Papers

• C. G. Johnson and A. J. Hogg (2012)
  Entraining gravity currents,
  Under review for J. Fluid Mech.
• M. J. Woodhouse, A. R. Thornton, C. G. Johnson, B. P. Kokelaar and J. M. N. T. Gray (2012)
  Segregation-induced fingering instabilities in granular free-surface flows,
  J. Fluid Mech. 709, 543–580, doi:10.1017/jfm.2012.348
  [Show abstract] [PDF ] [Movies] Particle-size segregation can have a significant feedback on the bulk motion of granular avalanches when the larger grains experience greater resistance to motion than the fine grains. When such segregation-mobility feedback effects occur the flow may form digitate lobate fingers or spontaneously self-channelize to form lateral levees that enhance run-out distance. This is particularly important in geophysical mass flows, such as pyroclastic currents, snow avalanches and debris flows, where run-out distance is of crucial importance in hazards assessment. A model for finger formation in a bidisperse granular avalanche is developed by coupling a depth-averaged description of the preferential transport of large particles towards the front with an established avalanche model. The coupling is achieved through a concentration-dependent friction coefficient, which results in a system of non-strictly hyperbolic equations. We compute numerical solutions to the flow of a bidisperse mixture of small mobile particles and larger more resistive grains down an inclined chute. The numerical results demonstrate that our model is able to describe the formation of a front rich in large particles, the instability of this front and the subsequent evolution of elongated fingers bounded by large-rich lateral levees, as observed in small-scale laboratory experiments. However, our numerical results are grid dependent, with the number of fingers increasing as the numerical resolution is increased. We investigate this pathology by examining the linear stability of a steady uniform flow, which shows that arbitrarily small wavelength perturbations grow exponentially quickly. Furthermore, we find that on a curve in parameter space the growth rate is unbounded above as the wavelength of perturbations is decreased and so the system of equations on this curve is ill-posed. This indicates that the model captures the physical mechanisms that drive the instability, but additional dissipation mechanisms, such as those considered in the realm of flow rheology, are required to set the length scale of the fingers that develop.
• C. G. Johnson, B. P. Kokelaar, R. M. Iverson, R. G. LaHusen, M. Logan and J. M. N. T. Gray (2012)
  Grain-size segregation and levee formation in geophysical mass flows,
  J. Geophys. Res. 117, F01032, doi:10.1029/2011JF002185
  [Show abstract] [PDF ] [Movies] Data from large-scale debris-flow experiments are combined with modeling of particle-size segregation to explain the formation of lateral levees enriched in coarse grains. The experimental flows consisted of 10m³ of water-saturated sand and gravel, which traveled ~80m down a steeply inclined flume before forming an elongated leveed deposit 10m long on a nearly-horizontal runout surface. We measured the surface velocity field and observed the sequence of deposition by seeding tracers onto the flow surface and tracking them in video footage. Levees formed by progressive downslope accretion approximately 3.5m behind the flow front, which advanced steadily at ~2m/s during most of the runout. Segregation was measured by placing ~600 coarse tracer pebbles on the bed, which when entrained into the flow, segregated upwards at 6–7.5cm/s. When excavated from the deposit these were distributed in a horseshoe-shaped pattern that became increasingly elevated closer to the deposit termination. Although there was clear evidence for inverse grading during the flow, transect sampling revealed that the resulting leveed deposit was strongly graded laterally, with only weak vertical grading. We construct an an empirical, three-dimensional velocity field resembling the experimental observations, and use this with a particle-size segregation model to predict the segregation and transport of material through the flow. We infer that coarse material segregates to the flow surface and is transported to the flow front by shear. Within the flow head, coarse material is overridden, then recirculates in spiral trajectories due to size-segregation, before being advected to the flow edges and deposited to form coarse-particle-enriched levees.
• C. G. Johnson and J. M. N. T. Gray (2011)
  Granular jets and hydraulic jumps on an inclined plane,
  J. Fluid Mech. 675, 87–116, doi:10.1017/jfm.2011.2
  [Show abstract] [PDF ] [Movies] A jet of granular material impinging on an inclined plane produces a diverse range of flows, from steady hydraulic jumps to periodic avalanches, self-channelised flows and pile collapse behaviour. We describe the various flow regimes and study in detail a steady-state flow, in which the jet generates a closed teardrop-shaped hydraulic jump on the plane, enclosing a region of fast-moving radial flow. On shallower slopes, a second steady regime exists in which the shock is not teardrop-shaped, but exhibits a more complex ‘blunted’ shape with a steadily breaking wave. We explain these regimes by consideration of the supercritical or subcritical nature of the flow surrounding the shock. A model is developed in which the impact of the jet on the inclined plane is treated as an inviscid flow, which is then coupled to a depth-integrated model for the resulting thin granular avalanche on the inclined plane. Numerical simulations produce a flow regime diagram strikingly similar to that obtained in experiments, with the model correctly reproducing the regimes and their dependence on the jet velocity and slope angle. The size and shape of the steady experimental shocks and the location of sub- and supercritical flow regions are also both accurately predicted. We find that the physics underlying the rapid flow inside the shock is dominated by depth-averaged mass and momentum transport, with granular friction, pressure gradients and three-dimensional aspects of the flow having comparatively little effect. Further downstream, the flow is governed by a friction–gravity balance, and some flow features, such as a persistent indentation in the free surface, are not reproduced in the numerical solutions. On planes inclined at a shallow angle, the effect of stationary granular material becomes important in the flow evolution, and oscillatory and more general time-dependent flows are observed. The hysteretic transition between static and dynamic friction leads to two phenomena observed in the flows: unsteady avalanching behaviour, and the feedback from static grains on the flowing region, leading to levéed, self-channelised flows.
• C. G. Johnson and C. J. Davis (2006)
  The location of lightning affecting the ionospheric sporadic-E layer as evidence for multiple enhancement mechanisms,
  Geophys. Res. Lett. 33, L07811, doi:10.1029/2005GL025294
  [Show abstract] [PDF ] We present a study of the geographic location of lightning affecting the ionospheric sporadic-E (Es) layer over the ionospheric monitoring station at Chilton, UK. Data from the UK Met Office's Arrival Time Difference (ATD) lightning detection system were used to locate lightning strokes in the vicinity of the ionospheric monitoring station. A superposed epoch study of this data has previously revealed an enhancement in the Es layer caused by lightning within 200km of Chilton. In the current paper, we use the same data to investigate the location of the lightning strokes which have the largest effect on the Es layer above Chilton. We find that there are several locations where the effect of lightning on the ionosphere is most significant statistically, each producing different ionospheric responses. We interpret this as evidence that there is more than one mechanism combining to produce the previously observed enhancement in the ionosphere.
• C. J. Davis and C. G. Johnson (2005)
  Lightning-induced intensification of the ionospheric sporadic E layer,
  Nature 435, 799–801, doi:10.1038/nature03638
  [Show abstract] [PDF ] A connection between thunderstorms and the ionosphere has been hypothesized since the mid-1920s. Several mechanisms have been proposed to explain this connection and evidence from modelling as well as various types of measurements demonstrate that lightning can interact with the lower ionosphere. It has been proposed, on the basis of a few observed events, that the ionospheric 'sporadic E' layer—transient, localized patches of relatively high electron density in the mid-ionosphere E layer, which significantly affect radio-wave propagation—can be modulated by thunderstorms, but a more formal statistical analysis is still needed. Here we identify a statistically significant intensification and descent in altitude of the mid-latitude sporadic E layer directly above thunderstorms. Because no ionospheric response to low-pressure systems without lightning is detected, we conclude that this localized intensification of the sporadic E layer can be attributed to lightning. We suggest that the co-location of lightning and ionospheric enhancement can be explained by either vertically propagating gravity waves that transfer energy from the site of lightning into the ionosphere, or vertical electrical discharge, or by a combination of these two mechanisms.

