Coastal and Maritime Engineering

31

F L Terrett MEng, CEng, FICE, MConsE Posford Duvivier Contents 31.1

31.2

Tides 31.1.1 Tide-raising forces 31.1.2 Tidal variations – effects of declination 31.1.3 Tidal currents – coastal effects – reflection and resonance 31.1.4 The Coriolis force 31.1.5 Prediction of tides Waves 31.2.1 General 31.2.2 Wave length, celerity and period as functions of depth 31.2.3 Fluid velocity and pressure 31.2.4 Superposition 31.2.5 Wave trains and wave energy 31.2.6 Transformation of waves 31.2.7 Reflection coefficients 31.2.8 Dissipation of wave energy 31.2.9 Finite amplitude theory – breaking of waves 31.2.10 The solarity wave 31.2.11 Wave generation 31.2.12 Wave generation in shallow water 31.2.13 Wave decay 31.2.14 Propagation of waves into shallow water – refraction 31.2.15 Wave forecasting 31.2.16 Diffraction

31/3 31/3 31/3 31/3 31/3 31/4

31.4.3 31.4.4 31.4.5 31.4.6

Stratification and densimetric flow 31.5.1 Saline wedge in estuaries 31.5.2 Silt movement in estuaries 31.5.3 Effluent outfalls 31.5.4 Density and turbidity currents

31/14 31/14 31/14 31/14 31/15

31.6

Wave and current forces 31.6.1 Forces on a circular cylinder or pile 31.6.2 Forces on sea walls and breakwaters

31/15 31/15 31/16

31.7

Scaling laws and models 31.7.1 General 31.7.2 Scaling and similarity 31.7.3 Tidal models 31.7.4 Harbour models 31.7.5 Forces on structures 31.7.6 Overtopping 31.7.7 Digital numerical models 31.7.8 Littoral processes

31/17 31/17 31/17 31/18 31/18 31/18 31/18 31/18 31/19

31.8

Surveys and data collection 31/19 31.8.1 Sources of information 31/19 31.8.2 General 31/19 31.8.3 Position fixing 31/19 31.8.4 Bathymetry 31/20 31.8.5 Nature of the sea-bed 31/20 31.8.6 Nature of material below the sea-bed 31/21 31.8.7 Fluid mud layer 31/21 31.8.8 Current measurement 31/21 31.8.9 Water properties 31/22 31.8.10 Waves and tides 31/22 31.8.11 Meteorological data 31/23 31.8.12 Coastal stability – movement of beach and sea-bed sediments 31/23

31/8 31/8 31/8 31/9 31/10 31/10 31/10 31/10

31.3

Exceptional water levels 31.3.1 Long waves - surge 31.3.2 Wind set-up 31.3.3 Wave set-up 31.3.4 Resonance in harbour basins 31.3.5 Ranging of moored ships

31/10 31/10 31/11 31/11 31/12 31/12

31.4

Sea-bed and littoral sediments 31.4.1 Sources of material 31.4.2 Modes of transport – currents and waves

31/12 31/12

31/12 31/13 31/13 31/14

31.5

31/4 31/4 31/4 31/5 31/5 31/6 31/7 31/7 31/7

Wave direction Effect of size of beach material Erosion and accretion Computation of littoral drift

31/12

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31.9

Design parameters and data analysis 31.9.1 Ground conditions 31.9.2 Waves, tides and currents

31/23 31/23 31/23

31.10 Materials 31.10.1 Rock 31.10.2 Brickwork 31.10.3 Concrete 31.10.4 Timber 31.10.5 Iron 31.10.6 Steel 31.10.7 Corrosion-resistant metals 31.10.8 Synthetic materials 31.10.9 Bitumen

31/24 31/24 31/24 31/24 31/25 31/25 31/25 31/25 31/26 31/26

31.11 Sea-defence and coast protection works 31.11.1 Sea walls 31.11.2 Groynes 31.11.3 Beach nourishment 31.11.4 Cliff stabilization

31/26 31/26 31/28 31/30 31/30

31.12 Breakwaters 31.12.1 Vertical-faced structures 31.12.2 Rubble-mound breakwaters 31.12.3 Rock-filled crib breakwaters 31.12.4 Piled breakwaters 31.12.5 Experimental breakwaters

