The performance of a sailing boat is affected by the presence of surface waves. In order to understand the boat’s behavior under waves, it is necessary first to model the irregular shape of the water surface. But, how?
We call sea state to the general condition of the free surface of the sea with respect to wind waves and swell at a certain location, a certain time, and for a time interval in which the sea state can be considered to be constant. As seen on “Wind-generated sea waves,” the surface of the sea is constantly monitored by experienced human observers, wave-buoys, radars, and satellites. The data gathered is commonly a record of the sea-surface elevation at one location as a function of time which can be later analyzed with a Fourier transform. Thus, the sea surface can be studied as a superimposition of regular harmonic waves, each with a different wavelength and a different height.
The sea state depends on several factors such as the wind speed, wind direction, wind duration (the time since the wind started to blow), water depth, and fetch (distance over which a wind acts without obstruction to produce waves). Based on the energy balance between de local wind and the waves, the sea can be considered as:
- Fully developed sea: if both the fetch and the wind duration are big enough, the waves grow to the maximum height allowed by the local wind speed. Under these conditions, the wind’s energy is balanced with the transfer of energy to the waves and the dissipation of energy by wave breaking. In this situation, for a fixed local wind speed, the sea state will not change even if the wind duration or fetch is further increased.
- Developing sea: the waves have not reached their maximum height, but they are still growing larger. In this case, the wind input energy is larger than the wave and the dissipation energy.
- Non-fully developed sea: the local wind is unable to impart its maximum energy to the waves. This situation can happen when the fetch is limited or when the wind has not been in contact with the sea for a sufficient time.
The most common method used for describing the sea state is by means of what is called the “wave spectral density,” also known as “wave energy spectrum” or simply “spectrum,” where a particular measure of the wave height is represented based on its angular frequency.
Different standard spectra formulations have been developed over time. When sea wind coexists with swells, multi-mode models (multi-peak models) such as the Ochi-Hubble spectrum are employed. On the other hand, single-modal spectrum models (single-peak models) are utilized to represent pure wind waves or swell-only cases.
For most ship, offshore structures, and boat applications, single-modal spectra models are used for describing the sea state. Among them, the most important and more extended ones are:
- The Bretschneider spectrum which is the one recommended by the ITTC (International Towing Tank Congress) for fully developed seas;
- and the JONSWAP (Joint North Sea Wave Project) spectrum recommended by the ITTC for fetch-limited situations.
Two parameters characterize both the Bretschneider and the JONSWAP spectra:
- The significant wave height, H1/3. It is the mean height of the one-third highest waves.
- The modal period, T0, also known as the peak period. It is the period belonging to the component with the highest wave height in a particular spectrum.
It has been shown that the average wave height estimated visually by an experienced observer approximates the significant wave height. In contrast, the visually observed wave periods tend to be shorter than those that have been measured with sensors.
In deep water, the significant wave height, H1/3, and the modal or peak period, T0, of a sea state can be estimated with the Breugem and Holthuijsen wave growth nomogram, where:
- red lines represent the growth of waves along an increasing fetch and correspond to a constant wind speed;
- green lines represent the fetch in nautical miles;
- the vertical lines indicate the duration in hours at which that stage of development will be reached from zero wave height.
For a given wind speed, fetch, and wind duration, the significant wave height, H1/3 (in meters), is obtained from the horizontal black lines, and the modal or peak period, T0 ( in seconds), is obtained from the blue lines in the nomogram.
The curves are nearly horizontal on the right‑hand side of the diagram. This implies that for a given wind speed, the waves stop growing and reach a fully developed state when the duration and fetch are long enough.
If the duration is limited, waves will not develop beyond that point, irrespective of the fetch length. Similarly, if the fetch is limited, the waves will not grow futher beyond the fetch point regardless of the wind duration.
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