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.
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 relation —
omega^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.
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.
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.
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.
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 →