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the possible 
interaction of the proposed changes with the large complex tidal circulations into 
account. For example, when Prince Edward Island (Fig 6.6) was to be ~ o ~ ~ t e d to 
mainland New Brunswick in 1997, a bridge was used. A causeway connection 
would have induced major changes in the large-scale tidal patterns and would have 
impacted currents and fisheries for hundreds of kms. 
In the deep, open ocean, the fluid velocity (tidal current or horizontal tide) is in 
phase with the tidal water level fluctuations (vertical tide). At high water there is a 
maximum current velocity in the direction of tide propagation. This is similar to 
progressive short waves discussed in Ch. 2, in which the horizontal component of 
orbital motion and the velocity of propagation are in the same direction at the 
moment of high water (Fig. 2.6). When the tide approaches land, however, the 
phase relationship between horizontal and vertical tide changes. In the case of a 
tidal inlet and bay as in Fig. 6.7, the water level fluctuations in the bay are driven by 
Chapter 4 - Tides and Water Levels 127 
the tidal water level in the sea. Rising water levels in the sea cause a current to flow 
into the bay, raising its water level. This inflow of water is called flood and the 
outflow current during the other half of the tidal cycle is called ebb. For a small bay 
and a large entrance, there is no phase lag between the vertical tide in the bay and in 
the sea. At the time of high water in the sea, the maximum water level is also 
reached in the bay and will begin to lower. Thus, at that moment of high water in 
both the sea and the bay the flood current through the inlet becomes zero. This is 
called high water slack tide. Similarly a low water slack tide occurs at low water. 
Currents flowing through the inlet are maximum at the time of mean water. If we 
call the in-flowing (flood) current positive then the current leads the water levels by 
90". This is demonstrated in Fig 6.8 where Curve B (the current) leads the vertical 
tide (Curve A) by 90'. This is characteristic of complete wave reflection and may be 
compared with Table 2.4, where the upstream (flood) velocity u is 90" out of phase 
with the water level change q. 
Sea 
Flood 
If the inlet is narrow or the bay is long, the maximum water level in the bay will 
occur later than in the sea, which means that flow will continue to enter the bay for 
some time after high water in the sea. In this case, the horizontal tide (current 
through the inlet) will lead the vertical tide (in the sea) by less than 90°, and the tidal 
wave is partly progressive, partly reflecting. This is demonstrated by Curve C in 
Fig. 6.8. 
128 Introduction to Coastal Engineering and Management 
0 2 4 6 8 10 12 14 
Time (hrs) 
Figure 6.8 Horizontal and Vertical Tide 
Figure 6.9 Tidal Prism in an Estuary 
Chapter 6 - Tides and Water Levels 129 
In an estuary (Fig. 6.9) the tide levels upstream of Section AA are the result of water 
flowing past AA. Because the distances along the estuary are substantial and may 
be of the order of the tidal wave length (200-500 km), the tide will take some time to 
travel upstream. Therefore the maximum water levels anywhere upstream of AA 
will occur later than at AA. Once again, because flood (inflow) continues after high 
water at AA, the horizontal tide at AA will lead the vertical tide by less than 90". 
The differences between the high and low water levels everywhere upstream of AA, 
multiplied by the surface area above AA define the volume of water that must flow 
past AA every half tide cycle. This is called the tidal prism above AA and can be 
used to compute average current velocities at AA. At Section BB, the upstream 
limit of the estuary (head of tide), the tidal prism becomes zero. The phase 
difference between the current and the water levels will be 0" at the deep, wide 
seaward limits of the estuary and tend toward 90°, just downstream of BB. 
Figure 6.10 shows an example of tides along the estuary of the St. Lawrence River. 
It is also seen that the tide shoals (increases in amplitude) as it moves upstream. 
Above Quebec City, however, the tidal amplitude decreases when the water 
becomes shallow and friction reduces the tidal motion. Figure 6.10 also shows that 
the tide becomes asymmetrical as it progresses upstream; the duration of the rising 
tide becomes shorter than the falling tide. If friction would not reduce the tide 
height, the wave would become a tidal bore, essentially a breaking tidal wave found 
in some relatively deep and short estuaries. 
Figure 6.1 I shows the horizontal and vertical tide at Portneuf. The asymmetry in the 
vertical tide is also reflected in the horizontal tide; the duration of the ebb flow is 
greater the flood. Because the head of tide is still 150 km further upstream, the tide 
at this location (400 km in the estuary) is still almost progressive in that the currents 
lead the water levels by about 20". Clearly, the horizontal tide is closely related to 
the vertical tide and hence, tide analysis and prediction methods discussed in Section 
6.2.5 can also be applied to tidal currents. The St. Lawrence is a very long estuary, 
used here to demonstrate the basic principles. Most estuaries are much shorter, will 
be more reflecting and behave much more like Fig 6.7. 
6.2.7 Stratification and Density Currents 
An estuary is defined as a tidal area where a river meets the sea. It has salt water on 
its downstream limit (sea) and fresh water on the upstream limit (river). The salt sea 
water normally has a salinity in the vicinity of 35 parts per thousand (ppt) and a 
density of 1035 kg/m3. The fresh water has a density of 1000 kg/m3. 
130 Introduction to Coastal Engineering and Management 
Pointe au Pere 
-Point. a u Perm 
-81. F r a n c o l s 
- -Puabac CIty 
- O r o n d i n e s 
-Charnplaln 
~~~~~~~ 
0 8 0 1 2 0 1 8 0 240 3 0 0 360 
T i m e After H W a t Po in te a u Pore lo’ 
Figure 6.10 Vertical Tides along the Si. Lawrence 
0 80 120 180 240 300 380 ... 
Time Ancr HWE a1 Poinlt au Ptm‘ 
Figure 6.1 1 Horizontal and Vertical Tides at Portneuf 
Chaprer 6 - Tides and Wuter Levels 131 
How the transition of salt to fresh water takes place depends on the amount of 
mixing in tbe estuary. In a well-mixed estuary (an estuayy with much turbulence), 
salt and fresh water are thoroughly mixed at any location. Salinity simply varies 
along the estuary &om 35 ppt in the sea to zero ppt in the river and at any specific 
location, salinity and density will vary with the tide as shown for Rotterdam in Fig. 
6.12. 
1.5 
-1.5 
0 2 4 6 8 ' 1 0 1 2 1 4 
Time (hrs) 
Figure 6.12 Salinities at Rotterdam 
c A 
Rive 
m 
L k m 
scaie 
Figure 6.13 Stratified Estuary 
132 Introduction to Coastal Engineering and Management 
If there is little mixing in the estuary, the lighter fresh water will lie over the heavier 
salt water, resulting in a stratified estuary. A suft wedge (AB) will form as shown in 
Fig. 6.13. Note that Fig 6.13 is highly distorted, since the estuary is many 
kilometers long, while the estuary depth is in meters. At any time and at any 
location, salinity will be a function of depth and there will be a sudden change in 
salinity and density at the interface of the salt water and the overlying fresh water. 
The sharpness of the interface is a function of the amount of mixing. 
The salt wedge moves up and down the estuary with the tide level. Flood and the 
rising tide will move the salt wedge from AB to CD. Ebb and the falling tide will 
return the wedge to near AB. The fresh water river flow will flow out over the salt 
water and the incoming tide will predominantly flow in along the bottom, below the 
fresh water. Along the bottom the currents are downstream above (upstream of) 
position D and upstream below (downstream of) position B. Between D and B the 
flow direction changes 180" and there will be a location in the estuary where 
predominantly