Sea states are described in seconds and analysed in hertz
Ask a mariner about the sea and you get periods: an eight-second wind sea, a sixteen-second swell running in from a distant storm. Open the buoy record or the motions report for the same day and the axis has changed — energy density plotted against frequency, the whole wave band squeezed between roughly 20 and 500 mHz. Naval architecture lives on that second axis, because a vessel’s response operators, its added mass and its resonances are all functions of frequency. Enter a millihertz value on the left and the hertz figure that a spectral plot or a MATLAB script wants appears as you type.
Reading the wave band as a frequency scale
Period is observed, frequency is modelled
The band a buoy actually reports
Two directions to escape the waves
From a measured period to a point on the spectrum
Turn the period into millihertz first
Divide 1 000 by the period in seconds: a 12-second peak period is 83.3 mHz, a 40-second slow-drift oscillation is 25 mHz. That is the number to enter on the left.
Read the hertz value against the spectral axis
Buoy output, JONSWAP fits and motion transfer functions are almost always drawn in hertz. With the figure in that unit you can point at where a given period lands relative to the spectral peak instead of estimating it by eye.
Copy it into the analysis script
The copy button places the digits alone on the clipboard — no unit, no thousands spaces — which is what a band-pass filter definition or a spectral bin edge in a script expects. Ctrl+C inside a field does the same.
Reverse it when a natural frequency arrives in hertz
Hydrodynamic software reports resonances in hertz while mooring and metocean reports discuss them in millihertz or seconds. Press the swap arrows (↔), or type into the right-hand field, to move back. Either selector can be searched if a figure comes in as something else.
Waves and hull motions on one frequency scale
The periods below are representative rather than absolute — hull dimensions, draught and mooring stiffness move them — but the ordering is what matters. Read down the table and the wave band is the crowded middle, with the deliberately-tuned platform resonances sitting outside it at either end.
| Wave component or motion mode | Typical period | Millihertz | Hertz | What it means offshore |
|---|---|---|---|---|
| Short wind chop | 2 s | 500 mHz | 0.500 Hz | Near the top of what a buoy spectrum resolves |
| Tension-leg platform heave | 3 s | 333 mHz | 0.333 Hz | Tuned stiff, deliberately above the wave energy |
| Fresh local wind sea | 5 s | 200 mHz | 0.200 Hz | Where a rising blow puts most of its energy |
| Fully developed wind sea | 8 s | 125 mHz | 0.125 Hz | Workboat comfort and crew transfer limits |
| Ship-shaped hull heave | 10 s | 100 mHz | 0.100 Hz | Inside the band, which is why an FPSO moves with the sea |
| North Sea storm peak | 14 s | 71.4 mHz | 0.0714 Hz | The design sea state for extreme loading checks |
| Ocean swell | 16 s | 62.5 mHz | 0.0625 Hz | Arrives from far away, long after the wind that made it |
| Long forerunner swell | 22 s | 45.5 mHz | 0.0455 Hz | Low, regular and easily missed by a short record |
| Semi-submersible heave | 25 s | 40.0 mHz | 0.0400 Hz | Tuned soft, just below the swell energy |
| Spar heave | 30 s | 33.3 mHz | 0.0333 Hz | Deep draught pushes the resonance clear of the band |
| Spar pitch | 60 s | 16.7 mHz | 0.0167 Hz | Slow enough that only wave groups excite it |
| Moored vessel slow-drift surge | 150 s | 6.67 mHz | 0.00667 Hz | Second-order response that sets mooring line tension |
Slow-drift values without a run of zeros
A 6.67 mHz surge resonance is easier to type and check than 0.00667 Hz, and the reading only switches to scientific notation far below anything a mooring analysis deals with.
Band edges converted in one pass
Enter the low cut-off, copy it, then the high one: a 30–485 mHz buoy range comes out as 0.03–0.485 Hz with both limits in the units a filter definition expects.
Fine enough for a resolution check
Eight decimals are kept, so the 0.56 mHz bin width of a 30-minute record survives the conversion instead of rounding away to nothing.
Questions from the metocean and motions desk
A wave period is in seconds — how does that become millihertz?
Frequency is the reciprocal of period, so divide 1 000 by the period in seconds and the answer is already in millihertz. Ten seconds gives 100 mHz, twenty seconds gives 50 mHz, and two and a half seconds gives 400 mHz. The relationship is not linear, which trips people up when they compare gaps: the step from 8 s to 10 s covers 25 mHz, while the step from 20 s to 22 s covers barely 4.5 mHz. That compression at the long-period end is exactly why swell needs finer frequency resolution than wind sea does.
Why are wave spectra plotted against frequency instead of period?
Because the mathematics underneath is a Fourier transform, and that produces energy per unit frequency in evenly spaced bins. Plot the same data against period and the bins bunch up at the short end and stretch enormously at the long end, so the area under the curve — which is what gives significant wave height — stops being readable by eye. Standard spectral forms are written the same way: the JONSWAP shape, its peak enhancement factor and the high-frequency tail that falls off as frequency to the fifth power are all defined on a frequency axis. Response operators come from the same world, which keeps everything in step.
Where do swell and wind sea sit on that axis?
Locally generated sea occupies the fast end, broadly 125–500 mHz for periods of eight seconds down to two, and its spectral peak is broad and messy because the wind is feeding many periods at once. Swell has left its generating storm behind and dispersed on the way, arriving as a narrow peak somewhere around 45–100 mHz — ten to twenty-two second periods. A bimodal spectrum with two clear humps means both are present, and the split between them is usually drawn near 100 mHz. It matters operationally: a modest swell at 55 mHz can stop a crane job that a much steeper wind sea would not.
Why are floating platforms tuned away from the wave band?
To avoid being driven at resonance for days on end. A hull whose vertical natural period lands inside the sea state it works in will amplify that motion enormously, and offshore the excitation does not stop — a storm can hold the same peak period for many hours. So the design pushes the resonance out of reach in one direction or the other: tension legs make heave stiff, with periods of a few seconds, well above the energy; spars and semi-submersibles use deep draught and small waterplane area to make heave slow, out beyond 25 seconds. Slow-drift surge, down near 5–10 mHz, escapes the waves themselves but is still excited by the beat between them, which is why mooring analysis treats it separately.
How long a record do I need to resolve low-frequency motion?
Frequency resolution is one divided by the record length, so the arithmetic is unforgiving at the slow end. Twenty minutes of data gives bins 0.83 mHz wide, thirty minutes gives 0.56 mHz, and a full three-hour sea state gives 0.09 mHz. For wind sea that is ample. For a slow-drift surge resonance near 6.7 mHz it is the difference between a peak you can identify and a smear across two bins — a twenty-minute window would contain only about eight complete cycles of that motion. Standard practice records twenty or thirty minutes for the sea state itself, and much longer runs when the low-frequency response is the thing under investigation.
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