Illustrated Physics
physics, drawn
Concept

Inertial oscillation — where it appears

The closed circular motion a body performs in a rotating frame with no other force acting, of radius the speed over the Coriolis parameter. Its period is half a pendulum day and it is the largest single feature in most long records of ocean current, excited whenever a storm accelerates a surface layer and stops.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

The deflection is a circle, not a bend. Trajectories integrated from Newton's law in a rotating frame with the Coriolis term and nothing else — no pressure gradient, no friction, no force of any kind. 0.5 m/s at 45°, 0.3 m/s at 30°. Each path closes on itself after one inertial period, checked to a millionth of its own radius, and the radius is the speed divided by the Coriolis parameter: 4.85 km, 4.11 km. The deflection usually described as a curving of the path is a complete circle, traversed clockwise in the northern hemisphere in half a pendulum day, and a body left alone in a rotating frame goes nowhere at all.

The deflection that closes on itself

The Coriolis term is usually described as bending a path to the right. Integrated rather than described, it does not bend the path — it closes it. A body left alone in a rotating frame travels a circle of radius U/f and comes back to where it started in half a pendulum day, having gone nowhere at all, and drifting buoys in every ocean draw exactly that.

mechanics · Circular motion Pushed one way, travelling another. A parcel released from rest under a steady pressure-gradient acceleration of 2.0e-4 metres per second squared pointing east, integrated for 36 hours at 60°, 30°, 10°. Without rotation it would accelerate east indefinitely. With it, the motion is an inertial circle about a mean velocity at right angles to the push, and the mean over a whole number of inertial periods is measured off each path and matches the geostrophic value a/f to two per cent. At high latitude the loops are tight and the drift is almost purely along the isobars; near the equator the parcel travels a long way down the gradient before the rotation has had time to turn it, which is why geostrophic balance is a high-latitude statement and the tropics need a different set of approximations.

The ratio that decides whether the planet is turning

Whether the rotating terms matter is not a question about size. It is one dimensionless ratio, U over fL, and it runs from ten thousand in a teacup to a millionth in the Earth's core. Where it is small the pressure gradient stops accelerating the fluid and starts balancing a force on fluid already moving across it — so the flow runs along the pressure contours instead of down them, and a weather map is a streamline plot.

mechanics · Circular motion The latitude past which the tide cannot shed its energy by halves. Frequency in cycles per day against latitude. The curve is the inertial frequency, 2Ω sin(latitude), below which no internal wave can oscillate; the shaded region above it is where internal waves exist. The horizontal lines are the semidiurnal and diurnal tides and the frequencies half of each, where a parametric instability would put the waves the tide decays into. Each line ends where it meets the curve, which is its critical latitude: M2, semidiurnal at 1.932 per day, 74.5°; M2 ÷ 2 at 0.966 per day, 28.8°; K1, diurnal at 1.003 per day, 30.0°; K1 ÷ 2 at 0.501 per day, 14.5°. Equatorward of 28.8° the semidiurnal tide can feed waves at half its frequency; poleward of it those waves cannot exist and that route is closed. The diurnal tide's subharmonic is confined within 14.5° of the equator, and the diurnal tide itself cannot propagate as a free internal wave poleward of 30°.

The latitude past which a tide cannot split

The ocean's internal tide carries about a terawatt, and somewhere it has to be broken into waves small enough to mix the water. One of the ways it breaks is by pumping waves at half its own frequency, the way a child on a swing pumps at twice the swing's. Those half-frequency waves cannot exist where the planet's rotation forbids oscillations that slow — poleward of 28.8° for the semidiurnal tide — so the route has an edge on the map, fixed by the Moon's period and the Earth's spin.

fluids · Stratification

Named alongside it

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

Coriolis forceFictitious forceLatitudeRotating frameAngular velocityApproximationBeta planeCentripetal accelerationConservation lawsCritical latitudeDimensionless numberEquilibrium

All concepts