that is, the pressure distribution may be assumed to vary linearly from
pgys at the bed to zéro at the surface.
Figures 2-9 and 2-10 show the dimensionless cnoidal wave surface
profiles for various values of the square of the modulus of the elliptic
intégrais k2, while Figures 2-11 through 2-15 présent dimensionless
plots of the parameters which characterize cnoidal waves. The ordinates
of Figures 2-11 and 2-12 should be read with care, since values of k2
are extremely close to 1.0 (k2 = 1-10”1 = 1-0.1 = 0.99). It is the
exponent a of k2 = l-10"a that varies along the vertical axis of
Figures 2-11 and 2-12.
Idéally, shoaling computations might best be performed using cnoidal
wave theory since this theory best describes wave motion in relatively
shallow (or shoaling) water. Simple, completely satisfactory procedures
for applying cnoidal wave theory are not available. Although linear wave
theory is often used, cnoidal theory may be applied by using figures such
as 2-9 through 2-15.
The following problem will illustrate the use of these figures.
************** EXAMPLE PROBLEM **************
GIVEN: A wave traveling in water depth of d = 10 feet, with a period of
T = 15 seconds, and a height of H = 2.5 feet.
FIND:
(a) Using cnoidal wave theory, find the wavelength L and compare this
length with the length determined using Airy theory.
(b) Détermine the celerity C. Compare this celerity with the celerity
determined using Airy theory.
(c) Détermine the distance above the bottom of the wave crest (y^)
and wave trough (yp .
(d) Détermine the wave profile.
SOLUTION:
(a) Calculate
and
32.2
----- = 26.92
10
2-49
pgys at the bed to zéro at the surface.
Figures 2-9 and 2-10 show the dimensionless cnoidal wave surface
profiles for various values of the square of the modulus of the elliptic
intégrais k2, while Figures 2-11 through 2-15 présent dimensionless
plots of the parameters which characterize cnoidal waves. The ordinates
of Figures 2-11 and 2-12 should be read with care, since values of k2
are extremely close to 1.0 (k2 = 1-10”1 = 1-0.1 = 0.99). It is the
exponent a of k2 = l-10"a that varies along the vertical axis of
Figures 2-11 and 2-12.
Idéally, shoaling computations might best be performed using cnoidal
wave theory since this theory best describes wave motion in relatively
shallow (or shoaling) water. Simple, completely satisfactory procedures
for applying cnoidal wave theory are not available. Although linear wave
theory is often used, cnoidal theory may be applied by using figures such
as 2-9 through 2-15.
The following problem will illustrate the use of these figures.
************** EXAMPLE PROBLEM **************
GIVEN: A wave traveling in water depth of d = 10 feet, with a period of
T = 15 seconds, and a height of H = 2.5 feet.
FIND:
(a) Using cnoidal wave theory, find the wavelength L and compare this
length with the length determined using Airy theory.
(b) Détermine the celerity C. Compare this celerity with the celerity
determined using Airy theory.
(c) Détermine the distance above the bottom of the wave crest (y^)
and wave trough (yp .
(d) Détermine the wave profile.
SOLUTION:
(a) Calculate
and
32.2
----- = 26.92
10
2-49