Prof. William Phillips   Professor - Applied Mathematics

Professor Phillips joined the Mathematics group at Swinburne in April 2007 from the University of Illinois at Urbana-Champaign where he spent much of his career in the (then) Department of Theoretical and Applied Mechanics. Prior to that he held appointments at Cornell, Clarkson and the National University of Singapore.

His main interests are nonlinear differential (and integro-differential) equations as they arise in geophysical fluid dynamical situations, most specifically through surface-wave mean-flow instabilities.

He is best known for his generalised theory for the aetiology of stadium sized rolls in the upper ocean known as Langmuir circulation.
He holds degrees from the University of Adelaide in Australia, McGill University in Canada and the University of Cambridge in England.

Qualifications

• PhD, University of Cambridge, UK, 1978

Areas of Expertise and Research

• Generalized Lagrangian mean theory
• Singular parabolic partial differential equations
• Nonlinear Instability theory
• Integro-differential equations
• Similarity theory
• Geophysical and biological fluid dynamics
• Wave mean interactions
• Langmuir circulation
• Scientific computing

Current Research Projects

• Langmuir circulation in shallow water with wave breaking; instability theory and large eddy simulation
• Low order dynamical descriptions of Langmuir circulation
• Instability to longitudinal roles over wavy terrain
• Drop pinch off and singularities in finite time

ARC, NSF and NIH Research Grants 2000+

Year	Project	Total Funding	Funding Organisation	DEEWR Category
2011-2015	Facility for extreme air/sea interaction studies (Marusic and others)	$500,000	ARC LIEF LE110100079	1
2010-2012	Wave-induced upper ocean mixing (Babanin and Phillips)	$310,000	ARC Discovery DP1093517	1
2008-2011	Oceanic conditions within extreme tropical cyclones (Babanin, Young and Phillips)	$510,000 (ARC) $300,000 (Wdside)	ARC Linkage LP0883888	1
2002-2007	Ultrasound-induced lung damage assessment (O'Brien, Zachary, Phillips and Harris)	US$2,666,170	NIH Heart Lung RO1-EB02641	1
2001-2005	Langmuir circulation beneath breaking waves (Phillips)	US$426,622	NSF Ocean-Math OCE-0116921	1
1999-2002	Langmuir circulations beneath growing and deforming surface waves (Phillips)	US$314,000	NSF Ocean OCE-9818092	1

Membership of Professional Organisations

• American Physical Society
• American Geophysical Union
• Australian Mathematical Society / ANZIAM
• New York Academy of Science
• SIAM
• Sigma Xi

Supervision of higher degree by research (HDR) (Current students)

Name	Degree	Research Centre	Start year	Role
Daniel Hayes	PhD	Faculty	2007	Primary Supervisor

Topics for Prospective Ph.D Students - View ALL topics for Prof. William Phillips

Singular Integrals


Langmuir Circulation Beneath Breaking Waves


Asymptotic analysis of non-linear spatio-temporal evolution


Low dimensional dynamical system modelling of subcritical nonlinear systems
The project will aim to overcome this difficulty by investigating the nature of the resonances and incorporating their appropriate model into the developed dynamical system.

Singular parabolic partial differential equations


Langmuir Supercells


Thermo-magnetic instabilities in ferro-magnetic nano-fluids
Ferrocolloids containing ferro-magnetic nano-particles suspended in water, kerosene or mineral oil have been industrially manufactured since 1960s.

Their unique magnetic and fluid properties found a wide range of applications from targeted drug delivery in cancer treatment to heat removal in spacecraft equipment where convective heat transfer impossible due to the lack of gravity.

Langmuir Supercells


Langmuir Circulation Beneath Breaking Waves


Asymptotic analysis of non-linear spatio-temporal evolution


Thermo-magnetic instabilities in ferro-magnetic nano-fluids
Ferrocolloids containing ferro-magnetic nano-particles suspended in water, kerosene or mineral oil have been industrially manufactured since 1960s.

Their unique magnetic and fluid properties found a wide range of applications from targeted drug delivery in cancer treatment to heat removal in spacecraft equipment where convective heat transfer impossible due to the lack of gravity.

Selected Recent Publications

1. Phillips, W.R.C., Dai, A. and Tjan, K.K."On Lagrangian drift in shallow-water waves on moderate shear", Journal of Fluid Mechanics 660, 221-239 (2010)
2. Babanin, A.V., Ganopolski, A. and Phillips, W.R.C., "Wave-induced upper-ocean mixing in a climate model of intermediate complexity", Ocean Modelling 29, 189-197 (2009)
3. Tjan, K.K. and Phillips, W.R.C., "On the impulsive generation of drops at the interface of two inviscid fluids", Proceedings of the Royal Society of London, series A464, 1125-1140 (2008)
4. Tjan, K.K. and Phillips, W.R.C., "On impulsively generated inviscid axisymmetric surface jet, waves and drops", Journal of Fluid Mechanics 576, 377-403 (2007)
5. Phillips, W.R.C., "On the spacing of Langmuir circulation in strong shear", Journal of Fluid Mechanics 525, 215-236 (2005)
6. Phillips, W.R.C., "Langmuir circulations beneath growing or decaying surface waves", Journal of Fluid Mechanics 469, 317-342 (2002)
7. Phillips, W.R.C., "On an instability to Langmuir circulations and the role of Prandtl and Richardson numbers", Journal of Fluid Mechanics 442, 335-358 (2001)
8. Phillips, W.R.C., "On the pseudomomentum and generalized Stokes drift in a spectrum of rotational waves", Journal of Fluid Mechanics 430, 209-229 (2001)
9. Sakakibara, J., Hishida, K. and Phillips, W.R.C., "On the vortical structure in a plane impinging jet", Journal of Fluid Mechanics 434, 273-300 (2001)
10. Phillips, W.R.C., "Eulerian space-time correlations in turbulent shear flows", Physics of Fluids 12, 2056-2064 (2000)
11. Phillips, W.R.C., "Finite-amplitude rotational waves in viscous shear flows", Studies in Applied Mathematics 101, 23-47 (1998)
12. Phillips, W.R.C. & Shen, Q., "A family of wave-mean shear interactions and their instability to longitudinal vortex form", Studies in Applied Mathematics 96, 143-161 (1996)
13. Phillips, W.R.C., "On a class of unsteady boundary layers of finite extent", Journal of Fluid Mechanics 319, 151-170 (1996)
14. Phillips, W.R.C. Wu, Z. & Lumley, J.L., "On the formation of vortices in a turbulent boundary layer over wavy terrain", Journal of Fluid Mechanics 326, 321-341 (1996)