Surface waves

Surface waves. Aerial view to tropical sandy beach and blue ocean. Top view of ocean waves reaching shore on sunny day. Palawan, Philippines.

In the ocean, we find waves moving along the surface (at the air-water interface), at deeper layers along what is called pycnoclines (the boundary between two adjacent layers of water of different densities), and along the seafloor. In this article, we will only focus on ocean surface waves.

Surface waves are created by disturbance forces applied to a specific water area. Wave-generating forces push water up across its boundary with the air. They can be either the wind, a surface vessel moving through the water, an earthquake, landslides, a splash, gravity (as is the case for tides), or any combination of them.

On the other hand, restoring forces push water back to where it originally was at rest, trying to restore the balance. They can be either the surface tension of the water (which is the force connecting the water molecules to one another) or the gravity force that pushes down the water.

Waves that are restored mainly by surface tension forces are small ripples on the water’s surface and are called capillary waves. For bigger waves, the restoring force is that of gravity. These waves are known, unsurprisingly, as gravity waves.

Wave’s anatomy

When studying ocean waves, we consider them to be the superimposition of single sinusoidal waves with different frequencies and amplitudes. This is done thanks to what is called Fourier analysis.

Sinusoidal waves can be easily described and modeled:

  • the equilibrium surface, also known as the still water level, is the ocean surface level when there are no waves;
  • the crest is the wave’s highest point;
  • the wave’s lowest point is known as the trough;
  • the amplitude is the vertical distance from the equilibrium surface to the crest or the trough;
  • the wavelength is the horizontal distance from one point to the next point located precisely at the same location in the wave (for example, from crest to crest or from trough to trough);
  • the vertical distance from crest to trough is called the height of the wave; this is twice the amplitude;
  • the period of the wave is the time that passes between waves (for example, 10 seconds, 5 minutes, etc.);
  • the frequency is the number of waves that pass a fixed point in a given amount of time. When the amount of time considered is one second, then the frequency is measured in hertz (number of waves per second);
  • the wave speed is the distance the wave travels in a certain amount of time. It can be calculated as the wavelength divided by the wave period.

Wave-generating forces transfer energy to the water’s surface in locations potentially very far away from the place where the waves are eventually seen. Contrary to intuition, waves do not move water but energy. When a wave passes, the water particles do not travel along but move instead in circular orbits around their original positions.

As we go deeper down, the circular orbits become smaller until reaching a depth where the water remains undisturbed. The wave depth is the depth under which the wave passage does not cause any significant water motion. In other words, the wave base is the boundary of water orbital motion. It is measured from the equilibrium surface. 

Deep and shallow-water waves

A wave is considered a deep-water wave if its wave depth is lesser than the water depth, or, in other words, its wave base is above the seafloor. On the other hand, in a shallow-water wave, the wave depth is greater than the water depth, and the wave “feels bottom.”

Deep-water waves approaching the coast will eventually become shallow waves when their bases hit bottom. At that moment, the waves will transfer part of their orbital energy to it, causing erosion and sediment transport. The waves will also slow down, become taller, and the water particle’s circular orbits will turn into elliptical ones.

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