Fetch Limited Wave Height

Evaluate a supplied deep-water fetch-limited bulk wave-growth correlation; wind reference height, duration, shallow-water limits and calibration applicability are external.

Description

Fetch limits the distance over which wind can grow surface waves.

Fetch limits the distance over which wind can grow surface waves. A calibrated bulk deep-water relation estimates significant wave height from wind, fetch and supplied correlation coefficients.^[1]

The tool returns predictedSignificantWaveHeightM. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Fetch Limited Wave Height

Use this for the following task: Evaluate a supplied deep-water fetch-limited bulk wave-growth correlation; wind reference height, duration, shallow-water limits and calibration applicability are external. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Fetch Limited Wave Height and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter windSpeedMPerSecond, fetchM, gravityMPerSecondSquared, heightCoefficient, growthCoefficient, fetchExponent according to the field table, then run the tool.
Read predictedSignificantWaveHeightM. Use the calculation below to interpret the selected mean or the model’s signs, units and comparison flags.
Review the supplied assumptions and calibration before comparing or reporting the result.

Input field	Meaning	Value type and bounds	Requirement
windSpeedMPerSecond	Wind speed m per second	number	Required
fetchM	Fetch m	number	Required
gravityMPerSecondSquared	Gravity m per second squared	number	Required
heightCoefficient	Height coefficient	number	Required
growthCoefficient	Growth coefficient	number	Required
fetchExponent	Fetch exponent	number	Required

Supply positive wind speed, gravity and all correlation coefficients/exponent, and nonnegative fetch. Evaluate the supplied growth relation; zero fetch gives zero height.

height=(heightCoefficient×wind²/gravity)×tanh(growthCoefficient×(gravity×fetch/wind²)^fetchExponent)

The symbols and boundary conditions refer to the supplied fields and the implementation described above.

Output field	Meaning	Value type
predictedSignificantWaveHeightM	Predicted significant wave height m	number

json

{
  "input": {
    "windSpeedMPerSecond": 10,
    "fetchM": 1000,
    "gravityMPerSecondSquared": 10,
    "heightCoefficient": 0.283,
    "growthCoefficient": 0.0125,
    "fetchExponent": 0.42
  },
  "output": {
    "predictedSignificantWaveHeightM": 0.24412693366179733
  }
}

Limitations and assumptions

Reference wind height, adequate wind duration and deep-water applicability must be checked externally. Shoaling, breaking and complex wave spectra are not modeled.

Numerical inputs must be finite. Input-shape and calculation checks do not establish measurement quality or the validity of a supplied calibration.

Alternative or Complementary methods

Choose Effective Fetch Length when you need its operation: Calculate the specified effective-fetch convention sum(F·cos²theta)/sum(cos theta) from measured radial fetches; no shoreline GIS or prevailing-wind inference. Choose Wedderburn Number for the complementary operation: Evaluate W=g′h²/(u*²L) from caller two-layer density contrast, upper thickness, friction velocity and fetch; no universal upwelling or turnover criterion.

Background reference: Hydrologic Engineering Requirements for Reservoirs: wave analysis.

References

Hydrologic Engineering Requirements for Reservoirs: wave analysis — U.S. Army Corps of Engineers, EM 1110-2-1420

Similar or alternative tools

Effective Fetch Length
Calculate the specified effective-fetch convention sum(F·cos²theta)/sum(cos theta) from measured radial fetches; no shoreline GIS or prevailing-wind inference.
Wedderburn Number
Evaluate W=g′h²/(u*²L) from caller two-layer density contrast, upper thickness, friction velocity and fetch; no universal upwelling or turnover criterion.