31/31 31/31 31/32 31/33 31/33 31/34

31.13 Sea-water intakes and outfalls 31.13.1 Jointed pipelines 31.13.2 Pipelines towed or floated into position 31.13.3 Tunnels and shafts

31/34 31/34 31/34 31/34

References

31/35

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31.1 Tides 31.1.1 Tide-raising forces The alternate rising and falling of sea-level is caused by the attractive forces of the Moon and the Sun on the rotating Earth. The predominant effect, that of the Moon, can be explained in a simplified form by omitting in the first place the rotation of the Earth and Moon about their own axes and considering the relative motion of the two bodies about their common centre of rotation G (Figure 31.1). They revolve about G independently, not as a single rigid body, and points P1 and P2 on the Earth's surface rotate about G1 and G2 in which GG1 and GG2 are respectively parallel to CP1 and CP2, and P1G1 and P2G2 are parallel to CG. The attractive force of the Moon on a particle of mass m at the centre of the Earth is gmMJL2 in which M1 is the mass of the Moon, L the distance between the centres of the Moon and the Earth and g is the gravitational constant. This attractive force is the centripetal force F which restrains the particle in its circular orbit round G.

Figure 31.1 Tide-raising forces If particles of water, also of mass w, are to remain in position at points P1 and P2 they must also be acted upon by forces F towards their centres of rotation G1 and G2. The attraction of the Moon on these particles is respectively F1 which is less than F, and F2 which is greater than F since P1C1 and P2C1 are respectively greater and less than L. The vector differences shown in the figure F minus F1, and F2 minus F, are the tideraising forces. The vertical components of these forces are small in relation to the Earth's gravity and are of little importance; the horizontal components which are towards A and B, respectively, generate the tidal wave. They are zero at points A and B in line with the Moon and near points O and P at right angles to AB, and are a maximum midway between these points. Their directions, indicated by the circumferential arrows in the figure, cause two high waters, one directly under the Moon and the other on the opposite side of the Earth. The Sun produces similar tide-raising forces but of barely half the magnitude of those due to the Moon. As the Earth rotates, the tides are phased with the apparent motion of the Moon so that the interval between successive high waters is approximately half the lunar day of about 24 h 50 min. 31.1.2 Tidal variations - effects of declination Variations in tide level result from the varying positions of the Sun and the Moon relative to the Earth; at times of new and full moon the tide-raising forces of the-Sun reinforce those of the Moon giving spring tides and when the Moon is at the first and third quarter the Sun's tide-raising forces counteract those of the Moon giving neap tides. In many places there is a marked inequality in the height and

range of succeeding tides which is largely due to the angles between the plane of rotation of the Earth about its axis and the planes of the orbit of the Moon round the Earth and of the Earth round the Sun. These varying angles, which are the declination of the Moon and the Sun, introduce a diurnal component which combines with the semidiurnal tides. It is possible for one high water to be suppressed altogether and for an inequality in time also to be caused by declination so that the interval from high to low water may not be the same as from low to high water. In the waters of northwestern Europe and the eastern seaboard of America the tides are essentially semi-diurnal, the tidal pattern, which is readily explained, being one large set of spring tides and one smaller set each lunar month. The tidal range varies from month to month with the varying distance of the Earth from the Sun, the largest range being at the equinoxes (March and September). In the Pacific and many other places away from the Atlantic Ocean the tides have a strong diurnal inequality; generally tides of large and small range alternate, the largest tides occurring in December and June at the solstice when the diurnal component of the tide-raising force most nearly coincides with the semidiurnal component. In these areas the tides cannot be classified simply as springs or neaps; the highest and lowest water levels do not precede or succeed one another and there are significant changes in mean sea-level from week to week. At times the diurnal component predominates and at others the semidiurnal component, so that the tidal pattern is extremely complex varying from one to two high- or low-water levels per day and from small to large tidal range in either mode. It is important to note that in these areas the greatest rate of change in level from high to low water or vice versa does not necessarily coincide with tides of greatest range nor is there an obvious relationship between tidal current and tidal range. 31.1.3 Tidal currents - coastal effects - reflection and resonance In the open oceans the tide generated by the attractive forces of the Moon and Sun takes the form of a progressive wave in which the associated currents are in the direction of wave propagation below the crest and in the opposite direction in the trough. The maximum current velocities are at the crest and trough, i.e. at high and low water, and zero at half tide on both rising and falling tides. This simple description of the tidal motion is, however, much altered by many factors, in particular by the shape and disposition of the land masses and the depth of the seas around them. Reflection of the tidal wave from the shores and resonance effects in enclosed or partially enclosed gulfs and straits result in standing oscillations in which the tidal current is zero at high and low water and a maximum at half tide or thereabouts. An example of such a standing oscillation is found in the eastern half of the English Channel where high water between the Isle of Wight and Dover occurs within about 10 min at all places along the English and French coasts. As the tidal wave enters shallow water, in an estuary, for example, it is distorted: the speed of propagation is reduced and the wave crest tends to overtake the preceding trough. Thus the time interval from low to high water is reduced and from high to low water increased, and the flood current becomes stronger than the ebb. Also, the height of the tide may increase as the estuary narrows inland. 31.1.4 The Coriolis force The ocean currents, whether tidal or wind-generated, or the

