0 (no friction) to 0.02 (strong damping, as over a porous reef) are shown in Fig. 8 for the
idealized basin. Amplitudes are normalized by the no-friction value of the corresponding
harmonics (3 and 5 cpd), and the first resonant mode (4.7 cpd) are present. The curves for
the fundamental and harmonic frequencies indicate steep damping for smaller values of
friction coefficients, tapering to mild slopes with greater values of friction. Curves for the
harmonic frequencies approach near-zero slope with increased friction coefficient. Motion
at these frequencies is present, even at large friction values, because it is forced over the
entire surface of the water body. In contrast, the resonant frequency damps to near zero for
even small values of friction, being a boundary-induced phenomenon.
0.15
WSEL
Speed
0.10
0.05
0.00
-0.05
-0.10
-0.15
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Elapsed Time, day
Fig. 6. Time series of water-surface elevation and current, 2-m depth
0.12
WSEL
Current
0.10
0.08
0.06
0.04
Peak u
Peak u
Peak η
0.02
0.00
0
1
2
3
4
5
6
7
8
Frequency, cpd
Fig. 7. Spectra of water-surface elevation and current, 2-m depth
9
Kraus & Militello
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