substituting
fore,
Equation 2-81 into the expression for the wavelength; there4jr^g
&
jg tanh (7rjd//B)
(2-82)
, j =
For an enclosed harbor, of approximately rectangular planform with length,
lBt waves entering through a breakwater gap having a prédominant period
close to one of those given by Equation 2-82 for small values of j, may
cause significant agitation unless some effective energy dissipation
mechanism is présent. The addition of energy to the basin at the résonant
(or excitation) frequency (fj = 1/Tj) is said to excite the basin.
Equation 2-82 was developed by assuming the end boundaries to be
vertical; however, it is still approximately valid so long as the end
boundaries remain highly reflective to wave motion. Sloping boundaries,
such as beaches, while usually effective energy dissipaters, may be significant ly reflective if the incident waves are extremely long. The effect of
sloping boundaries and their reflectivity to waves of differing characteristics is given in Section 2.54, Wave Reflection from Beaches.
Long-period résonant oscillations in large lakes and other large
enclosed bodies of water are termed seiches. The periods of seiches may
range from a few minutes up to several hours, depending upon the geometry
of the particular basin. In general, these basins are shallow with respect
to their length; hence, tanh (Trjd/fcg) in Equation 2-82 becomes approximately
equal to njd/Jtg and
24 1
Tï = ~
J = x’ 2’ ’ ' ’ ’
1
J (gû)
Equation 2-83 is termed Merian's équation. In natural basins, complex
geometry and variable depth will make the direct application of Equation
2-83 difficult; however, it may serve as a useful first approximation for
enclosed basins. For basins open at one end, different modes of oscillation exist since résonance will occur when a node is at the open end of
the basin and the fundamental oscillation occurs when there is one quarter
of a wave in the basin; hence, lB> = L/4 for the fundamental mode and
T = 4ty//gd. In general iB' = (2j - l)L/4, and
T
1
>
(2,-1) (gd)*4 j ~ 1> 2, * • • • (small values) .
(2-84)
Note that higher modes occur when there are 3, 5,
quarters of a wave within the basin.
- 1, etc.,
d
2-116
fore,
Equation 2-81 into the expression for the wavelength; there4jr^g
&
jg tanh (7rjd//B)
(2-82)
, j =
For an enclosed harbor, of approximately rectangular planform with length,
lBt waves entering through a breakwater gap having a prédominant period
close to one of those given by Equation 2-82 for small values of j, may
cause significant agitation unless some effective energy dissipation
mechanism is présent. The addition of energy to the basin at the résonant
(or excitation) frequency (fj = 1/Tj) is said to excite the basin.
Equation 2-82 was developed by assuming the end boundaries to be
vertical; however, it is still approximately valid so long as the end
boundaries remain highly reflective to wave motion. Sloping boundaries,
such as beaches, while usually effective energy dissipaters, may be significant ly reflective if the incident waves are extremely long. The effect of
sloping boundaries and their reflectivity to waves of differing characteristics is given in Section 2.54, Wave Reflection from Beaches.
Long-period résonant oscillations in large lakes and other large
enclosed bodies of water are termed seiches. The periods of seiches may
range from a few minutes up to several hours, depending upon the geometry
of the particular basin. In general, these basins are shallow with respect
to their length; hence, tanh (Trjd/fcg) in Equation 2-82 becomes approximately
equal to njd/Jtg and
24 1
Tï = ~
J = x’ 2’ ’ ' ’ ’
1
J (gû)
Equation 2-83 is termed Merian's équation. In natural basins, complex
geometry and variable depth will make the direct application of Equation
2-83 difficult; however, it may serve as a useful first approximation for
enclosed basins. For basins open at one end, different modes of oscillation exist since résonance will occur when a node is at the open end of
the basin and the fundamental oscillation occurs when there is one quarter
of a wave in the basin; hence, lB> = L/4 for the fundamental mode and
T = 4ty//gd. In general iB' = (2j - l)L/4, and
T
1
>
(2,-1) (gd)*4 j ~ 1> 2, * • • • (small values) .
(2-84)
Note that higher modes occur when there are 3, 5,
quarters of a wave within the basin.
- 1, etc.,
d
2-116