Associate Professor Michael Page

Contact information Research interests Teaching interests Other activities

Contact information

Postal

School of Mathematical Sciences, Monash University, Victoria 3800, Australia

Physical

Office: Room 326, Third floor, Building 28, Monash University Clayton campus
TomTom: 37º 54' 33.73" S 145º 07' 53.07" E

Wire

Phone and voicemail: +61 3 9905 4486
Fax: +61 3 9905 4403
E-mail: Michael.Page(at)monash.edu

Research interests

In summary

High-Reynolds-number flows and boundary-layer theory, including flow separation
Geophysical fluid dynamics on an f- and beta-plane, especially at small Ekman numbers
Diffusion-driven stratified flows
Computational fluid dynamics
Immersed interface methods for the solution of partial differential equations in irregular domains

A more-detailed overview of my research

My principal area of research for most of my career has been in the dynamics of viscous fluid motion relative to a rotating frame of reference – a field that has developed from the study of atmospheric and oceanic flows on the surface of the Earth. This research involves solving a modified form of the Navier-Stokes equations (with additional Coriolis terms) using a combined analytical and numerical approach, with asymptotic analysis supported, and sometimes guided, by the results of numerical calculations. Many of the issues studied in my research arise from the analysis of experimental studies, mostly based on photographs and laboratory results published by others, although earlier in my career I performed some limited laboratory experiments to complement the theory and numerical results on one project.

One particular interest has been the examination and prediction of boundary-layer separation in Stewartson E^1/4-layer flows in this context, first (and very successfully) for a one-layer flow but also for two-layer flows which model the simplest effects of stratification. Another interest has been upstream-influence and boundary-layer effects both in rotating flows on a beta plane and for motion along the axis of a rotating fluid. All of these are important for aiding the interpretation of both theoretical and experimental studies of geophysical fluid dynamical flows and, as noted above, I make a point of carefully comparing my results with published laboratory studies when they are available.

From this base, my research activities have developed into a number of other related areas of fluid dynamics, including both steady and unsteady boundary-layer motion at high Reynolds numbers (ranging from separated supersonic flows, to recirculation in curved-pipe flows, reattachment in incompressible flows and singularities which lead to eruption in unsteady boundary-layer flows), simple models of the ocean circulation (in particular in the western boundary layer) and the generation of ‘diffusion-driven’ flows in a contained density-stratified fluid. From the other end of the spectrum, I have also worked on the complex-valued equations that govern the motion of an inviscid vortex sheet, and in particular the development of finite-time singularities in that flow. My work makes extensive use of a wide range of techniques from computational fluid dynamics (including adapting finite-difference and finite-volume techniques, and developing novel methods for both free-streamline flows and conformal mapping) and I have written a variety of sophisticated computer programs for solving the Navier-Stokes or boundary-layer equations, as well as specialised codes for computer visualisation of the results (including animation, long before that was as easy to do as now).

Selected earlier papers

M.A. Page (1982), "A numerical study of detached shear layers in a rotating sliced cylinder", Geophys. Astrophys. Fluid Dyn. 22, pp51-69.
M.A. Page (1982), "Flow separation in a rotating annulus with bottom topography", J. Fluid Mech. 123, pp303-313.
M.A. Page and N. Riley (1985), "The free interaction in a supersonic flow over a porous wall", Quart. J. Mech. Appl. Math. 38, pp79-92.
M.A. Page (1987), "Separation and free-streamline flows in rotating fluids at low Rossby numbers", J. Fluid Mech. 179, pp155-177.
M.A. Page and S.J. Cowley (1988), "On the rotating-fluid flow near the rear stagnation point of a circular cylinder", J. Fluid Mech. 194, pp79-99.
A. Becker and M.A. Page (1990), "Flow separation and unsteadiness in a rotating-sliced cylinder", Geophys. Astrophys. Fluid Dyn. 55, pp89-115.
M.A. Page and M.D. Eabry (1990), "On the breakdown of jets in a low-Rossby number rotating fluid", J. Eng. Math. 24, pp287-310.
E.R. Johnson and M.A. Page (1993), "Flow past a circular cylinder on a beta plane", J. Fluid Mech. 251, pp603-626.
J.R. Stocker, P.W. Duck and M.A. Page (1997), "On the unsteady low-Rossby number flow of a rotating fluid past a circular cylinder", Phys. Fluids 9, pp600-614.
P. Blanchonette and M.A. Page (1998), "Boundary-layer separation in the two-layer flow past a cylinder in a rotating frame", Theoret. Comput. Fluid Dynamics 2, pp95-108.
M.A. Page and E.R. Johnson (2000), "Wavefields forced by long obstacles on a beta-plane", J. Fluid Mech. 406, pp221-245.

Teaching interests

Undergraduate units currently taught

ENG1090 Foundation Mathematics (for engineering students)
MTH3011 Partial Differential Equations (for third-year mathematics students)

Honours in applied mathematics

M4401 Introduction to Honours Computing (module on MATLAB)
Outline of some possible honours projects for 2013

Teaching experience

During my career I have taught across many areas in applied mathematics, and have current interests and extensive experience in the teaching of numerical methods, fluid dynamics and differential equations and their applications. I have also taught both general mathematical methods to engineering students and some advanced-level analysis subjects. As a computational applied mathematician with an analytical ‘bent’, I have a broad understanding of most areas of mathematics, classical physics, computational science and theoretical engineering.

Postgraduate supervision

I have supervised a number of PhD students to completion on my own, and co-supervised several others. Topics were mostly in the area of numerical and analytical studies of geophysical flows with one on combustible flows with a CFD emphasis. Several of the students that I co-supervised were undertaking applied projects in dynamical meteorology, but my assistance was mostly in relation to computational aspects of their studies.

If you are interested in undertaking studies towards a PhD under my supervision, some possible areas for research projects might include:

The dynamics of rotating fluids - especially for geophysical applications on an f- and beta-plane;
High-Reynolds-number flows, boundary-layer theory and flow separation;
Diffusive-driven flows in a viscous stratified fluid;
Singular perturbation theory and asymptotic expansions;
Computational fluid dynamics - mostly based on careful finite-difference approximation, as opposed to using packages;
Immersed interface methods for the numerical solution of partial differential equations, including for flexible membranes and for wave propagation.

Some suggestions of specific possible projects are available here, but this list is certainly not comprehensive. Alternatively, if you are seeking supervision on a broad area of interest that is within my areas of expertise (ie reasonably similar from those listed above), or on a specific project proposal of your own, then please contact me for further discussions.

Other activities

In addition, I:

graduated with a BSc (Hons) in mathematics from the University of Western Australia in 1978, and PhD in mathematics from University College London (part of the University of London) in 1981;
completed a three-year term as Head of the Department of Mathematics and Statistics at Monash University (now the School of Mathematical Sciences) from 1998-2000;
lead significant changes to the undergraduate mathematics curriculum at Monash University as the Director of Undergraduate Studies in the Department of Mathematics and Statistics from 1997-2000;
was Associate Dean (Teaching) in the Faculty of Science at Monash University from 2001-2004, and Deputy Dean 2002-2003;
am Director of Undergraduate Studies in the School of Mathematical Sciences, from 2012;
am a member of the Executive of the Victorian Branch of ANZIAM;
am an elected member of the Academic Board at Monash University.

Just for fun, this is what I was doing back in 1998 (albeit with lots of now-broken links)!

Last updated: 20 December 2012