EM 1110-2-1100 (Part II)
30 Apr 02
(2) Basins are generally shallow relative to their length. Hence, basin oscillations involve standing
waves in shallow water. The simplest basin geometry is a narrow rectangular basin with vertical sides and
uniform depth. The natural free oscillating period for this simple case, assuming water is inviscid and
incompressible, is given by
2 RB
Closed basin
Tn '
(II-7-9)
n gd
where
Tn = natural free oscillation period
n = number of nodes along the long basin axis (Figure II-7-46)
RB = basin length along the axis
d = water depth
(3) This equation is often referred to as Merian's formula. The maximum oscillation period T1
corresponding to the fundamental mode is given by setting n = 1 as
2 RB
T1 '
(II-7-10)
gd
(4) If the rectangular basin has significant width as well as length (Figure II-7-28), both horizontal
dimensions affect the natural period, given by
1
2
2 &
2
n
m
2
Tn , m '
(II-7-11)
Closed basin
%
R1
R2
gd
where
Tn,m = natural free oscillation period
n,m = number of nodes along the x- and y-axes of basin
R1,R2 = basin dimensions along the x- and y-axes
(5) Equation II-7-11 reduces to Equation II-7-9 for the case of a long narrow basin, in which m = 0.
Further discussion is provided in Raichlen and Lee (1992) and Sorensen (1993). Closed basins of more
complex shape require other estimation procedures. Raichlen and Lee (1992) present procedures for a
circular basin and approximate solution methods for more arbitrary basin shapes. Defant (1961) outlines a
method to determine the possible periods for two-dimensional free oscillations in long narrow lakes of
variable width and depth. Locations of nodes and antinodes can also be determined. Usually numerical
models are used to properly estimate the response of complex basins.
Harbor Hydrodynamics
II-7-35
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