EM 1110-2-1100 (Part II)
30 Apr 02
small vessels in particular. The ebb currents may be of sufficient strength to induce wave breaking and
turbulence in the entrance, a condition that is particularly hazardous to vessel operation.
(b) Bruun (1978) summarizes earlier literature and discusses the problem of sediment transport. Mehta
and zsy (1978) found that the effects of bottom friction are important in the hydrodynamics of two-
dimensional turbulent jets because it increases the rate of spreading of the jet, which has a significant effect
on incident wave characteristics. Sakai and Saeki (1984) measured the effect of opposing currents on wave
height transformation over a 1:30 sloping beach for a range of wave periods and steepness. They found an
increase in wave height and decay rate in the presence of the opposing current. Willis (1988) conducted
monochromatic wave and ebb current tests in a 1-m-wide rectangular entrance channel cut in a 1:30 sloping
beach. Current measurements were averaged over 3 min to obtain a quantitative picture of the mean currents.
They experienced major problems with the stability of the current field due to large-scale meandering
motions.
(c) Lai, Long, and Huang (1989) conducted flume tests of kinematics of wave-current interactions for
strong interactions with waves propagating with and against the current. They found the influence of the
waves on the mean current profiles was small, although opposing waves would give a slightly lower current.
They observed a drastic change in the spectral shape, especially higher harmonics, following wave breaking
in the presence of opposing currents. Their experiments confirmed blockage of waves by a current when the
ratio of depth-averaged current velocity to wave celerity without currents approaches -0.25.
(d) Raichlen (1993) conducted a laboratory investigation of waves propagating on an adverse jet to
simulate the effect of ebb currents on incoming waves at a tidal inlet. He tested regular waves (depth-to-
wavelength ratios from 0.086 to 0.496) for a range of relative channel entrance velocities to wave celerity for
locations both upstream (20 channel widths) and downstream (15 channel widths) of the channel entrance.
Wave height increased by a factor of 2.5 near the channel entrance in the presence of a current that was only
7 percent of the phase speed, primarily caused by wave refraction. He also found that the wave height
decreases significantly as waves propagate up the entrance channel. Refraction and entrainment of the still
fluid by the ebb current jet produces a lateral variation in the wave height across the channel width
downstream of the entrance.
(e) Briggs and Green (1992) and Briggs and Liu (1993) conducted three-dimensional laboratory
experiments of the interaction of regular waves with ebb currents offshore of a tidal entrance channel
(6 channel widths) on a 1:30 plane beach. Current velocity to wave celerity ratios ranged from 0.06 to 0.34.
Under the influence of ebb currents, waves experienced increases in steepness and corresponding wave height
up to a factor of nearly 2 for currents that were 20 to 30 percent of the phase speed. As waves shoal and
break, higher harmonics are formed as the wave becomes more nonlinear. Energy is transferred from the
fundamental mode due to nonlinear coupling between frequencies. Briggs and Liu found that ebb currents
also promote the nonlinear growth of the fundamental frequency, higher harmonics, and subharmonics of the
incident wave. This shift in energy can change the response characteristics of vessels in the entrance channel.
(4) Vessel sinkage and trim.
(a) The pressure distribution that develops around the hull of a moving vessel results in an above-average
pressure at the bow and stern and a below-average pressure at the midsection of the vessel. The reduced
pressure at the midsection dominates and causes a net sinkage of the vessel. The vessel sinkage is also
referred to as squat. Since there is usually an imbalance of upward forces between the bow and stern, the
vessel will often also trim by the bow (i.e. the vessel bow is lowered relative to the stern) or by the stern.
(b) Sinkage and trim of a vessel in a navigation channel depend on the factors that control the pressure
distribution along the vessel hull. Primarily, these are the vessel speed, the ratio of the channel cross section
Harbor Hydrodynamics
II-7-59
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