ERDC/CHL CETN-IV-29
September 2000
1.25
0.97 m/s
Flood
1.00
0.75
0.50
0.245 day
0.25
(5.9 hr)
0.00
0.276 day
(6.6 hr)
-0.25
-0.50
-0.75
1.15 m/s
Ebb
-1.00
-1.25
0.0
0.5
1.0
1.5
2.0
Elapsed Time, day
Figure 2. Ebb-dominated current formed by 30 deg lead of the M2 over the M4 tidal constituent
How can the net discharge be zero if the current is stronger on the ebb or flood tide? There are
two properties that control the relationship between discharge and tidal current. One is the shape
of the velocity curve, and the other is the difference in tidal phase between the water level and
and nonlinear interactions within the water motion and is described by the relative phases
between tidal constituents. (For detailed discussion on tidal constituents, see Defant 1961;
Dronkers 1964; Scheffner 1994, 1995.) Phase relationships between tidal constituents describe
whether the tidal curves are flood dominant, ebb dominant, or have no dominance (Aubrey and
Speer 1985; DiLorenzo 1988), in the absence of significant nontidal forcing. As an example,
diurnal, 6.21-hr period) having amplitudes of 1.0 and 0.1 m/s, respectively. The phase
relationship between the M2 and M4 components is described as
θ = 2φ M 2 - φ M 4
(1)
where θ is the phase difference between the two constituents, φM2 is the phase of the M2
constituent, and φM4 is the phase of the M4 constituent. This phase relationship holds because the
the combined tidal current has the ebb-dominated shape shown in Figure 2. The duration of the
flood tidal current (6.6 hr) exceeds that of the ebb tidal current (5.9 hr). The greater peak ebb
speed balances the longer flood duration such that there is a zero mean velocity through the inlet.
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