Essay on Ocean Waves by Gerbrant van Vledder

Some basic concepts about the origin
and life cycle of ocean waves

by Gerbrant van Vledder


Dolph Kessler’s photobook ‘The Wave – Crossing the Atlantic’ beautifully shows the wide variety in which ocean waves can manifest themselves. It is an example of many ways to look at waves; the artist sees intriguing patterns whereas the seafarer immediately recognizes their dangers and how to cope with them and the oceanographer speculates about the origin of each wave. This illustrates how waves can be viewed from different perspectives. As a scientist I can enjoy the beauty of waves, not only in these photographs, but also by appreciating the elegance of the mathematical equations describing their behaviour. In my work I usually see abstract pictures on my computer screen hoping they properly represent reality. However, in this book of photographs, taken on the Atlantic Ocean, Dolph Kessler shows a different aspect of waves. His photos display the various moods of ocean waves: from gentle wavelets to a raging mass of water. It is therefore a great pleasure for me to introduce to the reader some basic concepts about the origin and life cycle of ocean waves.

Out of the endless cycle of ocean waves, each picture represents a snapshot in time, from their origin in a gentle breeze until the moment they forcefully break onto the coast. This automatically leads us to question what happens in the intermediate phases. Before explaining this, I will first introduce the different kinds of waves occurring on the ocean. The most common waves are those generated by the action of the wind. Everybody recognizes them immediately as water waves, and they materialize everywhere, on the ocean, lakes but also in our ditches and ponds. It is important to emphasize that these wave images recorded by Dolph Kessler are the main focus of my introduction. Another common type of waves are the tides, recognizable by the twice-daily slow variation of water levels. This wave phenomenon is primarily generated by the gravitational interplay of the earth, moon and sun. Tidal waves reveal themselves in the coastal zone where the accompanying currents have to force themselves through narrow straits. From time to time, the ocean surface is disturbed by a tsunami caused by a sudden movement of the ocean floor. This in turn is caused by strong earthquakes or exploding volcanoes. In deep water such waves are hardly visible, but in the shallow coastal zones they can increase in size to towering heights destroying everything in their path.

To allow the reader to better understand the story behind each photograph I will describe the life cycle of wind waves. This will not be restricted to a single wave but rather to a collection of waves as they grow and propagate over the ocean until finally, they break. I will also introduce a number of concepts to enable definition of more complex situations. Pretor-Pinney wrote an illuminating book about the different kinds of wave phenomena we encounter in our daily life, including wind generated waves. For this introduction I will draw upon his distinction of the five phases in the life cycle of wind waves, which gradually pass from one phase to the next. In the first phase a light breeze is sufficient to generate small disturbances in the water surface. They often appear as diamond patterns criss-crossing rapidly over the water surface. As soon as the wind drops, these undulations quickly disappear because of the dampening effect of surface tension. Sailors see in these small disturbances an approaching wind strike, allowing them time to tighten up the sail. These initial waves only reach heights of a few centimetres, but they exist everywhere on the ocean as completely calm weather is rare.

As the wind gets stronger, we arrive at the second phase of wind wave growth. Small invisible vortices in the air create alternating pressure fluctuations pushing against the small waves so that they slowly grow. Now they have grown so large that they can’t be subdued anymore by the surface tension. The sea surface now looks like a chaotic collection of waves. Each single wave can be seen as an undulating movement of the water surface with the highest point called the wave crest and the lowest point the wave trough. Each wave can now be attributed some characteristics, such as their height (the vertical distance between the crest and the trough), their length (the horizontal distance between succeeding crests), their wave period (the time it takes wave crests to pass a certain point) and the direction in which they propagate. Generally speaking wave heights increase with increasing wave periods, and their wave lengths are proportional to the square of their period.

It took a long time before oceanographers unravelled the structure of a wave field. Fortunately there is, in spite of the apparent chaos, an underlying structure. For simplicity, we will consider the situation where the wind blows from a single direction. The first step is just counting how often waves come from a certain direction with respect to the wind direction. We then see that most waves travel in roughly the same direction as the wind and that the number of waves decreases with increasing angle to the wind direction. This distribution over directions is called directional spreading. Wind seas are usually more spread than regular swell waves, which appear to come from only one direction.

A second way to count waves is to look at the up and down movement of the water surface at a fixed location with respect to an average level. Each time the undulating water surfaces cross this level a new wave starts from which we can determine its height and period. The wave height then follows as the difference between highest and lowest water level and the wave period is the time between two crossings of this mean water level. Observations show that in stormy seas an increase in mean wave height is accompanied by an increase in wave period, whereas in swell conditions wave height decreases with increasing wave period. Despite the wide range of wave heights many people are able to attribute a characteristic wave height to such a collection of waves, often referred to as the ‘significant wave height’. Another property of waves is their steepness, the ratio of wave height over wave length. A growing wave field is steeper than a swell wave field.

With increasing wind speed the waves change character again and so we enter the third phase in the life cycle of wind waves. The sea gets rougher and whitecaps appear. These whitecaps indicate breaking conditions where some waves lose part of their energy. In storm conditions the troughs between the waves will gradually fill up with foam and droplets making it difficult to distinguish individual waves. In constant wind conditions the waves will grow to an equilibrium situation in which growth by wind and dissipation by breaking balance. In this situation, the wave surface still appears chaotic, but again a certain underlying order exists that is associated with various physical processes. One of these processes consists of interactions between the different wave components constituting a wave field. These interactions exchange energy such that a certain distribution emerges of waves with varying periods, lengths and directions.

