleigh number is increased, giving rise to branches of nonlinear solutions that are linked by mixed-mode branches emerging from Hopf, transcritical or pitchfork bifurcations. The fundamental Inode, in particular, gives rise to resonant interactions. Several specific examples of these generic features have already been described. Here we study resonant interactions in two-dimensional thermosolutal. convection (with point symmetry imposed), where behaviour is enriched by the presence of oscillations and of subcritical steady convection. Steady m-roll solutions are obtained numerically and their stability properties are investigated by computing the leading real and complex eigenvalues. We find that the branch of fundamental m = 1 solutions for a box with aspect ratio lambda = 1.5 develops loops that touch the m = 3 branch in transcritical bifurcations. As lambda is reduced these loops detach themselves from the m = 1 branch and eventually join the stacked m = 2 branch. Increasing lambda, on the other hand, leads to complicated triple resonances involving m = 1, m = 3 and m = 5 solutions. These resonant interactions are associated with pattern selection and the transfer of stability from single-roll to multiple-roll solutions in wider boxes.
Chan WL, Moore DR, Aston JAG, 2000, Linear convective instability in a radiating model atmosphere, GEOPHYSICAL AND ASTROPHYSICAL FLUID DYNAMICS, Vol: 93, Pages: 289-322, ISSN: 0309-1929
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- Citations: 2
Wallcraft AJ, Moore DR, 1997, The NRL layered ocean model, Parallel Computing, Vol: 23, Pages: 2227-2242, ISSN: 0167-8191
Moore DR, Weiss NO, Wilkins JM, 1991, ASYMMETRIC OSCILLATIONS IN THERMOSOLUTAL CONVECTION, Journal of Fluid Mechanics, Vol: 233, Pages: 561-585, ISSN: 0022-1120
Thermosolutal convection provides a testbed for applications of nonlinear dynamics to fluid motion. If the ratio of solutal to thermal diffusivity is small and the solutal Rayleigh number R(S) is large, instability sets in at a Hopf bifurcation as the thermal Rayleigh number R(T) is increased. For two-dimensional convection in a rectangular box the fundamental mode is a single roll with point symmetry about its axis. The symmetries of periodic and steady solutions form an eighth-order group with invariant subgroups that describe pure single-roll and multiroll solutions. A systematic numerical investigation reveals a rich variety of spatiotemporal behaviour in the regime where R(S) >> R(T) - R(S) > 0. Point symmetry is broken and there is a branch of spatially asymmetric periodic solutions. These mixed-mode oscillations lose their temporal symmetry in a subsequent bifurcation, followed eventually by a transition to chaos. The numerical experiments can be interpreted by relating the physical form of the solutions to an appropriate bifurcation structure.
KNOBLOCH E, MOORE D, 1991, CHAOTIC TRAVELING-WAVE CONVECTION, EUROPEAN JOURNAL OF MECHANICS B-FLUIDS, Vol: 10, Pages: 37-42, ISSN: 0997-7546
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- Citations: 12
Moore DR, Weiss NO, Wilkins JM, 1990, SYMMETRY-BREAKING IN THERMOSOLUTAL CONVECTION, Physics Letters A, Vol: 147, Pages: 209-214, ISSN: 0375-9601
Moore DR, Weiss NO, 1990, DYNAMICS OF DOUBLE CONVECTION, Philosophical Transactions of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, Vol: 332, Pages: 121-134
Moore DR, Weiss NO, Wilkins JM, 1990, THE RELIABILITY OF NUMERICAL EXPERIMENTS - TRANSITIONS TO CHAOS IN THERMOSOLUTAL CONVECTION, Nonlinearity, Vol: 3, Pages: 997-1014, ISSN: 0951-7715
Knobloch E, Moore DR, 1990, MINIMAL MODEL OF BINARY FLUID CONVECTION, Physical Review A, Vol: 42, Pages: 4693-4709, ISSN: 1050-2947
Knobloch E, Moore DR, 1988, LINEAR-STABILITY OF EXPERIMENTAL SORET CONVECTION, Physical Review A, Vol: 37, Pages: 860-870, ISSN: 1050-2947
Lennie TB, McKenzie DP, Moore DR, et al., 1988, THE BREAKDOWN OF STEADY CONVECTION, Journal of Fluid Mechanics, Vol: 188, Pages: 47-85, ISSN: 0022-1120
Knobloch E, Moore DR, Toomre J, et al., 1986, TRANSITIONS TO CHAOS IN TWO-DIMENSIONAL DOUBLE-DIFFUSIVE CONVECTION, Journal of Fluid Mechanics, Vol: 166, Pages: 409-448, ISSN: 0022-1120
Moore DR, Toomre J, Knobloch E, et al., 1983, PERIOD DOUBLING AND CHAOS IN PARTIAL-DIFFERENTIAL EQUATIONS FOR THERMOSOLUTAL CONVECTION, Nature, Vol: 303, Pages: 663-667, ISSN: 0028-0836
Galloway DJ, Moore DR, 1979, Axisymmetric convection in the presence of a magnetic field, Geophysical & Astrophysical Fluid Dynamics, Vol: 12, Pages: 73-105, ISSN: 0309-1929
Jones CA, Moore DR, 1978, The stability of axisymmetric convection, Geophysical & Astrophysical Fluid Dynamics, Vol: 11, Pages: 245-270, ISSN: 0309-1929
Graham E, Moore DR, 1978, ONSET OF COMPRESSIBLE CONVECTION, Monthly Notices of the Royal Astronomical Society, Vol: 183, Pages: 617-632, ISSN: 0035-8711
Jones CA, Moore DR, Weiss NO, 1976, AXISYMMETRIC CONVECTION IN A CYLINDER, Journal of Fluid Mechanics, Vol: 73, Pages: 353-388, ISSN: 0022-1120
Gough DO, Moore DR, Spiegel EA, et al., 1976, CONVECTIVE INSTABILITY IN A COMPRESSIBLE ATMOSPHERE .2, Astrophysical Journal, Vol: 206, Pages: 536-542, ISSN: 0004-637X
Huppert HE, Moore DR, 1976, NONLINEAR DOUBLE-DIFFUSIVE CONVECTION, Journal of Fluid Mechanics, Vol: 78, Pages: 821-854, ISSN: 0022-1120
Moore DR, Weiss NO, 1973, NONLINEAR PENETRATIVE CONVECTION, Journal of Fluid Mechanics, Vol: 61, Pages: 553-581, ISSN: 0022-1120
Moore DR, Peckover RS, Weiss NO, 1973, DIFFERENCE METHODS FOR TIME-DEPENDENT 2-DIMENSIONAL CONVECTION, Computer Physics Communications, Vol: 6, Pages: 198-220, ISSN: 0010-4655
Moore DR, Weiss NO, 1973, 2-DIMENSIONAL RAYLEIGH-BENARD CONVECTION, Journal of Fluid Mechanics, Vol: 58, Pages: 289-312, ISSN: 0022-1120
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