RESEARCH INTERESTS
My field of interest is the mathematical
modelling of
geophysical
fluid dynamics with a specific interest in buoyancy driven flows such
as internal
solitary waves in the stratified ocean and thermal
convection in superposed porous-fluid layers.
Please find below a list of my publications :
Journal
Papers
Internal
Solitary Waves
Carr, M., King, S. E.
& Dritschel, D. G.
2012 Instability in internal solitary waves with trapped cores.
Phys. Fluids. 24, 016601.
Carr, M., King, S. E.
& Dritschel, D. G.
2011 Numerical simulation of shear-induced instabilities in internal
solitary waves.
J. Fluid Mech. 683, 263-288.
Thiem.O, Carr, M., Berntsen, J.
& Davies, P. A.
2011 Numerical simulation of internal solitary wave - induced reverse flow and associated vortices in a shallow, two-layer fluid benthic boundary layer.
Ocean Dynamics. 61, 857-872.
King, S. E., Carr, M.
& Dritschel, D. G.
2011 The steady-state form of large-amplitude internal
solitary waves.
J. Fluid Mech. 666, 477-505.
Carr, M.
Stastna, M. & Davies, P. A.
2010 Internal
solitary wave-induced flow over a corrugated bed.
Ocean Dynamics. 60, 1007-1025.
Carr, M.
& Davies, P. A.
2010 Boundary layer flow beneath an internal
solitary wave of elevation.
Physics of Fluids. 22, 026601.
Fructus, D., Carr, M.,
Grue, J., Jensen, A., & Davies, P. A.
2009 Shear induced breaking of large amplitude internal solitary waves.
J. Fluid Mech. 620,
1-29.
Carr,
M., Fructus, D., Grue, J., Jensen, A., &
Davies, P. A. 2008 Convectively induced shear instability in large
amplitude internal
waves. Physics of Fluids. 20, 126601.
Carr, M., Davies, P. A., &
Shivaram, P. 2008 Experimental evidence of internal
solitary wave-induced global instability in shallow water benthic
boundary layers. Physics of Fluids. 20,
066603.
Dalziel, S. B.,
Carr, M., Sveen, J. K., &
Davies, P. A. 2007 Simultaneous synthetic
schlieren and PIV measurements for internal solitary waves. Meas. Sci. Technol. 18,
533-547.
Carr, M.
& Davies, P. A. 2006 The motion of
an internal solitary wave of depression over a fixed bottom boundary in
a shallow, two-layer fluid.
Physics of Fluids. 18, 016601.
Convection
Hill, A. A & Carr, M. 2010
Nonlinear stability of the one-domain approach to modelling convection in superposed fluid
and porous layers. Proc. R. Soc A. 466,
2695-2705.
Hill, A. A & Carr, M. 2010
Sharp global nonlinear stability for a fluid overlying a highly porous
material. Proc. R. Soc A. 466,
127-140.
Hirata, S. C., Goyeau, B., Gobin, D., Carr,
M., & Cotta, R. M.
2007 Linear stability of natural convection in superposed fluid and
porous layers: influence of the interfacial modelling. Int. J. Heat and Mass
Transfer. 50(7),
1356-1367.
Carr, M. 2004 Penetrative
convection in a superposed
porous-medium-fluid layer via internal heating. J. Fluid
Mech. 509, 305-329.
Carr, M. 2003 Unconditional
nonlinear stability for temperature
dependent density flow in a porous medium. Math. Models.
Methods. Appl Sci. 13 (2), 207-220.
Carr, M. 2003 A model for
convection in the evolution of under-ice melt
ponds. Continuum Mech. Thermodyn. 15
(1), 45-54.
Carr, M. & de Putter, S.
2003 Penetrative convection in a
horizontally isotropic porous layer. Continuum
Mech. Thermodyn. 15 (1), 33-43.
Carr, M.
& Straughan, B. 2003 Penetrative
convection in a fluid overlying a porous layer.
Advances in water resources. 26, 262-276.
Carr, M. 2003 Covection in
fluid and porous media. PhD thesis,
University of
Durham.
I am a member of the Scottish Oceans Institute in St Andrews, you can see more about my research profile there.
ISW Movies
Please find below movies of internal solitary wave motion;
(i) generated in the laboratory:
ISW of elevation reverse jet in deceleration phase (210509)
ISW of elevation over a corrugated bed - this wave was stable on approach (120908)
Unstable ISW of elevation (260608)
ISW of depression - reverse jet in deceleration phase (25538)
ISW of depression - reverse jet and vortices in deceleration phase (080207)
ISW of depression over a corrugated bed (120106)
Unstable ISW of depression in 3 layer fluid moderate amplitude (130605)
Unstable ISW of depression in 3 layer fluid large amplitude (310505)
Unstable ISW of depression in 2 layer fluid (240406)
Generation - gate effect (170909)
(ii) generated numerically (colour scheme is vorticity):
Unstable ISW of depression in a 3 layer fluid
Unstable ISW of depression in 2 layer fluid in which the trapped core region is modelled as a stagnant core