# School of Mathematics

## Dr Stephen D Griffiths

Lecturer

Applied Mathematics

### Contact details

Room: 8.25

Tel: +44 (0)113 3435186

Email: S.D.Griffiths @ leeds.ac.uk

### Keywords

Applied mathematics

Numerical modelling

Fluid dynamics

Linear and nonlinear waves

Mathematical geosciences

Atmospheric and oceanic flows

Stability and instability theory

Ocean tides

## Research interests

My research lies within the mathematical geosciences, and is mainly oriented towards the fluid dynamics of the Earth's atmosphere and ocean. My aims are to understand observed dynamical phenomena, either by numerical simulations or through mathematical analysis of simplified theoretical models. Particular interests are:

Instability theory: analytical and numerical modelling of linear and nonlinear instabilities in rotating, stratified shear flows.

Nonlinear waves: analytical and numerical modelling of coupled nonlinear wave equations.

Waves in the atmosphere and ocean: analytical and numerical modelling; internal waves; equatorial waves.

Ocean tides: global numerical modelling; regional numerical modelling of internal tides; paleotides and climate; ice-tide interactions.

Martian dynamics: numerical modelling of subsurface temperature and ice.

Numerical methods: finite-difference schemes in irregular domains.

### Useful links

## Current postgraduate students

Thomas Goodfellow (2014)

Oliver Halliday (2014)

Lucy Recchia (2016)

Daniel Rumgay (2016)

Sam Williams (2014)

Muhamad Najib Zakaria (2014)

## Publications

**Mak J, Griffiths SD, Hughes DW** Shear flow instabilities in shallow-water magnetohydrodynamics *Journal of Fluid Mechanics*, **788**, 767-796, 2016

DOI:10.1017/jfm.2015.718

View abstract

**Griffiths SD, Hill DF** Tidal modeling In *Handbook of Sea-Level Research*, 438-451, 2015

DOI:10.1002/9781118452547.ch29

View abstract

**Stammer D, Ray RD, Andersen OB, Arbic BK, Bosch W, Carrère L, Cheng Y, Chinn DS, Dushaw BD, Egbert GD, Erofeeva SY, Fok HS, Green JAM, Griffiths S, King MA, Lapin V, Lemoine FG, Luthcke SB, Lyard F, Morison J, Müller M, Padman L, Richman JG, Shriver JF, Shum CK, Taguchi E, Yi Y** Accuracy assessment of global barotropic ocean tide models *Reviews of Geophysics*, **52**, 243-282, 2014

DOI:10.1002/2014RG000450

View abstract

**Griffiths SD** Kelvin wave propagation along straight boundaries in C-grid finite-difference models *Journal of Computational Physics*, **255**, 639-659, 2013

DOI:10.1016/j.jcp.2013.08.040

View abstract

**Hill DF, Griffiths SD, Peltier WR, Horton BP, Törnqvist TE** High-resolution numerical modeling of tides in the western Atlantic, Gulf of Mexico, and Caribbean Sea during the Holocene *Journal of Geophysical Research: Oceans*, **116**, 2011

DOI:10.1029/2010JC006896

View abstract

**Griffiths SD, Peltier WR** Modeling of Polar Ocean Tides at the Last Glacial Maximum: Amplification, Sensitivity, and Climatological Implications *J CLIMATE*, **22**, 2905-2924, 2009

DOI:10.1175/2008JCLI2540.1

**Griffiths SD** The limiting form of inertial instability in geophysical flows *Journal of Fluid Mechanics*, **605**, 115-143, 2008

DOI:10.1017/S0022112008001407

View abstract

**Griffiths SD, Peltier WR** Megatides in the Arctic Ocean under glacial conditions *Geophysical Research Letters*, **35**, 2008

DOI:10.1029/2008GL033263

View abstract

**Griffiths SD** Weakly diffusive vertical scale selection for the inertial instability of an arbitrary shear flow *Journal of Fluid Mechanics*, **594**, 265-268, 2008

**Griffiths SD, Grimshaw RHJ** Internal Tide Generation at the Continental Shelf Modeled Using a Modal Decomposition: Two-Dimensional Results *Journal of Physical Oceanography*, **37**, 428-451, 2007

DOI:10.1175/JPO3068.1

View abstract

**Griffiths SD, Grimshaw RHJ, Khusnutdinova KR** Modulational instability of two pairs of counter-propagating waves and energy exchange in a two-component system *Physica D: Nonlinear Phenomena*, **214**, 1-24, 2006

DOI:10.1016/j.physd.2005.11.011

View abstract

**Griffiths SD, Grimshaw RHJ, Khusnutdinova KR** The Influence of Modulational Instability on Energy Exchange in Coupled Sine-Gordon Equations *Theoretical and Mathematical Physics*, **137**, 1448-1458, 2003

DOI:10.1023/A:1026008907682

View abstract

**Griffiths SD** Nonlinear Vertical Scale Selection in Equatorial Inertial Instability *Journal of the Atmospheric Sciences*, **60**, 977-990, 2003

DOI:10.1175/1520-0469(2003)060<0977:NVSSIE>2.0.CO;2

View abstract

**Griffiths SD** The nonlinear evolution of zonally symmetric equatorial inertial instability *Journal of Fluid Mechanics*, **474**, 245-273, 2003

DOI:10.1017/S0022112002002586

View abstract

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