When wave steepness pinpoints worst case sea states for mooring design (and not wave height)

Vintage wind-up toys may seem simple, but they are mechanical marvels. Many intricate details turn a compressed spring into something like a walking robot. But while these designs are clever, they have their limits. For example, nothing stops them from tumbling off the edge of a table or down the stairs – they wander entirely aimlessly.

Wandering aimlessly is not exclusive to wind-up toys. In the early stage of any design, you may find yourself wandering between the many factors to consider. Finding ways to zero in on key design conditions saves a lot of time. In the case of mooring design, there may be a wide range of sea states the system needs to withstand. In this article, we’ll talk about how wave steepness helps pinpoint the worst-case sea states you may want to check first in a mooring design process.

Wind-up toys wander aimlessly, even off the edge of a table.

When we talk about sea states, the wave height quickly comes up

It’s no wonder, either, as typically it’s what we think of when we look at pictures of the sea. After all, the wave height is the vertical distance from the trough to the crest, so it is often a visual cue that hints at how severe a sea state actually is. It is one of the most essential and fundamental parameters of ocean waves.

Another critical parameter is the wavelength. The wavelength is the horizontal spacing between successive wave crests. Now, both wavelength and height are a part of wave steepness, which is the ratio of wave height to the wavelength. So a high wave with a short wavelength means a really steep wave. So why is wave steepness useful?

Irregular ocean waves

The ratio of the wave height to wavelength – the steepness – is often what can give you a hint at how really severe a sea state is for design and analysis

Wave steepness gives hints about what the resulting forces may be like

Waves with low steepness are often not very exciting: they don’t typically cause rapid changes in loads like buoyancy, drag, or wave excitation forces on a floating system.

On the other hand, waves with high steepness can cause all kinds of problems. High steepness often means rapid changes in buoyancy, drag, and wave excitation. These can mean large accelerations and forces in a floating system. If there are large forces, it can mean significant stresses in the hull or mooring system and the risk of structural failures.

Wave steepness can act as a filter

When there are so many sea states to consider for a specific project, it’s helpful to pinpoint conditions that may cause a problem in the design. You can save a lot of time in the design phase by considering the harshest sea states first – because the mooring will surely survive more benign conditions. The sea states with the steepest waves are likely to be the most problematic conditions. In this way, considering steepness then acts as a filtering mechanism. You can spend less time looking through a wide range of conditions that are possible and zero in on what specific sea states may drive your mooring design.

Checking wave steepness is also important because you might miss the worst-case scenario. It’s definitely a mistake to zero in on the maximum wave height without checking wave steepness. Often, sea states with the maximum wave height can cause the biggest loads in a mooring system. But this is not always the case.

It’s possible at a certain location that the maximum wave steepness comes up in lower wave heights that happen to have much shorter wavelengths. Without considering steepness, you might miss this by initially zeroing in on only the maximum wave height.

You also need to be thorough when looking at wave steepness. Remember that wave steepness changes with both wave height and wavelength. Beware that there may be more than one set of sea state conditions that give large wave steepness depending on the wave climate at a specific location.

But wave steepness is not a perfect filter

Remember that wave steepness is a ratio – and a ratio that may mislead you in some cases. For example, you may have relatively small wave heights from wind chop – but if the wavelengths are small too, it might result in a large wave steepness. But most often, wave chop isn’t going to drive a mooring design. In this way, it still makes sense to do a reality check on the absolute wave heights along with wave steepness – be sure to check both wave steepness and total wave height together.

Ultimately, you need to check your floating system’s response to environmental conditions. Many floating systems have one or more natural periods of motion – these are conditions in which resonance may be possible. The resulting large motions in resonance (and loads in the moorings) may result from relatively small environmental forces. Environmental conditions that may excite the system in these conditions often need to be carefully considered regardless of the wave steepness in those conditions.

It’s time for an example

The SOFS mooring, deployed and maintained by CSIRO and IMOS, is located in almost 5000m deep water in the southern ocean. This full ocean depth mooring has provided a valuable time-series of measurements for many years at that location. The single largest wave measured there topped 22m. So does this kind of extreme wave height drive the maximum loads in the mooring?

Not necessarily. In all locations in the ocean, there is a wide range of sea states and wave heights. The largest wave heights occur in sea states with a 17m significant wave height and 19 second wave spectrum peak period. But the maximum loads tend to occur in conditions with lower significant wave height, around 10m and 12 second wave spectrum peak period.

A rough estimate of the steepness is possible from the wavelength of a 19 second wave and 12 second deepwater wave and the significant wave height. In the 17m sea, the steepness is only 0.03, while in the 10m sea, the steepness is 0.044.

In this particular case, the larger wave steepness in the 10m sea corresponds with more rapid loading and motions in the mooring, creating larger loads. This is also seen in field measurements and ProteusDS Oceanographic dynamic analysis modelling of the SOFS mooring tension.

SOFS buoy in ocean waves

SOFS buoy riding through ocean waves. Picture credit: Eric Schulz from Australia Bureau of Meteorology / IMOS

In summary

There’s often a range of environmental conditions to consider when designing a floating system and its mooring. Finding a way to narrow down the driving environmental load cases helps save time. Wave steepness, which is the ratio of wave height to wavelength, can help filter down critical load cases. It’s a mistake to assume the maximum wave height will be your worst-case scenario because it isn’t always the steepest wave condition. But steepness alone is not a perfect filtering mechanism, so you still need to do a reality check on the maximum wave height.

At the start of a design project, you may feel like you are a clockwork toy, zinging around aimlessly when digging through mounds of environmental data. But if you consider wave steepness, you may find you can quickly identify crucial sea states to start a mooring design and get to the next step faster.

Next step

We have a few ProteusDS Oceanographic sample moorings on our website. Check out a mooring layout for SOFS in the downloads area here.

Thanks to CSIRO

Thanks to Pete Jansen from CSIRO Marine National Facility / IMOS for sharing technical pointers, sharing data, and helping assess the SOFS mooring system and buoy dynamics.