Conference presentations

• AGU Fall Meeting, San Francisco, December 2011
  Grain-size segregation and levee formation in geophysical mass flows
• Worldwide Universities Network Earth Surface Sedimentary Flows Symposium, Bristol, April 2011
  Grain-size segregation and levee formation in geophysical mass flows
• Gordon Research Conference in Granular and Granular-Fluid Flow, Colby College, June 2010
  My poster was presented by Nico Gray in my absence.
• MPGF09: Joint IUTAM-ISIMM Symposium on Mathematical Modeling and Physical Instances of Granular Flows, Reggio Calabria, September 2009
  Granular jets and hydraulic jumps on an inclined plane
• Beyond Part III: Young Researchers in Mathematics, Cambridge, April 2009
  The flow generated by oblique impingement of granular material on an inclined plane
• GEOFLOWS09: Workshop on Mathematical and Computational Aspects of Modeling Hazardous Geophysical Mass Flows, Seattle, March 2009
• IMA Conference on Dense Granular Flows, Cambridge, January 2009
  The flow generated by oblique impingement of granular material on an inclined plane
• EFMC7, EUROMECH Fluid Mechanics conference, Manchester, September 2008
• Gordon Research Conference in Granular and Granular-Fluid Flow, Colby College, June 2008
  Regularisation of the earth-pressure coefficient in time-independent Savage-Hutter flows
• British Applied Maths Colloquiem, Manchester, March 2008
  Shallow-Layer Modelling of Three-Dimensional Granular Avalanches