Biography
I graduated with a degree in physics at Oxford University in 1987, where I also obtained a DPhil in physics in 1991. My doctoral thesis was supervised by Tom Mullin and Dave Broomhead (both now professors at Manchester University) and was concerned with the analysis of phase spaces reconstructed from time series data, and how these techniques can help us to understand the bifurcations and complex behaviour of dynamical systems.
In 1991 I was appointed to a postdoctoral position in the Engineering Department at Cambridge University to work with Professor Mike Gaster FRS on the laminarturbulent transition of boundary layers. I developed the time series methods I had studied in my DPhil for application to hotwire data from windtunnel experiments on boundary layers. In 1993 I continued this work with a second postdoctoral position jointly supervised by Professor David Crighton FRS and Mike Gaster. I carried out windtunnel experiments on boundary layers, but also became increasingly interested in more 'classical' theories of hydrodynamic stability and how they relate to boundary layer experiments.
In 1996 I was appointed first to a temporary lectureship in the Mathematics Department at Brunel University, and then to a lectureship in the Mathematics Department at Keele University. I became a Reader at Keele in 1998.
Research and scholarship
My research is still concerned with instabilities in fluid flows, and has included thermal boundary layers, threedimensional boundary layers and swirling jets. I use asymptotic techniques to develop theories in largeReynolds number and longwavelength limits, and also to obtain largetime descriptions of initial value problems for determining absolute and convective instability characteristics. I also use numerical methods for solving viscous and inviscid stability equations.
Most of my research papers can be divided between three main areas.
1.Time series analysis
In the qualitative theory of dynamical systems one can represent complicated behaviour in terms of a state space, or phase space. The instantaneous state of the system is represented by a point in this space, and the evolution of the system is represented by the trajectory taken by this point. Thus, an equilibrium state is represented by a fixed point, a periodic behaviour by a closed orbit, a quasiperiodic behaviour by a path on a torus and chaotic behaviour by a path on a strange attractor with fractal properties. Remarkably, this trajectory, called a phase portrait, can often be reconstructed from a series of measurements of a single characteristic of the system (a time series).
Summary of results and selected publications in Time Series Analysis.pdf
2. The Blasius boundary layer
When a fluid flows at high speed past a solid surface a boundary layer forms in the fluid close to the surface. It is a region where viscosity is important and arises from the noslip boundary condition on the fluid at a solid surface. Boundary layers are present however small the viscosity. In the absence of viscosity objects moving through a fluid experience no drag and no lift. It is the presence of boundary layers that always produces drag on a body and can also produce lift. A boundary layer can separate from a surface, dramatically increasing the drag (as when an aeroplane wing stalls). When the boundary layer is attached (like around a streamlined body) the amount of drag, and also the heat transfer characteristics, depends sensitively on whether the boundary layer is laminar or turbulent. Being able to predict the state of a boundary layer is of importance in the design of aeroplane wings and turbine blades in jet engines. Fuel consumption of commercial aircraft could be halved, and their range doubled, if laminar boundary layers could be maintained over their wings. However, laminarturbulent transition, and turbulence, remain major outstanding problems in fluid mechanics, and affect many other flows in many other situations.
The simplest boundary layer arises when a flat plate is placed parallel to a uniform stream. This is called the Blasius boundary layer, and has been much studied experimentally, numerically and theoretically. Although it doesn't often arise in practical applications, and despite having certain peculiarities (an inflexion point at the wall), a greater understanding of its laminarturbulent transition is expected to be helpful in understanding other boundary layers.
Summary of results and selected publications in The Blasius boundary layer.pdf
3. Absolute and convective instabilities
Unstable disturbances in a shear layer, like a boundary layer, might all propagate downstream, in which case the flow is called convectively unstable. If unstable disturbances travel both upstream and downstream in the shear layer then the flow is called absolutely unstable. Although this classification depends on the velocity of the reference frame being used, there is usually a frame of particular interest, e.g. the laboratory frame, or the frame moving with an aeroplane wing, and then the distinction is of crucial importance in determining the dynamics of the flow. Convectively unstable flows act as spatial amplifiers of whatever external disturbances are imposed on the flow. Absolutely unstable flows can generate their own intrinsic modes which are insensitive to the disturbance environment, and thus behave as selfexcited oscillators. These modes are called global modes and arise through an interplay of local instability characteristics, nonlinearity and weak inhomogeneity of the basic flow in the streamwise direction. From a practical point of view, an unstable flow that is only convectively unstable will remain in a laminar state if the freestream turbulence level is low enough, but an absolutely unstable flow giving rise to a global mode will have the original basic flow replaced by the global mode regardless of how small the external disturbance levels are.
The local absolute/convective characteristics are obtained by assuming that the local basic velocity profile is independent of the streamwise coordinate and examining the solution produced by an impulsive localized disturbance to an otherwise undisturbed basic flow (the Green's function) at large times. The flow is absolutely unstable if there is growth in time in the rest frame. This behaviour can be determined using residue theory and saddlepoint methods on the integrals appearing in the inverse FourierLaplacetype transforms of the initial value problem. At large times these integrals are dominated by the contribution from the highest saddle point whose valleys contain the real wavenumber axis. (In the BriggsBers interpretation, this dominant saddlepoint is called the 'pinchpoint' and represents a coalescence of upstream and downstream travelling waves). Contour deformations in the complex wavenumber plane are required to locate the dominant saddle, and in the case of convective instability this also gives information about the direction of propagation of waves (the socalled 'signalling problem').
Summary of results and selected publications in this area.pdf
Teaching
 MAT10041: Calculus II
 MAT30002: Nonlinear Ordinary Differential Equations
Further information
Jonathan Healey's Homepage
Selected Publications

