Dr Simon Clarke

Research Overview

Evolution of non-linear waves and their application to geophysical flows. Topics of research in this field include; effect of shear of finite-amplitude waves, trapping of non-linear internal waves, internal solitary waves with oscillatory tails, dynamics of finite-amplitude interfacial waves, non-linear critical layers, non-linear wave groups, numerical methods for nonlinear waves.

Selected Publications

[1] Clarke, Simon R ; Johnson, Edward R. "The weakly nonlinear limit of forced Rossby waves in a stepped channel". In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2001 ; Vol. 457. pp. 2361 - 2378.

[2] Cullen, Andrew C. ; Clarke, Simon R. "A fast, spectrally accurate homotopy based numerical method for solving nonlinear differential equations". In: Journal of Computational Physics. 2019 ; Vol. 385. pp. 106-118. https://doi.org/10.1016/j.jcp.2019.01.057

[3] Korostil, Igor Andriy ; Clarke, Simon Rex. "Fourth-order numerical methods for the coupled Korteweg-de Vries equations". In: ANZIAM Journal. 2015 ; Vol. 56, No. 3. pp. 275-285. https://doi.org/10.1017/S1446181115000012

[4] Hattam, Laura ; Clarke, Simon. "Steady periodic solutions of a variable coefficient KS-KdV equation". In: IMA Journal of Applied Mathematics. 2016 ; Vol. 81, No. 6. pp. 999-1019. https://doi.org/10.1093/imamat/hxw040

[5] Hattam, Laura-Jane Louise ; Clarke, Simon Rex. "Modulation theory for the steady forced KdV-Burgers equation and the construction of periodic solutions". In: Wave Motion. 2015 ; Vol. 56. pp. 67-84. https://doi.org/10.1016/j.wavemoti.2015.02.004