CETN IV-18
March 1999
A more useful form of Equation 3 is obtained by multiplying both sides by h8 and rearranging to
get an expression for the equilibrium discharge per unit depth, i.e.,
qe = C e [g (S s - 1)]
1/ 2
d e3 / 8 h 9 / 8
(4)
where the qe is defined as the Equilibrium Maximum Discharge per unit width, given by
qe = V h
(5)
and Ss = s/w is the sediment specific gravity (about 2.65 for quartz sand). As expected,
Equation 4 indicates that the equilibrium maximum discharge is primarily a function of water
depth with sediment size having a relatively minor effect.
MEASUREMENTS: The unknown coefficient in Equation 4 was empirically evaluated by
comparision to field measurements at two dual-jetty tidal inlets. Vertical profiles of horizontal
velocity were measured along transects at Shinnecock Inlet, New York, and at Ponce de Leon
Inlet, Florida, using a boat-mounted acoustic Doppler current profiler. Discharge per unit width
was estimated from the measurements by integrating the velocity profiles over the depth.
Profiling transects across the inlet throats occurred at or around the maximum ebb or flood flow.
The results are shown in Figure 1 where calculated discharge per unit width is plotted versus the
([g (S
)
- 1)]
1/ 2
d e3 / 8 h 9 / 8 on the right-hand side of Equation 4. Grain size for the
term
s
Shinnecock Inlet channel was taken as 0.6 mm, whereas a size of 0.21 mm was used for Ponce
de Leon Inlet. Both sands were assumed to have the same density as quartz.
The data points on Figure 1 show a wide range of discharge per unit width measured at the
different depths. However, there is an upper limit to the data as indicated by the straight dashed
line. This dashed line represents the maximum discharge per unit width (qe) that can be
([g (S
)
- 1)]
1/ 2
d e3 / 8 h 9 / 8 . The discharge
sustained at a particular value of the parameter
s
indicated by the dashed line is termed the equilibrium maximum discharge. Any increase in
discharge beyond the equilibrium value will result in an increase in water depth.
The scatter of measurements beneath the dashed line is pronounced, and this indicates that the
discharge calculated for those measurements was less than could be tolerated by the depth at that
location. Points just beneath the dashed line might be locations where the present bottom was
eroded by discharges slightly greater than those measured during the field exercises. Many of the
data points well below the line came from inlet cross sections either slightly seaward of the
jetties where depths are controlled by waves and longshore currents or landward of the entrance
channel where the tidal current is insufficient to scour the channel and depths have been
increased by dredging.
3