Fractal sets of neutral curves for stably stratified plane Couette flow. JOURNAL OF FLUID MECHANICS, 697728, vol. 872. link> doi> full text>2019.
 2013.
 2012.
 2012.
 2011.
Full Publications Listshow
Journal Articles

Fractal sets of neutral curves for stably stratified plane Couette flow. JOURNAL OF FLUID MECHANICS, 697728, vol. 872. link> doi> full text>2019.
 2013.
 2012.
 2012.
 2011.
 2010.
 2009.
 2004.
 2008.

Enhancing the absolute instability of a boundary layer by adding a faraway plate. J Fluid Mech, 2961, vol. 579. doi>2007.
 2007.

A new convective instability of the rotating disk boundary layer with growth normal to the disk. J Fluid Mech., 279310, vol. 560. doi>2006.

Inviscid longwave theory for the absolute instability of the rotatingdisc boundary layer. Proceeding Royal Society London A, 14671492, vol. A462. doi>2006.
 2005.

On the relation between the viscous and inviscid absolute instabilities of the rotatingdisk boundary layer. J. Fluid Mech., 179199, vol. 511. doi>2004.
 2000.
 2000.
 1998.
Other

Axisymmetric absolute instability of swirling jets. ADVANCES IN TURBULENCE XI (pp. 3537, vol. 117). link>2007.

A strange instability with growth normal to a boundary layer. Sixth IUTAM Symposium on LaminarTurbulent Transition (pp. 115120, vol. 78). link>2006.

Convective and absolute instability in the mixed convection boundary layer over a vertical flat plate. LAMINARTURBULENT TRANSITION (pp. 339344). link>2000.

On why oblique waves in the Blasius boundary layer show stronger nonparallel effects than planar waves. LAMINARTURBULENT TRANSITION (pp. 187192). link>2000.
Admin roles
Seminar Coordinator
Research themes
School of Computing and Mathematics
Keele University
Staffordshire
ST5 5AA
Email: scm.admin@keele.ac.uk
Tel:+44 (0) 1782 733075