Waves

A full description of waves is beyond the objectives of this course, but very rigorous and sometimes complex theories and mathematical models have been developed to explain waves in water. It also turns out that no singular theory or mathematical model adequately describes the full range of waves and wave behavior within water bodies. An equation that perhaps quite adequately describes wave behavior in deep water might be completely useless when attempting to quantify the behavior of shallow water waves. Because waves are the most common energy source along most coastal zones, understanding them is paramount to understanding how coasts evolve through time.

Fundamentally, a wave can be considered to be a disturbance of the water as energy is passing through the water. In open ocean basins, wind is the source of this energy that is transferred to the body of water as the wind blows across it. Consider what happens when you blow on the surface of a cup of hot tea or coffee to cool it down, the energy of your moving breath is transferred to the surface of the tea or coffee and causes small ripples or waves to develop.

The characteristics of waves are geometrically described by several different parameters including the: 1) wave height or amplitude, 2) wave length, and 3) wave period. As the name implies, the wave height is the vertical distance between the trough of a wave and the top or crest of a wave. Wave length refers to the horizontal distance between successive wave crests or troughs, and the wave period refers to the number of waves that pass a set point within an established period of time (Fig. 2.10).

Overall, the height, length and period of a wave fundamentally are governed by 1) wind speed, 2) the duration of time that the wind has been blowing, and 3) the fetch, or distance across open water that the wind has traveled. Wave height and the steepness of the wave increase through time as the amount of energy transferred from the wind to the water increases. For example, an increase in wind speed will cause more energy to be imparted to the water, and the result is that the wave heights correspondingly increase. A wind-generated wave can however not grow indefinitely in the open ocean, at some point waves will grow so large that they break, and this is how whitecaps are generated.

Waves have the ability to travel great distances in the open ocean, and some studies have been able to track waves more than 10,000 km in the open ocean after many days of traveling. Importantly, one should keep in mind that the water of the waves does not actually travel with the wave but rather the waveform itself does. Fundamental to this fact is the process of circular orbital motion, wherein the energy of the wave is passed along as individual water particles move in a circle below the water surface. These circles of travel, or orbitals, are stacked on top of one another with the largest orbital diameter at the top and the smallest orbital diameter at the bottom. The diameter of the orbitals becomes negligible at a water depth that is equal to half of the wavelength, and this water depth is known as the wave base of the wave. In water depths that are less than half the wavelength, the orbitals become deformed and progressively evolve from being perfectly circular to elliptical. The speed of the wave decreases towards the coast but other waves moving in behind are still traveling at a speed that was equal to the first waves speed before it began to slow down. All of the waves, therefore, begin to get crowded together and the height and the steepness of the waves increase. Eventually, the waves become unstable because they are too high relative to the water depth, the front of the wave collapses and the wave breaks onto the coastline to create surf (Fig. 2.11). The energy of the traveling wave is then transferred onto the shoreline either carrying sediment up onto a coastal environment such as a beach or removing sediment and transporting it offshore or alongshore.

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Figure 2.10 Conceptual diagram of an open ocean wave where 1 = wave propagation direction, 2 = the wave crest, and 3 = the wave trough. The wave height is the vertical distance between the wave trough and wave crest, and wavelength is the horizontal distance between successive wave crests or wave troughs. Example A shows the idealized orbital motion of water particles in deepwater, whereas example B shows how fluid particle pathways become progressively more elliptical, assuming that the ocean floor is now at elevation B.
Credit: Wikipedia https://creativecommons.org/licenses/by-sa/3.0/ CC BY-SA 3.0

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Figure 2.11: Waves breaking along a beach in southern Brazil. As the waves approach the shore, the lower parts of the wave begin to interact with the seafloor, which slows the forward movement of the orbital pathways while the upper part of the wave maintains its forward velocity. The result is the development of an over steepened wave that leads to breaking and the creation of a surf zone as the waves run up on the beach and gravitational forces return some of the water back to the sea.
Credit: M. Kulp

• Longshore Currents