Amphidromic points
A Socratic walk-through of amphidromic points — reasoned out one step at a time, not lectured.
The question we started with
THE QUESTION #Why does the tide barely rise at one spot in a sea while swinging metres a short distance away?
Somewhere in the middle of the North Sea there is a patch of water where the semidiurnal tide is essentially absent. A day's sail away, the same tide swings the sea surface by metres. The Moon is equally overhead in both places.
So whatever produces the difference cannot be the forcing. A companion piece here works out why the driving force is twice-daily — the gradient of the Moon's pull across the Earth's width. This one takes that forcing for granted and asks a different question: what does an ocean basin do with a rhythmic push, such that the answer is "nothing at all" in one spot and "several metres" nearby?
Reasoning it through
REASONING #Start by dropping the picture of a heap of water sliding around the planet. The tide in a real sea is a wave — it has a crest, a wavelength, and a speed set by the water's depth. And a wave in a basin does what all waves do at a wall: it reflects.
So consider the simplest case, a long channel with no rotation at all. A tidal wave runs up it and comes back. What do an incident wave and its reflection make together? A standing wave — some places where the two always cancel, others where they always reinforce. At a cancelling place the surface never rises. Notice what shape those places take: a line drawn across the channel. Every station along it has no tide.
That is halfway to the answer, but it is the wrong shape. Charts of real seas do not show lines of no tide; they show isolated points, with the hours of high water fanning out from them like the hours on a clock face. What is missing?
Rotation. The Earth turns beneath the moving water, and water in motion is deflected — to the right in the Northern Hemisphere. What does that do to a wave running up a channel? The flow is pushed against the right-hand coast, and the wave becomes lopsided: tall against that coast, decaying as you move away from it. A wave held against a wall this way is a Kelvin wave.
Here is the step that matters. The reflected wave runs the opposite way, so its right-hand coast is the other one. Instead of two waves of equal size everywhere, we have two waves each hugging opposite walls, each fading toward the middle.
What happens to the cancellation? On the old nodal line the two are no longer the same size except at one place — the point where the decaying amplitude of the incoming wave has fallen to exactly match that of the outgoing one. Cancellation survives at that single spot and nowhere else. The nodal line has collapsed to a nodal point. That is the amphidromic point, and rotation produced it.
And once you have a point of zero range surrounded by water that is not zero, the phase has to go somewhere. Walk a circle around the point and the moment of high water shifts continuously, running through the whole twelve-and-a-bit hours before returning to where you started. The crest does not jump between places; it sweeps around, anticlockwise in the Northern Hemisphere and clockwise in the Southern, because that is the direction a Kelvin wave must travel to keep its coast on the correct side.
Does the account predict something sharp enough to be wrong? Two things. First, the sense of rotation is fixed by hemisphere — a Northern Hemisphere amphidrome found rotating clockwise, with no local explanation, would sink the argument outright. Second, and more usefully, this is a node in elevation, not in motion. A standing wave's currents are strongest exactly where its surface is stillest. So a current meter moored at an amphidromic point should record vigorous tidal streams reversing on the tidal period while a tide gauge beside it records almost nothing. If the water there were genuinely slack as well as level, the standing-wave account would be refuted and something else — local damping, say — would be doing the work.
The analogy
THE ANALOGY #Think of the hour hand of a clock laid flat on the sea. The tip of the hand sweeps a long way each hour; the pivot at the centre never moves at all, though it is part of the same rigid hand. High water is the position of the hand, and the amphidromic point is the pivot.
the clock hand is rigid, so displacement grows in exact proportion to distance from the pivot, whereas real tidal range grows irregularly with distance because depth and coastline shape distort the pattern; and a hand is driven at its pivot, while a tidal wave is driven across the whole basin at once and steered by its coasts.
Clarifying the model
THE MODEL #Three refinements, and the first is a correction of the idealisation just built.
Real seas dissipate energy on the bottom and in shallows, so the reflected wave comes back weaker than the one that went out. If the outgoing wave is always the stronger, the two amplitudes may never match anywhere in the water and perfect cancellation cannot occur. The point is then displaced toward the weaker side — sometimes far enough to lie on land. Such degenerate or "virtual" amphidromes appear on real charts, with co-tidal lines converging on a spot inland where no sea exists to have zero range.
Second: "the tide" does not vanish anywhere. Each tidal constituent — the principal lunar semidiurnal, the solar semidiurnal, the diurnal terms — has its own basin response and its own amphidromic system in a different place. A station on the semidiurnal node still sees the other components, plus shallow-water and meteorological effects. The near-zero range is a statement about one constituent.
Third, an honest limit on the derivation. The two-Kelvin-wave picture is a textbook idealisation for a rectangular channel of constant depth. Actual amphidromic charts come from numerical models fitted to gauge and satellite altimetry data, in basins with irregular coasts and depths, and the resulting pattern is far messier. What survives is the mechanism — interference plus rotation converting a line into a point — not the tidy geometry.
A picture of it
THE PICTURE #How to readThe family is repurposed: this is a cycle drawn out straight, not a history, and the last entry is the same event as the first. Each stop names where in the basin high water is at that hour — the crest is never absent, only elsewhere. Reading the stops in order traces the crest anticlockwise around the basin, the Northern Hemisphere sense. The pivot of that sweep is the amphidromic point itself, which appears nowhere in the list because high water never occurs there.
What became clearer
WHAT CLEARED #The place with no tide is not a place the tide fails to reach. It is the pivot of a rotating wave. Interference between an incoming tidal wave and its reflection would, on a non-rotating Earth, give a line of no tide; rotation makes the two waves lean on opposite coasts, so they can only cancel at the one point where their fading amplitudes agree. Everything else follows — the hours of high water fanning out around it, the range climbing with distance, the strong currents in the middle of the stillness. The tide there is not weak; it is all motion and no rise.
Where to go next
ONWARD #- Why a basin whose natural period is close to the tidal period amplifies the range enormously, as at the Bay of Fundy.
Key terms
TERMS #| Term | What it means |
|---|---|
| Amphidromic point | a point in a basin about which the tidal wave rotates and at which the range of a given constituent is near zero. |
| Kelvin wave | a coastally trapped wave held against a boundary by rotation, decaying in amplitude away from that coast. |
| Co-tidal line | a line joining places where high water occurs at the same hour; these radiate from an amphidromic point. |
Every term the collection defines is gathered in the glossary.