Professor Roger Grimshaw: Homepage

Contact me at:

Department of Mathematical Sciences

Loughborough University

Loughborough, LE11 3TU

Ph: +44-1509-223480

Fax: +44-1509-223969

Email: R.H.J.Grimshaw@lboro.ac.uk

RESEARCH: FLUID DYNAMICS AND NONLINEAR WAVES

Nonlinear waves, with an emphasis on applications in geophysical fluid dynamics, theoretical oceanography and dynamical meteorology. There is a particular interest in solitons and soliton equations, internal solitary waves in the ocean and atmosphere, vortices and ocean eddies, and related topics. The mathematics involved is pertubation techniques and asymptotic analyses of partial differential equations, combined with numerical simulations.

Current Projects:

FLOW INTERACTION WITH TOPOGRAPHY: The generation of solitary-like waves and undular bores by critical (or resonant) flow over topography. Applications to stratified flows in the ocean and atmosphere.
LARGE AMPLITUDE WAVES: Numerical and analytical methods for the study of the shape and stability of large amplitude waves, including those with vortex cores. Applications to internal waves, and planetary-scale waves.
COASTAL OCEAN DYNAMICS: Theoretical and numerical studies in coastal oceanography, emphasising the role of coastally-trapped waves, coastal current stability and eddy formation.
INTERNAL GRAVITY WAVES. Theoretical and numerical studies of the generation, propagation and dissipation of internal gravity waves in the atmosphere and ocean, emphasising wave-breaking and the interaction with the background wind and current.
VORTEX DYNAMICS: Theoretical and numerical studies of vortices in rotating and stratified fluid flows, with applications to meso-scale meteorology and oceanography.
EXPONENTIAL ASYMPTOTICS: The detection and calculation of exponentially small terms in asymptotic expansions, with application to the study of nonlinear waves in a variety of physical contexts.

Sample of Recent Publications

El, G.A., Grimshaw, R.H.J. and Pavlov, M.V. (2001). Integrable shallow water equations and undular bores. Stud. Appl. Math., 107, 157-186.
Reznik, G.M. and Grimshaw, R.H.J. (2001). Ageostrophic dynamics of an intense localised vortex on the $\beta$ -plane. J. Fluid Mech., 443, 351-376.
Grimshaw, R. and Christodoulides, P. (2001). Short-wave instability in a three-layered stratified shear flow. Q.J. Mech. Appl. Math., 54. 375-388.
Grimshaw, R.H.J., Kuznetsov, E.A., and Shapiro, E.G. (2001) The two-parameter soliton family for the interaction of a fundamental and its second harmonic. Physica D, 152-153, 325-339.
Grimshaw, R., Pelinovsky, D., Pelinovsky, E. and Talipova, T. (2001). Wave group dynamics in weakly nonlinear long-wave models. Physica D, 159, 35-57.
Grimshaw, R. and Skyrnnikov, Y. (2002). Long-wave instability in a three-layer stratified shear flow. Stud. Appl. Math., 108, 77- 88.
Derzho, O. and Grimshaw, R. (2002). Solitary waves with recirculation zones in axisymmetric flows. J. Fluid Mech., 464, 217-250.
Grimshaw, R., Malomed, B. and Gottwald, G. (2002). Singular and regular gap solitons between three dispersion curves. Phys. Rev. E, 65, 066606 (14pp).
Grimshaw, R., Pelinovsky, E. and Poloukhina, O. (2002) Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface. Nonlinear Processes in Geophysics, 9, 221-235.
Grimshaw, R.H.J., Chan, K.H. and Chow, K.W. (2002) Transcritical flow of a stratified fluid: the forced extended Korteweg-de Vries model. Phys. Fluids, 14, 755-774.
Reznik, G.M. and Grimshaw, R. (2002). Nonlinear geostrophic adjustment in the presence of a boundary. J. Fluid Mech., 471, 257-283.
Grimshaw, R. and Iooss, G. (2003). Solitary waves of a coupled Korteweg-de Vries system. Mathematics and Computers in Simulation, 62, 31 - 40.
El, G.A. and Grimshaw, R. (2003). Generation of undular bores in the shelves of slowly-varying solitary waves. Chaos, 12, 1015-1026.
Grimshaw, R., Pelinovsky, E. and Talipova, T. (2003) Damping of large-amplitude solitary waves. Wave Motion, 37, 351-364.
Grimshaw, R., Pelinovsky, D., Pelinovsky, E. and Slunyaev, A. (2002). The generation of large-amplitude solitons from an initial disturbance in the extended Korteweg-de Vries equation. Chaos, 12, 1070-1076.
Grimshaw, R.H.J. and Khusnutdinova, K.R. (2004). The effect of bubbles on internal waves. J. Phys. Ocean., 34, 477-489.
Broutman, D., Grimshaw, R.H.J. and Eckermann, S.D. (2004). On internal waves in a Lagrangian reference frame. J. Atmos. Sci., 61, 1308-1313.
Grimshaw, R., Pelinovsky, E., Talipova, T. and Kurkin, A. (2004). Simulation of the transformation of internal solitary waves on oceanic shelves. J. Phys. Ocean., 34, 2774-2779.
Maleewong, M., Asavanant, J. and Grimshaw, R. (2005). Free surface flow under gravity and surface tension due to an applied pressure distribution. I Bond number greater than one-third. Theor. Comp. Fluid Dyn., 19, 237-252.
Maleewong, M., Asavanant, J. and Grimshaw, R. (2005). Free Surface Flow under Gravity and Surface Tension due to an Applied Pressure Distribution. II Bond number less than one-third. European J. Mechanics B/Fluids, 24. 502-521.
Fochesato, C., Dias, F. and Grimshaw, R. (2005). Generalized solitary waves and fronts. Physica D, 210, 96-117.
Griffiths, S.D., Grimshaw, R.H.J. and Khusnutdinova, K.R. (2006). Modulational instability of two pairs of counter-propagating waves and energy exchange in two-component media. Physica D, 214, 1-24.
El, G.A. , Grimshaw, R.H.J. and Kamchatnov, A.M. (2005). Analytic model for a frictional shallow-water undular bore. Chaos, 15, 037102 (13 pages).
El, G.A., Grimshaw, R. H.J. and Smyth, N.F. (2006). Unsteady undular bores in fully nonlinear shallow-water theory. Phys. Fluids, 18, 027104 (17 pages).
Griffiths, Stephen D. and Grimshaw, R.H.J. (2007). Internal tide generation at the continental shelf modelled using a modal decomposition: two-dimensional results. J. Phys. Ocean., 37, 428-451.
Grimshaw, R. (2007). Internal solitary waves in a variable medium. Gesellschaft fur Angewandte Mathematik, 30, 96-109.
Grimshaw, R. H. J., El, G. A. and Kamchatnov, A. M. (2007). Evolution of solitary waves and undular bores in shallow-water flows over a gradual slope with bottom friction. J. Fluid Mech., 585, 213-244.
Grimshaw, R. H. J., Zhang D.-H. and Chow , K. W. (2007). Generation of solitary waves by transcritical flow over a step. J. Fluid Mech., 587, 235-354.
Akylas, T. R., Grimshaw, R. H. J., Clarke, S. R. and Tabaei, A. (2007) Reflecting tidal wave beams and local generation of solitary waves in the ocean thermocline. J. Fluid Mech., 593, 297-313.
Grimshaw, R., Pelinovsky, E. and Talipova, T. (2007). Modeling internal solitary waves in the coastal ocean. Surveys in Geophysics, 28, 273-298.

All publications, brief CV