Rich Kerswell

Granular collapse in two dimensions

An experimental investigation is conducted into the collapse of granular columns inside rectangular channels. The final shape is documented for slumps inside relatively wide channels, and for collapses inside much narrower slots. In both cases, the collapse is initiated by withdrawing a swinging gate or sliding door, and the flow remains fairly two-dimensional. Four different granular media are used; the properties of the materials vary significantly, notably in their angles of friction for basal sliding and internal deformation. If H is the initial height of the column, h∞ the maximum final height of the column and a the initial aspect ratio, then the data suggest that H/h ∞ ∼ a 0.6 in wide channels and H/h ∞ ∼ a 0.5 for narrow slots. For the runout, we find that (l∞ − L)/L ∼ a 0.9±0.1 for wide channels, and (l∞ − L)/L ∼ a 0.65±0.05 or l∞/L ∼ a 0.55±0.05 for narrow slots, where l∞ is the maximum runout of the material and L the initial length of the column along the channel (a := H/ L). In all cases, the numerical constant of proportionality in these scaling relations shows clear material dependence. In wide slots, there is no obvious universal scaling behaviour of the final profile, but such a behaviour is evident in narrow slots. The experimental results are compared with theoretical results based on a shallow granular-flow model. The qualitative behaviour of the slump in the wide slot is reproduced by the theoretical model. However, there is qualitative disagreement between theory and the experiments in the narrow slot because of the occurrence of secondary surface avalanching.

Transition in pipe flow: the saddle structure on the boundary of turbulence

The laminar–turbulent boundary Σ is the set separating initial conditions which relaminarize uneventfully from those which become turbulent. Phase space trajectories on this hypersurface in cylindrical pipe flow appear to be chaotic and show recurring evidence of coherent structures. A general numerical technique is developed for recognizing approaches to these structures and then for identifying the exact coherent solutions themselves. Numerical evidence is presented which suggests that trajectories on Σ are organized around only a few travelling waves and their heteroclinic connections. If the flow is suitably constrained to a subspace with a discrete rotational symmetry, it is possible to find locally attracting travelling waves embedded within Σ. Four new types of travelling waves were found using this approach.

Planar collapse of a granular column: experiments and discrete element simulations

The collapse of a granular column is an intriguingly simple table-top experiment which exhibits a host of interesting phenomena. Here, we introduce a planar version in which the collapsing column is only one particle deep perpendicular to the plane of motion to make observations of the internal motion possible. This configuration also particularly lends itself to comparison with discrete element simulations which are performed in tandem. Our experiments confirm that this planar system displays all the same features as collapsing cylinders and rectangular blocks. In particular, the dominant dependence on the initial parameters of the column runout is through a power law of the initial height-to-width aspect ratio. Discrete element simulations, which are found to reproduce the experimental behavior very well, are then used to analyze the velocity field of the collapse process. A predominantly linear velocity profile is found in a moving layer over an evolving static pile. The time-dependent strain rate in t...

Relative periodic orbits in transitional pipe flow

A dynamical system description of the transition process in shear flows with no linear instability starts with knowledge of exact coherent solutions, among them traveling waves (TWs) and relative periodic orbits (RPOs). We describe a numerical method to find such solutions in pipe flow and apply it in the vicinity of a Hopf bifurcation from a TW which looks to be especially relevant for transition. The dominant structural feature of the RPO solution is the presence of weakly modulated streaks. This RPO, like the TW from which it bifurcates, sits on the laminar-turbulent boundary separating initial conditions which lead to turbulence from those which immediately relaminarize.

Bounds on horizontal convection

For a fluid layer heated and cooled differentially at its surface, we use a variational approach to place bounds on the viscous dissipation rate and a horizontal Nusselt measure based on the entropy production. With a general temperature distribution imposed at the top of the layer and a variety of thermal boundary conditions at the base of the layer, the horizontal Nusselt number is bounded by

Highly symmetric travelling waves in pipe flow

cR_H^{1/3}

Genesis of Streamwise-Localized Solutions from Globally Periodic Traveling Waves in Pipe Flow

as the horizontal Rayleigh number

Infinite-Prandtl-number convection. Part 2. A singular limit of upper bound theory

R_H \,{\rightarrow}\, \infty

New results in rotating Hagen–Poiseuille flow

, for some constant

Maximal mixing rate in turbulent stably stratified Couette flow

c.