Illustrated Physics
physics, drawn
Concept

Avalanche — where it appears

The sudden downslope flow of snow, sand, rock or grains once a slope exceeds the angle at which friction holds it. Its runout depends on how its friction changes with speed and confinement, which granular rheologies such as μ(I) try to predict from grain properties.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

A magnetisation curve, and the same curve magnified. On the left, the position of a domain wall against the applied field, over the whole of a crystal. It looks like a curve. On the right, a window 2.0% of its width, taken 42% of the way across, at the magnification a sensitive measurement reaches: the wall does not move at all while the field rises, then jumps, then stops again. The largest jump in the window covers 0.67 units of wall position in no field change at all. There is nothing smooth underneath this — the smooth curve on the left is a staircase with 1400 steps in it, drawn small.

The curve that is really a staircase

A magnetisation curve is drawn as a smooth line and is nothing of the sort. Measured finely enough it is a sequence of jumps of every size, audible as a crackle in a coil, with no typical jump and no smooth motion underneath.

electromagnetism · Magnetisation How a layer of grains moves down a slope. The velocity through a steady layer of 0.5 mm glass beads 20 grains deep flowing down slopes of 22°, 25° and 28°, against height above the rough base in grain diameters; the dashed curve is a Newtonian liquid's parabola, scaled to the 25° surface speed. Because every depth must have friction tan θ, every depth has the same inertial number, and the shear rate grows with the square root of the pressure above it: Bagnold's profile, u ∝ h^(3/2) − (h − z)^(3/2). Its surface speeds are 8.0, 41.0, 113.7 cm/s; compared with a liquid's parabola the shear is spread more evenly through the depth, because the shear rate falls off only as the square root of the depth below the surface rather than in proportion to it.

The sand whose friction depends on how fast it flows

A heap of sand stands at its angle of repose and starts to slide a few degrees steeper; between those angles there are steady avalanches, and their speed is decided by one number. The inertial number compares how long a grain takes to fall into a gap opened under it with how long the flow takes to open the gap. Friction rises with it, from the static value to a ceiling, and that single dependence explains why grains flow steadily on only a twelve-degree window of slopes, why a flowing layer has the velocity profile Bagnold measured, and why a deeper avalanche is faster — but not as a liquid would be.

fluids · Granular matter

Named alongside it

The objects these essays reach for when they reach for this one.

Dimensionless numberDomain wallFluctuationsFrictionGranular matterGranular temperatureHysteresisInstabilityIrreversibilityMagnetisationMetastabilityRheology

All concepts