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.

Description

The Wedderburn number compares two-layer buoyancy resistance with wind-driven forcing over a fetch.

The Wedderburn number compares two-layer buoyancy resistance with wind-driven forcing over a fetch. It combines reduced gravity, upper-layer depth and water-side friction velocity.^[1]

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

When to use Wedderburn Number

Use this for the following task: Evaluate W=g′h²/(u*²L) from caller two-layer density contrast, upper thickness, friction velocity and fetch; no universal upwelling or turnover criterion. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Wedderburn Number and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter densityContrastKgPerM3, referenceDensityKgPerM3, gravityMPerSecondSquared, upperLayerThicknessM, waterFrictionVelocityMPerSecond, windFetchM according to the field table, then run the tool.
Read wedderburnNumber. 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
densityContrastKgPerM3	Density contrast kg per m3	number	Required
referenceDensityKgPerM3	Reference density kg per m3	number	Required
gravityMPerSecondSquared	Gravity m per second squared	number	Required
upperLayerThicknessM	Upper layer thickness m	number	Required
waterFrictionVelocityMPerSecond	Water friction velocity m per second	number	Required
windFetchM	Wind fetch m	number	Required

Supply nonnegative density contrast and positive reference density, gravity, thickness, water friction velocity and fetch. Evaluate the dimensionless ratio.

g′=gravity×densityContrast/referenceDensity; W=g′×upperThickness²/(frictionVelocity²×fetch)

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

Output field	Meaning	Value type
wedderburnNumber	Wedderburn number	number

json

{
  "input": {
    "densityContrastKgPerM3": 2,
    "referenceDensityKgPerM3": 1000,
    "gravityMPerSecondSquared": 10,
    "upperLayerThicknessM": 10,
    "waterFrictionVelocityMPerSecond": 0.1,
    "windFetchM": 100
  },
  "output": {
    "wedderburnNumber": 1.9999999999999996
  }
}

Limitations and assumptions

Use water-side friction velocity, not raw wind speed. The tool does not impose a universal upwelling or turnover threshold or represent complex basin geometry.

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 Lake Number Inertial when you need its operation: Evaluate a Lake Number convention using Schmidt stability already in J/m² and water-side friction velocity; no extra gravity factor, wind-to-water conversion or universal mixing threshold. Choose Effective Fetch Length for the complementary operation: Calculate the specified effective-fetch convention sum(F·cos²theta)/sum(cos theta) from measured radial fetches; no shoreline GIS or prevailing-wind inference.

Background reference: Lake Physics Tools: rLakeAnalyzer reference manual.

References

Lake Physics Tools: rLakeAnalyzer reference manual — Winslow, Read and colleagues; GLEON

Similar or alternative tools

Lake Number Inertial
Evaluate a Lake Number convention using Schmidt stability already in J/m² and water-side friction velocity; no extra gravity factor, wind-to-water conversion or universal mixing threshold.
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.