As the wind drops, the wave field will change character again and we enter the fourth phase. The wind doesn’t transfer energy to the waves anymore and the whitecaps quickly disappear. Now the waves are no longer under the influence of wind and oceanographers call such waves swell waves. Now another interesting property of ocean waves appears. The propagation velocity of a wave is proportional to its wave period. This means that longer period waves move faster over the ocean surface than shorter waves with smaller wave periods. The effect is that the wave field is gradually broken up into groups of waves propagating in the same direction with the same speed. As the waves spread over the ocean surface they will appear more regular with time and space. Such regular waves are experienced as swell waves. In the 1960s it was discovered that swell waves could propagate over enormous distances as they lose hardly any energy by breaking. In a famous experiment it was found that swell waves approaching the coasts of Alaska were generated 10 days earlier in a severe storm near Antarctica. That is a distance of more than 14.000 km! This further illustrates that swell waves behave independently of the local weather conditions where they are measured. This unique property of swell waves was exploited for hundreds of years by the seafarers of the Marshall Islands to support navigating between their distant islands, long before the time of a GPS device. As these islands lie in about the middle of the Pacific Ocean they encounter a rather constant influx of swells generated in the northerly and southerly storm zones of the Pacific Ocean. In June 2015 I participated in a scientific expedition to the Marshall Islands to study this old art of reading the waves for navigation purposes. It was special to experience the undulating motion of ocean swells in the midst of the ocean and rely on the craftsmanship of the navigator to bring us safely to the nearest island.

Even waves have a finite life. At a certain moment they will hit the coast. Before they reach the coast, however, they are slowed down and weakened by shallows only to break on the Atlantic coasts. Especially in stormy weather it is wonderful to see how these towering waves explode in enormous splashes. In this way one can feel the power of the waves. Also in calm weather and in areas with mildly sloping bottoms, as is the case near Nazaré in Portugal, swell waves may steepen to gigantic breakers. But also in the open ocean, waves coming from different directions may collide in sudden fountains of water. This is well illustrated in a number of photos in this book, like the one on page 46.

In the above summary I gave a description of the fascinating life cycle of wind generated ocean waves. Interestingly, we can also reverse the problem. What do the waves tell us about the wind? It is already more than 200 years ago that Francis Beaufort addressed this question. He was in search of a method to systematically log the condition of the weather from ships. On the basis of visible characteristics of the sea surface he was able to derive an objective scale reaching from 1 (small ripples) to almost-impossible-to-measure scale 12 (hurricane force). As there were thousands of ships navigating on the ocean he was able to derive a worldwide climate atlas of wind and wave conditions. Such an atlas gives a statistical description of the weather conditions that can be expected on a given day. It was soon recognized as indispensable for planning safe journeys. With the arrival of computer based forecasting techniques these atlases soon became obsolete.

These computer models make use of the forecasted wind on the ocean and translate this information into a prediction of the expected wave conditions, similar to well-known weather forecasts. The art of predicting the wave conditions made a significant leap in the Second World War when there was a strong need for reliable wave forecasts for safe amphibious landings. At that time, making such a prediction required a lot of tedious and intricate handwork. With increasing knowledge about the generation and behaviour of wind-generated waves and with the development of computer techniques it is nowadays relatively easy to make a useful prediction. Wave prediction models now cover the entire globe and are able to produce reliable forecasts for a week to come. This allows seafarers to optimize their route and avoid dangerous storm systems.

Despite this progress, predictions still have their limitations. One example comprises the inability to predict freak waves. Such waves rise unexpectedly from the ocean surface as a steep wall of water. The first stories about such waves were met with scepticism by scientists. Only when reliable wave measurements taken from offshore platforms confirmed the existence of such waves, was this subject seriously studied by researchers. It is likely that freak waves are the cause of the sudden disappearance of tens of ships on world’s oceans. Fortunately, enormous progress has been made to predict the probability for such a freak wave to happen in a certain area and time frame.

In arctic regions the ocean is bordered by ice fields. The edges of these ice fields are continuously attacked by waves. The wave motion propagates into the ice gradually breaking the ice into smaller pieces. When the wind is blowing towards the ice, the ice floes heap together into a compact zone, whereas with seaward winds the ocean surface is littered with thousands of little ice packets. This drifting ice damps the wave motion leading to the experience of quiet water for anyone sailing through such an area. In the polar regions of the Atlantic Ocean, Greenland and Antarctica, icebergs calve from glaciers leading into the sea. These majestic mountains of ice can be quite dangerous as most of their volume is under water. The large humps of ice slowly drift with the ocean currents while waves nibble at them causing these icebergs to take wildly varying shapes. Despite the beauty of icebergs, seafarers should be very careful when venturing in the vicinity of them.

In the above summary I presented the multitude of wave phenomena on the ocean and how they can be experienced by seafarers. Although it has never been Dolph Kessler’s intention to interpret the science of waves, the intricate details and stylistic richness of these wave photographs, continue to fascinate me.

Gerbrant van Vledder
Olst, October 2016
Pretor-Pinney, G., 2010: The Wavewatcher’s Companion