Calculate ocean wave dimensionless Keulegen Carpenter number, Ursell number and other wave numbers for Airy, Stokes and cnoidal waves.
The Keulegan Carpenter number approximates the ratio of drag force to inertia force on a circular structure.
`Kc = (V T) / (OOD) = V^2 / (A.OOD) `
`A = V / T `
where :
Kc = Keulegan Carpenter number
V = velocity amplitude
T = oscillation period
OOD = structure outer diameter or characteristic length
A = approximate acceleration amplitude
For small Keulegen-Carpenter numbers inertia forces dominate. At large Keulegen-Carpenter numbers drag forces dominate. The maximum horizontal wave velocity is calculated at zero degrees phase angle. Use the wave velocity reduction factor for structures which are not perpendicular to the wave velocity. The drag force over inertia force ratio varies with heading.
The Ursell number is a measure of the non linearity of ocean waves.
`Ur = (h l^2) / d^3 = (h/d)^3 / (l/d)^2 `
where :
Ur = Ursell number
h = wave height
l = wave length
d = water depth
The Airy wave is suitable for Ur < 1. Stokes wave should be used for Ur < 40. Cnoidal wave should be used for Ur > 40.
Other ocean wave numbers include:
`kw = (2 pi) / l = (2 pi fw) / c `
`fw = 1 / T `
`H^* = H / (g t^2) `
`d^* = d / (g t^2) `
where :
kw = wave number (dimesion 1/length)
fw = wave frequency (dimension 1/time)
H* = dimensionless wave height
d* = dimensionless water depth
l = wave length
f = wave frequency
c = wave celerity or propagation speed
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