result of density gradients due to salinity and temperature differences, are affected by the rotation of the Earth, being deflected to the right in the northern hemisphere and to the left in the southern. This is known as the Coriolis effect after the French scientist of that name (1792-1843). In a narrow sea, such as the English Channel, deflection of the flood current to the right is inhibited by the proximity of the shore lines and the Coriolis force leads to higher tides along the French than the English coast. In a more open sea the tidal wave and its associated currents may become rotary about an amphidromic point at which the currents are zero and there is no tidal variation in level. There are three such amphidromic points in the North Sea (Figure 31.2). In small tidal inlets the Coriolis force is not significant, but where the width exceeds about 20 km it has an important effect on the currents which flush pollutants from these waters and erode and transport fine sediments.

31.2 Waves 31.2.1 General Coastal and estuarine processes are complex and it is seldom possible to find solely analytical solutions to practical problems. A great deal of theoretical work has, however, been carried out and the more important results are given below with notes on their significance and application. For their derivation see Ippen.2 In Figure 31.3, T is the wave period ( = time interval for motion to recur at a fixed point), c is the velocity of wave propagation or wave celerity, rj(x,t) is surface elevation at position jc and time /, u is the horizontal component of instantaneous velocity of fluid element, v is the vertical component of instantaneous velocity of fluid element, p the instantaneous 'static' pressure, H the wave height ( = 2a), p the density (mass per unit volume) and v the kinematic viscosity.

Wave celerity c Water surface profile 'sin 2ir( f-J.) at r = C

Wavelength X Norway

Still water level Still water depth d Denmark

Figure 31.3 Coordinate system

31.2.2 Wave length, celerity and period as functions of depth c' = ^ t a n h ( ^ )

OLD

^cT

(31.2)

\* J

2n

Holland Figure 31.2 Amphidromic points in the North Sea

31.1.5 Prediction of tides The astronomical tide-raising forces create semidiurnal and longer frequencies in the tidal cycle; shallow-water effects introduce higher frequencies. The recorded tidal curve at any place can be broken down into these various frequencies and the individual constituents recombined to give tidal predictions. For most places in the world, such predictions are made by national government agencies for their own territorial waters, and where available, should be used in preference to the worldwide tables prepared by Her Majesty's Stationery Office, as they are often more detailed and likely to be related to a local land datum. However, the quality of tidal predictions varies widely and should be checked by examination of the basic data before starting work at any unfamiliar coastal site. In the absence of published tables, predictions can now be readily prepared for any site for which a month or more of good-quality record is available, using a small digital computer following the method of working set out in the Admiralty Manual of Tides,*

Equation (31.1), derived from theoretical work by Stokes,3 is strictly accurate only for waves of small amplitude but the error resulting from its application to practical problems is small and the theory may be used with confidence. When a wave moves from deep to shallow water (or vice versa), c and A both change, while T necessarily remains constant. Published tables and graphs2-3 relating the variables are available so that manipulation of the equations is not necessary. Waves are conveniently classified into types according to the relative depth d/A as follows: Shallow-water (long) waves

d/l = 0 to 1/20 tanh(27M/M)*2jM//A

Deep-water (short) waves

d/A = 1/2 to oo tanh(2*H//;i)sl

Intermediate waves

d/A= 1/20 to 1/2

Using these approximations, Equations (31.1) and (31.2) become: (1) For shallow water: fe