(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

(II-7-9)

where

RB = basin length along the axis

(3) This equation is often referred to as Merian's formula. The maximum oscillation period *T*1

corresponding to the fundamental mode is given by setting *n *= 1 as

2 RB

(II-7-10)

(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

2

(II-7-11)

Closed basin

%

R1

R2

where

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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