Illustrated Physics
physics, drawn
Concept

Critical velocity — where it appears

A speed at which the behaviour of a flow or a moving object changes qualitatively, such as the onset of waves, turbulence or dissipation. For water waves it is the slowest speed any wave travels, about 23 cm/s, below which an object crossing the surface leaves no wake.

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

A beaker that empties at a steady rate. The height of liquid helium inside a beaker 1 cm across, held 1 cm above the level of the bath it stands in, against time, as the film carries liquid up the inner wall, over the rim and down into the bath. The film carries a fixed volume per centimetre of rim — 7.5·10⁻⁵ cm³/s at 1.4 K — whatever the difference of levels, so the level falls in a straight line, 180 μm a minute, and the beaker is level with the bath in 56 minutes. At 1.9 K, with less superfluid, it takes 95 minutes; at 2.1 K, 279. Dashed, a flow driven by the difference of levels, like a siphon, starting at the same speed: it slows exponentially as the difference shrinks and never quite finishes. The film's straight line is the signature of a flow set by a critical speed, not by the push.

The film whose thinnest point sets the flow

Leave a beaker of superfluid helium standing in a bath and it empties itself, the liquid creeping up the inside wall as a film eighty atoms thick, over the rim and down the outside. The film itself is nothing special: ordinary liquid helium coats the wall just as thickly. What is special is that it flows without friction, and so its flow is set not by how hard it is pushed but by how fast it can go. The level falls in a straight line rather than slowing as it nears the bath's, and the whole flow is decided at one place, the rim, where the film is thinnest and has to run fastest.

quantum · Superfluidity Which waves a moving object can make. The phase speed of waves on deep water against wavelength (red), with horizontal lines at the speeds of an object moving steadily across the surface: 15.0 cm/s, 23.1 cm/s, 30.0 cm/s, 50.0 cm/s. A steady object can only feed waves that keep pace with it, whose phase speed equals its own, and those are where its line meets the curve. At 15 cm/s the line misses the curve entirely: no wave can keep up, and the object leaves no wake. At 23.1 cm/s it touches the curve once. Above that it meets it twice: at 30 cm/s a ripple of 5.6 mm and a gravity wave of 5.2 cm; at 50 cm/s a ripple of 1.9 mm and a gravity wave of 15.8 cm.

The speed below which nothing on water leaves a wake

Every wave on clean water travels at 23 centimetres a second or faster: long waves are fast because gravity drives them, short ones because surface tension does, and in between there is a slowest wave. A boat, a duck or a fishing line can only make waves that keep pace with it, so anything crossing the water more slowly than 23 centimetres a second makes no waves at all. Faster, it makes two kinds at once — short ripples that run ahead of it and long waves that trail behind — and the threshold between nothing and both is set by gravity, surface tension and density alone.

waves · Wave motion

Named alongside it

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

Capillary waveDispersion relationGravity waveGroup velocityLambda pointPhase velocitySuperfluiditySurface tensionThin filmThird soundTwo-fluid modelVan der waals force

All concepts