PhysWall · The Physical-Logic Gateway · four-dimensional gap decomposition

Wave period and depth: which shortcut is true here

A physics engine, and a verification tool enforced on top of it. PhysWall inverts a closed, published, non-linear physical law at a single measurement point — and refuses when the inverse is not unique. Seven laws, one engine, and the same refusal in all of them.

A wave period and a water depth, and which of the two shortcuts every textbook gives you is actually true here.

Between the two lies intermediate depth — water between one-twentieth and one-half of a wavelength, where neither shortcut holds and the full dispersion relation has to be solved.

THERE ARE TWO ANSWERS, AND A GAP

Shallow water: speed depends on depth alone. Deep water: speed depends on period alone. Both are taught, both are simple, and between them is a region where neither one is a statement about your wave.

The dispersion relationomega^2 = g k tanh(k h) — is exact everywhere. The shortcuts are what happens when the tanh saturates at one end and goes linear at the other. In between it does neither.

AND THE GAP IS WHERE HARBOURS ARE

kh < pi/10     shallow  -- the depth form holds
kh > pi        deep     -- the period form holds
between        NEITHER  -- and that is most of a coast

A 10 s swell in 15 m of water sits at kh = 0.86. That is not an edge case; it is an ordinary sea state on an ordinary shelf, and both shortcuts are wrong there.

AND ONE MORE REFUSAL, EARLIER THAN YOU EXPECT

Past a wave height of 0.78 of the depth, linear theory has already stopped describing the wave — McCowan, 1894. The tool says BREAKING and stops, rather than handing back a speed for something that is no longer a wave.

That is a bound and not an approximation, which is the same structure as a Bode-Fano floor: no amount of care on the method moves it.

WHERE THE NUMBERS CAME FROM

Airy linear wave theory, and g as CODATA standard gravity. The breaking ratio is McCowan's solitary-wave value, and it is chosen rather than derived — real breaking scatters around it with beach slope.

Where this stops: one frequency, one depth, no current and no wind. A real sea is a spectrum, and this answers for a single component of it.

AND WHAT IT IS NOT

Not a forecast and not a design code. It names the region you are in and tells you which formula stops being true there.

PhysWall was developed and architected by Gadi Zion.

Built on PhysWall — the same engine reads antenna bandwidth, conductor loss, bit erasure and heat limits. It answers what the measurement implies, and refuses when the measurement cannot say.

Check this instead of believing it. Every number here reproduces from a source that is named, and the claims that turned out wrong are still printed next to what replaced them. The same engine runs all of these — it asks how much a measurement allows you to conclude, and refuses the same way in every field. The same engine runs all of these — it asks how much a measurement allows you to conclude, and refuses the same way in every field. How to check each one →