How waves are formed (and how surfers manage to tame them)

If you choose the sea (that dances along the clear cliffs) as your holiday destination, with its changing reflections, privileged witnesses to the vagaries of the sky, you will undoubtedly find yourself waiting for a wave to carry you away before it does not come to beach on the edge. We’ve all experienced it: Nothing is more complicated than predicting how a wave is going to carry us away, or how to get out of the water once in the violent waves.

The moment you understand the magnitude of a wave, for a few seconds and in an improvised way, you become a physicist, modeling a very complex phenomenon to predict its effects.

Waves are natural phenomena as spectacular as they are dangerous. The height of the waves varies from a few centimeters to 32.3 meters for the highest wave recorded by an instrument, or even more than 34 meters for the highest wave observed visually.

The origin and nature of the waves

A wave is a deformation of the surface of a body of water, most often caused by another fluid: the wind. At the interface, the wind creates waves on the seas, oceans and lakes.

The Ninth Wave, painting by Hovhannes Aivazovsky (1850) – Hovhannes Aivazovsky / Wikimedia CC0

Other phenomena, much less frequent, are also a source of waves: certain earthquakes, volcanic eruptions or meteorite falls create waves called tsunamis or tidal waves. The tide is also the origin of very special waves, called tidal bores, sudden elevations of the water in a river or estuary, caused by the surge of the rising tide in the estuary and the lower course of certain rivers during high tide. Finally, ships are also sources of waves.

Waves are waves, that is, phenomena that move periodically in time (we talk about period) and in space (we talk about wavelength). They can spread for miles before making landfall and gain strength depending on the slope of the ocean floor. To understand this phenomenon, it is necessary to seek a physical model of the wave.

A brief history of waves

Astronomer and mathematician George Biddell Airy provided the simplest theory for regular (periodic) waves. The airy wave has a free surface, the water surface, with a sinusoidal shape. This is a very simplified vision of reality, valid for waves with low “camber”, that is, the relationship between height and wavelength.

If we look closely at the waves on the ocean, we see that most of them are not sinusoidal: the crests are more pointed, the troughs flatter.

But what is interesting to us today in Airy’s theory is that fluid particles describe nearly closed ellipses whose size decreases with depth. We always mistakenly believe that a wave carries us: in fact, if we swim in the depth during the propagation of a wave, we realize that there is a back and forth movement, not necessarily intuitive from the point of view of everyday experience, but well emphasized by Airy’s theory.

A wave moves forward and the particles carried by the waves have elliptical trajectories
A wave moves forward and the particles carried by the waves have elliptical trajectories – Kraaiennest / Wikimedia CC BY-SA 4.0

In deep water, that is, for depths greater than half the wavelength, these ellipses are circles. The fact that the ellipses are not completely closed is a manifestation of “Stokes drift”. Near the free surface, the velocity of a water particle below a crest is greater than the opposite velocity as it passes the next trough. This results in a drift in the direction of propagation of the waves, which can be reversed in depth.

What Freedom!, painting by Ilya Repin (1903)
What Freedom!, painting by Ilya Repin (1903) – Ilya Repin / Wikimedia CC0

Breakwater approaches the beach

Let’s get back to what will concern us this summer: facing the waves… with dignity! In fact, “owning a wave” means understanding its wave.

Some waves are actually too steep to be stable: they break.

Approaching a coast, the depth decreases, the shape of the waves changes, first in a fairly symmetrical manner, then generally with an increasingly steep front as soon as the wave height is of the same order as the depth. When the wave breaks, most of its energy is dissipated in eddies and air bubbles. The associated impulse helps to accelerate the current in the direction of the refraction.

The shape of a wave near the shore essentially depends on the slope of the bottom. If we go in the direction of increasing slopes, we usually distinguish three types of fractures. Progressive or smooth breaks generally occur on beaches with very low slopes. The waves begin to break away from the shore with a frothy crest that steepens as it advances, leaving a layer of foam.

The crashing wave is particularly spectacular with its rolls appreciated by surfers. The wave wraps around an air pocket and then collapses, creating a noticeable splash. This tends to happen most often on a steep slope or a sudden change in depth (a sinkhole), which is why “spots” are popular with surfers.

Drawing energy from the waves

There is much more scattered energy than reflected energy on the beach. The energy that spreads on the surface of the collapsing wave is beneficial to the surfer, who can use it as a source of kinetic energy: the wave gives him the necessary dynamism to move and perform the shapes he wants on his board in motion thanks to the wave.

Frontal or swell surf shapes like diving surf, but the wave moves up the beach before the crest can roll up. The breaking zone is very narrow, and a large part of the energy is reflected towards the greater depths. When the top moves faster than the wave itself, a thick layer of comb foam forms at the top. We are then talking about a smooth wave, typical of a gently sloping coast. This type of break completely disadvantages the surfer as the energy is given to the depths. The surfer’s talent as a “casual physicist” is to be able to recognize the types of surf for this purpose.

Types of waves
Types of waves – SL Douglas and J. Krolak / FHWA / Wikimedia CC BY-SA 4.0

There is also an intermediate case between diving and frontal fracture. Instead of forming a roll, the wave presents a vertical surface before collapsing.

Surfers are often nicknamed the “tamers” of waves. The good wave conditions allow good surfing practice (at least with a lot of technique!). This means good wind or swell conditions, which can vary from place to place.

Hollow waves, with a falling break, are a favorite among “shortboarders” who use short boards. Hollow waves are the strongest waves, but not necessarily the biggest. Some waves that can be described as hollow are actually much stronger than a soft wave of the same size. The principle of the shortboard (short board) is to allow a more “dynamic” surfing practice with more changes of direction on the wave to achieve different shapes. This is made possible with a wave whose refraction is better controlled.

Finally, a surfer primarily does applied research in the discipline of “good waves”.
In general, whether you play with them, contemplate them, or face them, take advantage of these moments of freedom that nature offers. And let’s remember that there is only one planet Earth to spend beautiful summers!

This analysis was written by Waleed Mouhali, teacher-researcher in physics at ECE Paris.
The original article was published on the website of The conversation.

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