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downstream flow changes to predominantly upstream flow. This is a 
crucial point in any stratified estuary. 
Since an estuary is the downstream limit of a river, all the sediment carried by the 
river ends up in the estuary, usually as fine silt and clay. The clay is suspended in 
the flow and the clay particles carry a negative electrical charge that keeps them in 
suspension. When these particles meet the saline water, this charge is neutralized. 
The clay flocculates and settles out of the water, forming abundant layers of very 
loose mud on the bottom. This mud has a density of less than 1300 kg/m3 and 
behaves essentially as a viscous fluid. The bottom currents move this material 
downstream past D to the point where the predominant flow direction reverses from 
downstream to upstream. That is the area where the large volumes of estuarine 
sediments will be deposited and form shoals. It is the most treacherous section of 
the estuary for navigation and usually it requires constant maintenance by dredging. 
Figure 6.13 is a simplistic explanation of salinities and currents. In reality, there are 
daily variations in tides and seasonal variations in the fresh water discharge. Also, 
Fig. 6.13 is two-dimensional but the actual patterns of the tides, the tidal currents, 
salinities, densities and the currents resulting from density differences are three- 
dimensional, varying also across the estuary. This makes an estuary a very complex 
system that requires special care in design. Contrary to design in the open sea, much 
of the construction in an estuary will affect the tides. Dredging to improve 
navigation in the treacherous shallow water areas must be done with cure. All the 
dredge spoil must be removed from the estuary, otherwise the converging currents 
Chapter 6 - Tides and Water Levels 133 
will simply return it to the same location. Dredging the shoals increases the 
salinities further upstream and may affect marine habitat. For example, oysters can 
only live within a very narrow range of salinities and thus dredging sediment 
deposits may inadvertently kill oyster beds upstream. Similarly, water intake and 
sewer outfalls will be affected by the changes in salinity. Filling in low-lying land 
adjacent to the estuary not only destroys valuable, productive habitat, but it also 
decreases the tidal prism. This will in turn decrease tidal flow, encouraging 
sedimentation, and it will change salinities upstream, with its attendant 
consequences to the environment. 
One other major design consideration in estuaries is that all basins (harbours, 
marinas, cooling water reservoirs) adjacent to an estuary will receive suspended 
sediment with each incoming flood and through density currents. This sediment 
settles into the basin and cannot be removed by the ebb currents. Thus such basins 
fbnction as one-way sediment pumps, often resulting in very large maintenance 
6.2.8 Tidal Computation 
The tides and tidal flows in an estuary are complex and require computational 
models to calculate water levels, flows, salinities, and densities. A detailed 
discussion of such models is beyond the scope of this text and may be found in many 
technical papers, as well as in Abbott (1 979), Abbott and Basco (1 989), Cunge et al. 
( 1 980), Dronkers ( 1 964) and Murthy ( 1 984). Such models use the equations of 
continuity and motion. The most sophisticated formulation uses three-dimensional 
versions of these equations, but most often a two-dimensional (horizontal) 
formulation (2-DH) is used'. In 2-DH models, it is assumed that all variables are 
constant over the depth of water. For stratified estuaries this assumption is 
obviously not valid, and it is customary to use several 2-DH models stacked on top 
of each other to represent layers in the flow. 
For estuaries with a regular geometry, sometimes the equations can be simplified to 
give a one-dimensional (1-D) computation, which uses averaged values over the 
whole estuary cross-section. Such a I-D model has severe limitations, but if the 
available input data are insufficient to calibrate a 2-DH model properly, as is often 
the case, then more sophisticated models will not yield better results than the simple 
I-D models. Finally, for inlets as in Fig. 6.7, there exist very simple computational 
methods to compute water levels and flows. 
1. Further discussion of this terminology may be found in Ch 13. 
134 Introduction to Coastal Engineering and Management 
6.3 Storm Surge 
The water level fluctuation of greatest concern in design is storm surge, which is an 
increase in water level resulting from shear stress by onshore wind over the water 
surface (Fig. 6.14). This temporary water level increase occurs at the same time as 
major wave action and it is the cause of most of the world's disastrous flooding and 
coastal damage. Parts of Bangladesh are flooded regularly by storm surge generated 
by passing cyclones, resulting in the loss of thousands of lives. In a 1990 cyclone, 
the water levels rose by 5-10 m and it was estimated that more than 100,000 lives 
were lost. The shorelines along the southern borders of the North Sea were flooded 
in 1953 because storm surge caused dike breaches. Property damage was very 
extensive and 1835 lives were lost in the Netherlands. The threat of severe storm 
surge from Hurricane Floyd in 1999 caused the evacuation of 3 Million people 
along the East coast of the United States and Canada. It resulted in 50 deaths in the 
United States, Bahamas and other Atlantic Islands. 
D S 
a) Open Shore b) Lake 
Figure 6.14 Definition Sketch for Storm Surge 
During storm surge, the water level at a downwind shore will be raised until gravity 
(the slope of the water surface) counteracts the shear stress from the wind. 
Computations of storm surge are carried out using the same depth-averaged two 
dimensional equations of motion and continuity that are used for tidal computations. 
In this case wind-generated shear stress is the main driving force. For simple 
problems, the equations can be reduced to a one-dimensional computation 
where S is the storm surge (the setup of the water level by the wind), x is the 
Chapter 6 - Tides and Water Levels 135 
Ax (km) 
d (m) 
D (m) 
AS fmb 
distance over which the storm surge is calculated, C, is a constant (=3.2.10-6), U is 
the wind speed, I$ is the angle between the wind direction and the x-axis and D is the 
new depth of water (=d+S). Equation 6.4 shows that storm surge is greatest in 
shallow water; that is why Bangladesh on the delta of the Ganges, Brahmaputra and 
Meghna rivers and the Netherlands on the delta of the Rhine, Meuse and Scheldt are 
very susceptible to storm surge. 
1 2 3 4 5 6 
3 2 2 1 I 1 
15 10 5 2.8 I .9 1.4 
15.0 10.03 5.05 2.90 2.05 1.61 
0.026 0.026 I 0.052 0.045 .064 ,081 
Example 6.1 One-Dimensional Surge Calculation@ 
Equation 6.4 may be solved numerically. The simplest numerical integration (Euler) 
starts in deep water with an initial condition S = 0 and moves toward shore. The 
distance to shore is divided into sections of length Ax for which depth is assumed to 
be constant. A value of AS is calculated for the first Ax and D=d+S may be 
calculated for the end of this first section. This value of D is then used to compute S 
for the second section and so on until the calculation reaches shore. 
The following table presents S for a 10 km long offshore profile, divided into 6 
sections for which the depth is assumed to be constant. For U = 20 d s e c and $ = 
Oo, the storm surge at the shore is shown to be 0.29 m. 
I S (m) I 0.03 I 0.05 I 0.10 I 0.15 I 0.21 1 0.29 I 
Equation 6.4 assumes steady conditions; the wind blows forever in one direction. 
Thus, it computes maximum surge, a value that can be used in feasibility studies and 
conservative desk design. 
On an enclosed body of water such as a lake, the wind stress obviously results in a 
negative storm surge at the upwind shore as

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