Outer Earth processes and systems - Physical Processes in Earth and Environmental Sciences - page 273

Uniform incoming waves

Small Small

Large

breakers breakers

breakers

Momentum flux
out

Momentum flux
out

Antinode
reinforcement
of edge wave
crests

Momentum Flux
in

Rip Cell Rip Cell

Long s hore cur re nts

Large setup

Swash

Swash

Edge wave
crests reinforced

Edge wave ray

Beach Beach

Fig. 6.48 Rip current cells located in areas of small breakers where incoming waves and standing edge waves are out of phase.

convergence effect . Thus for wave energy, E , per unit length
of an estuary, Eb is the energy per unit length, where b is
total estuary width. Multiplying by the wave speed, c , gives
the energy flux up the estuary as Ebc

circulatory advection. Viewed in this way, water dynamics
in estuaries may be conveniently represented by four major
end-members (Fig. 6.49). However, it is important to
realize that a single estuary may change its hydrodynamic
character with time according to changing river, tidal, and
wave conditions.
Type A well-stratified estuaries are those river-dominated
estuaries where tidal and wave mixing processes are
permanently or temporarily at a minimum. The stratified
system is dominated by river discharge, with the
tidal : river discharge ratio being low, less than 20. An
upstream tapering salt wedge occurs, over which the fresh
river water flows as a buoyant plume (Fig. 6.50). Shear
waves of Kelvin-Helmholtz type may occur at the halocline
interface, the waves cause upward advective mixing of salt
water with fresh water. Should flow occur over topography
then internal solitary wave trains may be triggered at the
interface. A prominent zone of deposition and shoaling at
the tip of the salt wedge arises when sediment deposition
from bedload occurs in both fresh water and seawater. This
zone of deposition shifts upstream and downstream in
response to changes in river discharge and, to a much
lesser extent, to tidal oscillation.
Type B partially stratified estuaries are those in which tur-
bulence destroys the upper salt-wedge interface, producing

constant. Writing

ga 2 )/2 and the wave equation for sha llow water
waves as c

E (

( gh ) 0.5 , we have ga 2 ) b 0.5( gh 5 constant ,

b 0.5 h 0.25 . We can see that narrowing has more
effect on changing wave amplitude than shallowing.
Shallowing also causes the wave speed to decrease and,
since wave frequency is constant, the wavelength m ust
decrease by the argument c

or, a ∝

f . Since c / f gh / f ,

h 0.5 . Thus tidal waves increase in amplitude
and decrease in wavelength up many estuaries. But we can-
not ignore frictional retardation of the tidal wave in this
discussion; this causes a reduction in amplitude of the tide
upstream and is greatest when channel depth decreases
rapidly. In some estuaries the tidal wave changes little in
amplitude since the convergence effect is balanced by
frictional retardation. Resonant effects with tide or wave
may also affect currents in estuaries (Section 6.6).
The most fundamental way of considering estuarine
dynamics is through the principle of mass conservation,
which states that the time rate of change of salinity or sus-
pended sediment concentration at a fixed point is caused
by two contrasting processes: turbulent diffusion and

we have ∝