The wavelength of a water wave depends upon several factors, with the most important being the
depth of the water. Let's define some terms:
L = the wavelength (feet)
h = the water depth (feet)
H = the wave height (feet)
pi = 3.14159...
In the following reference, Airy describes the limiting relationships between the above
parameters. Waves steeper than this will always tend to break:
Airy, G.B., (1845). Tides and Waves. Encyc. Metrop., Art., 192: 241-396
For h/L > 0.1 (i.e. "deep water") H/L <= 0.142 * tanh(2*pi*h/L)
In deep water (say h/L = 10) H/L <= 0.142 * tanh(2*pi*10) <= 0.142 or L => 8 / 0.142 => 56.34
feet. The water depth would have to be 10 * 56.34 = 563.4 feet for h/L = 10 in this example.
Remember, this is the steepest or most closely spaced that it is theoretically possible to
have water waves without having them break. My experience with rolling Great Lakes waves of
this size has them spaced out about 4 - 5 boat lengths or approximately 100 feet.
Roger Pihlaja
S/V Dynamic Equilibrium
28 Feb 2002
