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), but also at deeper layers along what is called pycnoclines ( which is the boundary between two adjacent layers of water of different densities), and along the seafloor. Here we will focus on ocean surface waves.

Surface waves are created by disturbance forces applied to a specific area. A wave-generating force is the one that pushes water up across its boundary with the air. It 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.

A restoring force is the one that pushes water back to where it originally was at rest, trying to restore the balance. The restoring force can be either the surface tension of the water ( which is the force connecting the water molecules one another) or the gravity force that pushes down the water, whose density is higher than that of the air.

The waves that are restored mainly by surface tension forces are small ripples in the water’s surface and are called capillary waves. On the other hand, 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 the 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 that 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 surface of the water in a location potentially very far away from the place where the wave is actually seen. But, contrary to intuition, waves do not move water but energy. In fact, the particles of water move in circular orbits around its original position.

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

Deep and shallow-water waves

A wave is considered as a deep-water wave if the wave depth is lesser than the depth of the water. That means that as it moves along, the wave does not hit bottom. In other words, a deep-water wave is any wave with a wave base above the seafloor.

A shallow-water wave is that whose wave depth is greater than the depth of the water it is in. That means that the wave “feels bottom”.

At a certain point, deep-water waves approaching the cost will become shallow-water waves as their base hits bottom. When the wave base enters into contact with the seafloor, the wave transfers part of its orbital energy to it, causing erosion and sediment motion. The wave also slows down, becomes taller, and their circular orbits turn into elliptical ones.

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