tte refractive index of the Transmi ,Tît~ i mg medium. W^à-ag 1411 s acialG^y,
D” Brien (1942) soaggested the aase of Smell's law of georaetrica! optics for
solving the problem of water—wave réfraction by «franges in depth. The
validity of this approach has been verified experimental ly by Chiem (1954),
Rails (1956) , and Wiegel and Arnold (1957). Chao (1970) showed amalytically that Fermof s principale and hence Snell’s law followed from the
goveraing hydr adynamie équations, and was a valid approximation wfoeu Applied
to the réfraction profolem. Generally, two basic techniques of réfraction
analysis are avallabié - graphical and mamerical. Several graphical procedures are arailable, but fundamentally ail methods of réfraction analyses
are based on Snell’s law.
The assumptions usually -made are:
(1)
Wave energy between wave rays or orthogonals remaias constant.
{«Orthogonals are limes drawn perpendicular to the wave crests, and extemd
in the direction ©f wave advance.)
[See Figure 2-17.)
(2) Direction of wave advance is perpendicular to the wave crest,
that is, in the direction of the orthogonals.
(3) Speed of a wave of given period at a particnlar location
dépends only on the depth at that location.
(4) Changes in bottom topography are graduai.
(5) Waves are long-crested, constant-period, small-aïqplitude, and
monochromatic.
(6) Effects of currents, winds, and reflections from beaches, and
imderwater topographie variations, are considered negligible.
2.32 GENERAL - REFRACTION BY BATHYMETRY
In water deeper than one-half the wavelength, the hyperbolic tangent
fonction in the formula
C2 = — tant
2n
2k d
L
(2-2)
is æarly ©quai to unity, and Equation 2-2 reduces to
In this equatinn, the velocity C.o, does not dépend on depth; therefore
in those régions deeper than one-half the wavelength (deep water), refraction by hathymetiy will not be significant. Where the water depth is
between 1/2 and 1/25 the wavelength (transitional water), and in the régi»
where the water depth is less than 1/25 the wavelength (shallow water),
réfraction effects may be significant. In transitional water, wave velocity
2-65
D” Brien (1942) soaggested the aase of Smell's law of georaetrica! optics for
solving the problem of water—wave réfraction by «franges in depth. The
validity of this approach has been verified experimental ly by Chiem (1954),
Rails (1956) , and Wiegel and Arnold (1957). Chao (1970) showed amalytically that Fermof s principale and hence Snell’s law followed from the
goveraing hydr adynamie équations, and was a valid approximation wfoeu Applied
to the réfraction profolem. Generally, two basic techniques of réfraction
analysis are avallabié - graphical and mamerical. Several graphical procedures are arailable, but fundamentally ail methods of réfraction analyses
are based on Snell’s law.
The assumptions usually -made are:
(1)
Wave energy between wave rays or orthogonals remaias constant.
{«Orthogonals are limes drawn perpendicular to the wave crests, and extemd
in the direction ©f wave advance.)
[See Figure 2-17.)
(2) Direction of wave advance is perpendicular to the wave crest,
that is, in the direction of the orthogonals.
(3) Speed of a wave of given period at a particnlar location
dépends only on the depth at that location.
(4) Changes in bottom topography are graduai.
(5) Waves are long-crested, constant-period, small-aïqplitude, and
monochromatic.
(6) Effects of currents, winds, and reflections from beaches, and
imderwater topographie variations, are considered negligible.
2.32 GENERAL - REFRACTION BY BATHYMETRY
In water deeper than one-half the wavelength, the hyperbolic tangent
fonction in the formula
C2 = — tant
2n
2k d
L
(2-2)
is æarly ©quai to unity, and Equation 2-2 reduces to
In this equatinn, the velocity C.o, does not dépend on depth; therefore
in those régions deeper than one-half the wavelength (deep water), refraction by hathymetiy will not be significant. Where the water depth is
between 1/2 and 1/25 the wavelength (transitional water), and in the régi»
where the water depth is less than 1/25 the wavelength (shallow water),
réfraction effects may be significant. In transitional water, wave velocity
2-65