Infragravity Waves: Part 2

First published in The Surfers Path

© Tony Butt 2010 - Please be decent enough to contact me before plagiarizing my stuff

In the first part of this article I introduced infragravity waves – those mysterious tsunami-like waves that cause the entire shoreline to surge in and out hundreds of metres during large swells and storms.  Even though they go almost unnoticed, they can cause untold grief to the population by destroying shoreline structures and sweeping away human artefacts.  In this, the second part, I’m going to describe a classic field experiment that proved how, in large-wave conditions where the ordinary waves break a long way out, the shoreline motions can be completely dominated by infragravity waves.  I’m then going to delve a little into the mechanisms behind the formation of infragravity waves, which are still not fully understood by scientists.

In stormy or large swell conditions on gently-sloping beaches, if the offshore wave height gets bigger, the infragravity waves at the shoreline also get bigger, but the ordinary waves at the shoreline stay the same size.  The ordinary waves just break further and further out, dissipating that extra energy over a longer distance between the breakpoint and the shore, but always ending up the same size at the shoreline.  Therefore, as the offshore wave height increases, the shoreline motions due to the infragravity waves become far more significant than those motions due to the ordinary waves; in other words, the shoreline becomes more and more ‘infragravity-dominated’.

That concept was proved spectacularly in a now classic experiment by Bob Guza and Ed Thornton in the early 1980s.  On a gently-sloping beach, over a period of several days, Guza and Thornton continuously measured the position of the waterline using a stack of special wires called run-up wires.  At the same time, the offshore wave height was continuously measured by pressure sensors deployed beyond the breakpoint. 

Once all the data had been collected, the computers spewed out a graph of shoreline water movement as a function of time (a run-up excursion time series).  A special filtering technique was used to split the run-ups into two separate time series: one containing run-ups with periods shorter than 20 seconds (ordinary-wave motions), and the other containing run-ups with periods longer than 20 seconds (infragravity-wave motions).  Daily averages were then taken of the ordinary-wave run-ups, the infragravity-wave run-ups and the offshore wave height.  Then, to compare the ordinary waves with the infragravity waves, each day’s average run-ups were plotted against each day’s corresponding average offshore wave heights.

The results were strikingly clear.  The ordinary-wave run-up had no relation whatever to the offshore wave height.  The ordinary-wave run-up just stayed constant (and very small) no matter how big the offshore waves got.  In contrast, the infragravity run-up increased in size in direct proportion to the offshore wave height.  This proved beyond doubt that it is the infragravity waves, not the ordinary waves that transmit the offshore energy through to the shoreline. 

A schematic representation of what would happen if you did a similar experiment to Guza and Thornton is shown in Figure 1.  I must point out that it is not the actual results of that experiment; rather just an illustration to give you the general idea.




Figure 1: Hypothetical graph based on a classic experiment showing that, on gently-sloping beaches, the shoreline motions corresponding to infragravity waves (red line) increase with offshore wave height, whereas shoreline motions corresponding to ordinary waves (blue line) don’t.  Each point on the graph represents the average of one day’s worth of data, the numbers inside the points referring to ‘day 1’, ‘day 2’ etc.  You can see that, on day 5, for example, with a large offshore wave height, the shoreline is completely dominated by infragravity motions

Where do infragravity waves come from?

Infragravity waves are another one of those things so difficult to measure that scientists are still partly relying on theories derived from mathematical modelling to explain their existence.  There are two standard theories.  The first, and most popular, was proposed way back in the early 1960s by mathematicians Michael Longuet-Higgins and Robert Stewart, and the second, slightly less popular, by Graham Symonds in the early 1980s.  Both of these theories, dare I say it, are rather speculative.  The truth is that scientists are still not a hundred percent sure where infragravity waves really come from.  I’ll explain the two theories below and you can make up your own mind.

The Longuet-Higgins and Stewart theory, or bound-long-wave theory, intimately links the infragravity waves with the groups, or sets, of ordinary waves.  An infragravity wave is generated somewhere seaward of the breakpoint, and is ‘fixed’ or ‘bound’ to a wave group.  To explain this, Longuet-Higgins and Stewart introduced the concept of radiation stress.  In simple terms, radiation stress can be thought of as a kind of pressure exerted in the water by the waves: the bigger the waves, the higher the radiation stress.  Between groups where the waves are small, you don’t have much radiation stress, but in the middle of a group, where the waves are big, you have a lot of radiation stress.  This causes a pressure gradient between the middle and the ends of the group – high pressure in the middle and low pressure at the ends.  This, in turn, tries to expel water away from the middle of the group and push it towards the edges.  As a result, a long wave, or infragravity wave, emerges with its trough in line with the middle of the group and its crest in line with the end of the group.  The infragravity wave is of the same wavelength as the group and travels along with it, but it is upside down, or 180 degrees out of phase with the group (Figure 2).



Figure 2: The Longuet-Higgins and Stewart theory of infragravity-wave formation

The other theory is called the time-varying set-up theory, put forward by Graham Symonds and co-workers around 1982.  It also involves wave groups and radiation stress, just like the Longuet-Higgins and Stewart theory.  But this time it is based around the supposition that location of the breakpoint varies with the size of the waves in an incoming group.  The bigger waves in the group break further out and the smaller ones further in, which causes the main focus of the radiation stress under the breaking waves to sweep back and forth, seaward and shoreward.  This generates a pressure wave of much longer wavelength than the ordinary waves, which propagates in both directions away from the breaker zone. In both theories the waves lose their grouping structure at the breakpoint.  The infragravity wave is ‘released’ and ends up travelling on towards the shore as a ‘free’ wave. 

I know all this seems a bit bizarre and far-fetched, but Longuet-Higgins and Stewart, and Symonds and colleagues used rigorous mathematical proofs and published them in prestigious peer-reviewed scientific journals.  But even after all that, they are still really only theories, and after several more decades of research, we still can’t be sure which one, if any, is correct.  Perhaps we need a couple more decades of research before we really find out where infragravity waves come from.  Meanwhile, the consequences of infragravity waves on the shoreline itself are also a subject of active research.  The fact that, in large-wave conditions, the shoreline motions are often dominated by the long, powerful motions of infragravity waves has very important implications.  Apart from people, cars, roads, sea walls and other human artefacts, infragravity waves also pick up and carry offshore natural material such as coastal sediments.  This suggests that infragravity waves could be a link between storms and coastal erosion, which is what we will talk about in the third and last part of this article.