the physics of waves

Ocean wave characteristics and definitions:

Wave height – vertical distance from highest point of crest to lowest point of wave trough
Wave amplitude – vertical distance between highest or lowest point of a wave and a horizontal reference level, such as the unperturbed sea surface
Wavelength – the horizontal distance between successive wave crests or troughs
Wave number – two pi divided by wavelength
Wave frequency – the number of waves passing a specific point per unit of time
Radian frequency – two pi times wave frequency
Phase speed – wavelength times frequency
Wave steepness – wave height divided by wavelength

Wave transformations

Wave transformation takes place because the waves are affected by the seabed through processes such as refraction, shoaling, bottom friction and wave-breaking. 

Underwater surge due to waves

In shallow waters, waves create sediment movement felt as a back-and-forth movement of the water at the bottom.

As a wave passes by, each little element of the water undergoes a closed-loop trajectory or orbit motion. In deep-water waves the size of the orbits decreases sharply with increasing depth until they are negligible (4%) at depths greater than 1/2 the wavelength; at lower depths the oscillation interacts with the bed to form an oscillatory boundary layer

In shallow water, the orbits becomes more elliptical and become back-and forth straight lines at the bottom, with the speed in the direction of the wave being faster (and for a shorter period of time) compared to the opposite backward movement, with a zero net result in term of movement.

Use the surge calculator to see how much surge to expect (it works well from a computer, but not sure via phone).

In summary: on the surface the surge is equivalent to the height of the wave. Going deeper, it decreases exponentially, but at a rate which is dictated by the wave period (the longer the period the deeper it's propagated).

The formula takes also into account the depth of the seafloor below the diver,  to determine whether to expect a shallow water (seafloor depth < 1/20 wavelength) or a deep water behaviour.

Thanks to Prof. Nick Hall from the University of Toulouse for the support on this


When a wave approaches underwater contours at an angle, the sections of the crest in the deeper parts travel faster than those in the shallower sectors. This causes the wave crest to turn towards the depth contour. This bending effect is called refraction, and is analogous to similar phenomena in physics (light, sound). It takes place in addition to the effects of shoaling and continues up to the shoreline.
The energy of the wave gets dispersed in divergent refraction and concentrated in convergent refraction.  Source


Diffraction occurs when a wave encounters an obstruction in its path and will change direction, or wrap around it. Normally both diffraction and refraction happen at the same time. In ocean waves, we see this occur when a wave encounters an object like a jetty and the wave rotates around it. The ‘wrapping’ or turning potential of a wave is larger in waves with a longer wavelength (i.e. longer period). This is why a long period Groundswell wave can sometime wrap a full 180 degrees around a barrier/jetty, whereas short-period Windswell wave will often shoot straight by it. Diffraction can occur in shallow or deep water and is separate from refraction since it is not a result of a change in ocean depth. However, both refraction and diffraction will involve a change in a wave’s direction. Source


Wave reflection is the process of waves bouncing off a hard surface, such in the case of the path between Mnly and Shelly Beach . The angle of incidence and the angle of reflection are equal, based on a perpendicular line to the coast. Generally, the energy, frequency, period and speed of the wave are not impacted by this reflection. Source


Shoaling is the deformation of incident waves on the lower shoreface that starts when the water depth becomes less than about half of the wavelength, causing the waves to become steeper: increase in amplitude and decrease in wavelength. 

For us divers, it means that the waves we face near the access point are higher than what forecasted, and after the break the vertical oscillation is converted into horizontal speed which is our ultimate measure of comfort in entering/exiting the water. Source

Wave interference

When waves from different directions meet, they interfere with one another. Wave interference can be:

Lastly, the best course on ocean waves I could find, by Professor Nick Hall, free to download in PDF and to listen on Youtube