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RESEARCH: FLUID DYNAMICS AND NONLINEAR WAVES
My main research area is Nonlinear Waves, with an emphasis on applications in geophysical fluid dynamics, theoretical oceanography and dynamical meteorology. The mathematics involved is pertubation techniques and asymptotic analyses of partial differential equations, combined with numerical simulations.- Current Projects:
- INTERNAL SOLITARY WAVES. Theoretical and numerical studies of the generation, propagation and dissipation of internal solitary waves and undular bores in the atmosphere and ocean. The dynamics and stability of large-amplitude waves, especially with vortex cores.
- 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.
- COASTAL OCEAN DYNAMICS: Theoretical and numerical studies in coastal oceanography, emphasising the role of coastally-trapped waves, coastal current stability and eddy formation.
- 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.
- 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 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.
- Helfrich, K. R. and Grimshaw, R.H.J. (2008). Nonlinear disintegration of the internal tide. J. Phys. Ocean., 38, 686-701.
- Grimshaw, R. and Christodoulides, P. (2008). Gap-solitons in a three-layered stratified flow. Wave Motion, 5, 758-769.
- Grimshaw, R. and Helfrich. K.R. (2008). Long-time solutions of the Ostrovsky equation. Stud. Appl. Math., 121. 71-88.
- Grimshaw, R. H. J., Zhang D.-H. and Chow , K. W. (2009). Transcritical flow over a hole. Stud. Appl. Math., 122, 235-248.
- Derzho, O. and Grimshaw, R. H. J. (2009). On vorticity waves propagating between critical layers. J. Fluid Mech., 629, 161-171.
- El, G. A., Grimshaw, R. H. J. Grimshaw and Smyth, N. F. (2009). Transcritical shallow-water flow past topography: finite-amplitude theory. J. Fluid Mech., 640, 187-214.
- Nitsche, M., Weidman, P.D, Grimshaw,R., Ghrist, M. and Fornberg, B. (2010). Evolution of solitary waves in a two-pycnocline system. J. Fluid Mech., 642, 235-277.
- Sutyrin, G. G. and Grimshaw, R. (2010). Generation of coastally trapped waves and secondary cyclones by an eddy approaching shelf topography. Ocean Modelling, 32, 25-35.
- Grimshaw, R., Slunyaev, A. and Pelinovsky, E. (2010) Generation of solitons and breathers in the extended Korteweg-de Vries equation with positive cubic nonlinearity. Chaos, 20, 013102 (11 pages).
- Grimshaw, R. and Christodoulides, P. (2010). Steady gap solitons in a coupled Korteweg-de Vries system: a dynamical systems approach. Physica D, 239 , 635-639.
- Grimshaw, R., Pelinovsky, E. and Talipova, T. (2010) Non-reflecting internal wave beam propagation in the deep ocean. J. Phys. Ocean., 40, 802-813.
- Grimshaw, R. Pelionvsky, E. Talipova, T. and Sergeeva, A. (2010) Rogue internal waves in the ocean: long wave model. Eur. J. Phys., 185, 195Ð208.
- Maderich, V., Talipova, T., Grimshaw, R., Terletska, E., Brovchenko, I., Pelinovsky, E., and Choi, B.H (2010) Interaction of a large amplitude interfacial solitary wave of depression with a bottom step, Phys. Fluids, 22, 076602 (12 pages).
- Grimshaw, R., Pelinovsky, E., Talipova, T. and Kurkina, A. (2010) Internal solitary waves: propagation, deformation and disintegration, Nonlinear Processes in Geophysics, 17, 633-649.
- Grimshaw, R. (2010) Transcritical flow past an obstacle. ANZIAM J., 52, 1-25.
- Magalhaes, J. M., Araujo, I.B., da Silva, J. C. B., Grimshaw, R., Davis, K., and Pineda, J. (2011) Atmospheric gravity waves in the Red Sea: a new hotspot, Nonlinear Processes in Geophysics, 18, 71-79.
- Grimshaw, R.H.J. and Annenkov, S. Y. (2011) Water wave packets over variable depth, Stud.Appl. Maths., 126, 409-427.
- Ee, B. K., Grimshaw, R. H. J., Chow, K. W. and Zhang, D-H. (2011) Steady transcritical flow over an obstacle: parametric map of solutions of the forced extended Korteweg-de Vries equation. Phys. Fluids}, 21, 046602 (11 pages).
- Grimshaw, R., Helfrich, K. R. and Scotti, A. (2011) Preface: Large amplitude internal waves in the coastal ocean. Nonlinear Processes in Geophysics, 18, 653-655.