Waves and Coastal Processes

1The same wind, two different seas

Lake Kivu is about 89 km long and at most about 48 km wide. When a strong afternoon wind blows down the lake, it raises short, choppy waves that break on the sandy beaches at Rubavu. Let the same wind blow across the Indian Ocean towards the coast of Kenya and it has thousands of kilometres of open water to work on: the waves it raises there are longer, taller and carry many times more energy. That difference explains why ocean coasts have cliffs tens of metres high, sea caves and long sand spits, while most lake shores show these features, if at all, on a small scale. This lesson sets out the terms and the physics of waves, and the processes by which waves erode, carry and deposit material. Lessons 2 and 3 use them to explain the landforms.

2The zones of a coast

Figure 1: the zones of a coast, seen in profile.

Seawards of the low-water mark lie the nearshore zone, where waves feel the seabed, steepen and break, and beyond it the offshore zone, too deep for waves to move the bed. On the ocean the shoreline moves twice a day with the tide. Lakes have almost no tide, but their shoreline still moves when the lake level rises or falls with the seasons.

3How waves form and break

As wind blows over water, friction and pressure differences pass some of its energy to the surface. Three things set how big the waves become: the wind speed, the duration for which it blows and the fetch. Waves that are still being driven by the wind form a choppy sea; waves that have travelled far beyond the storm that made them form a regular, long-period swell.

A wave moves energy, not water. As a crest passes, each particle of water near the surface travels round a near-circular orbit and returns almost to where it started, which is why a floating bottle bobs up and down but is not carried to the shore. The orbits shrink with depth and die out at the wave base (Figure 2A).

Figure 2: (A) the parts of a wave and the motion of the water beneath it; (B) what happens as the wave reaches the shore.

When the depth becomes less than about half the wavelength, the orbits touch the bed. Friction slows the base of the wave, the orbits flatten into ellipses, the waves behind catch up so the wavelength shortens, and the energy is squeezed into a smaller depth so the wave grows taller. The crest, now in deeper water than the trough in front of it, moves faster than the base and finally topples: the wave breaks, at a depth of roughly 1.3 times its height. On a gently sloping beach waves usually break as spilling breakers, foam tumbling down the front; on a steeper beach the crest curls over as a plunging breaker; and on a very steep beach the wave may surge up the shore without breaking.

4Measuring wave speed and energy

Simple (linear) wave theory gives, for deep water (depth greater than $\frac{L}{2}\backslash frac\{L\}\{2\}$), with $g=9.81\mathrm{m}{\mathrm{s}}^{-2}g\; =\; 9.81\backslash ,\backslash mathrm\{m\backslash ,s^\{-2\}\}$:

where $cc$ is the speed of the wave in $\mathrm{m}{\mathrm{s}}^{-1}\backslash mathrm\{m\backslash ,s^\{-1\}\}$. Long-period waves are long and fast. In shallow water (depth $dd$ less than about $\frac{L}{20}\backslash frac\{L\}\{20\}$) the speed depends only on the depth:

which is why waves slow down as they come ashore. The energy stored in each square metre of sea surface is

where $\rho \backslash rho$ is the density of the water (about $1025\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}1025\backslash ,\backslash mathrm\{kg\backslash ,m^\{-3\}\}$ for sea water, $1000\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}1000\backslash ,\backslash mathrm\{kg\backslash ,m^\{-3\}\}$ for fresh water). Energy rises with the square of the height: a wave twice as high carries four times the energy. This is why a few storms each year do most of the erosion on a coast.

5Constructive and destructive waves

Figure 3: constructive and destructive waves on a beach.

The two are not fixed types but the ends of a range, and one beach can meet both. After a storm the beach has lost material to an offshore bar; in the calm weeks that follow, constructive waves carry it back. The beach is a store of sediment whose shape keeps adjusting to the waves.

6Wave processes: erosion, transport and deposition

The rate of erosion depends on the wave energy (fetch, storms and the angle of approach), the rock (its hardness, and its joints, faults and bedding, which give the sea lines of weakness), the beach in front of the cliff (a wide beach makes waves break early and spend their energy) and people, who can protect a coast with sea walls or weaken it by removing beach sand.

Waves move material by the same four processes as rivers: traction (rolling large boulders), saltation (bouncing pebbles and coarse sand), suspension (fine silt and clay held in the water) and solution (dissolved minerals). They deposit it where they lose energy: in sheltered bays, where the coast changes direction and the water deepens, behind islands and headlands, and wherever constructive waves dominate. In estuaries, fine clay particles carried by rivers clump together when they meet salt water (flocculation) and settle as mud.

7Longshore drift

Figure 4: longshore drift, in plan view.

Where the prevailing wind drives waves towards the shore at an angle, the swash runs up the beach in the direction the wave is travelling, carrying sand and pebbles with it at the same angle. The backwash then runs straight back down the slope of the beach under gravity, at right angles to the shoreline. Each wave therefore moves a grain a short distance along the beach in a zigzag, and over months millions of waves move thousands of tonnes of sediment along the coast. Groynes, low walls built across a beach, interrupt the drift: sand piles up on the side the drift comes from (the updrift side) and the beach on the far side is starved. Longshore drift feeds the depositional landforms of lesson 3.