Sunday, July 13, 2014

The Barrel Equation

Waves break when they become too steep and the velocity of the water particles at the crest exceeds the phase speed (the overall wave speed), so essentially they trip over themselves.  A wave will break when it reaches a depth of 1.3 times the wave height.  If the depth of the seabed is gradually decreasing (for instance, on a relatively flat beach) then this theory holds true and the wave will "spill" slowly, however if a wave comes out of deep water and hits a shallow reef then it will break much faster and hollower.

The Iribarren number can be used to classify breaker types depending on wave height (H), period (T) and beach slope gradient (B):

=(1.25H)T tanB

Spilling <0.4
0.4< Plunging >2.0
2.0> Surging

If you don't have an accurate measurement of the inshore bathymetry to hand though, and let's face it who does, then you can use Galvin's Breaker Type Parameter from 1968:

B=Hb/gT tanB

Where Hb = wave height at break point and g = gravity at 9.8m/s.

Surging B<0.003
Plunging 0.003<B>0.068
Spilling B<0.068

The length:width ratio of the cross-section of a barreling wave can be used to determine the intensity of the tube, from "wider then it is tall" through to the sort of head-dippers that you really have to contort yourself into:

Square <1:1
1:1< Round> 2:1
2:1> "Almond"

Have a think about that next time you see a photograph of Pipeline or Teahupoo shot from the channel, showing somebody stood in a keg wide enough to drive a car through with their arms outstretched and unable to touch the sides.  Maths for surfers:  Don't ever say that An Tor Orth An Mor isn't educational!

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