Richardson Number Water Column

Compute signed bulk Richardson number for a supplied shear-layer scale and density contrast; density inversion remains negative and no critical instability diagnosis is imposed.

Description

Bulk Richardson number compares buoyancy and resolved velocity shear across a layer.

Bulk Richardson number compares buoyancy and resolved velocity shear across a layer. A signed density contrast preserves the distinction between stable and inverted stratification.^[1]

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

When to use Richardson Number Water Column

Use this for the following task: Compute signed bulk Richardson number for a supplied shear-layer scale and density contrast; density inversion remains negative and no critical instability diagnosis is imposed. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Richardson Number Water Column and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter signedDensityContrastKgPerM3, referenceDensityKgPerM3, gravityMPerSecondSquared, shearLayerThicknessM, velocityDifferenceMPerSecond according to the field table, then run the tool.
Read signedBulkRichardsonNumber. 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
signedDensityContrastKgPerM3	Signed density contrast kg per m3	number	Required
referenceDensityKgPerM3	Reference density kg per m3	number	Required
gravityMPerSecondSquared	Gravity m per second squared	number	Required
shearLayerThicknessM	Shear layer thickness m	number	Required
velocityDifferenceMPerSecond	Velocity difference m per second	number	Required

Supply positive density, gravity and layer thickness, a signed density contrast and nonzero velocity difference. Return the signed dimensionless result.

Ri=gravity×signedDensityContrast×layerThickness/(referenceDensity×velocityDifference²)

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

Output field	Meaning	Value type
signedBulkRichardsonNumber	Signed bulk richardson number	number

json

{
  "input": {
    "signedDensityContrastKgPerM3": 2,
    "referenceDensityKgPerM3": 1000,
    "gravityMPerSecondSquared": 10,
    "shearLayerThicknessM": 10,
    "velocityDifferenceMPerSecond": 0.2
  },
  "output": {
    "signedBulkRichardsonNumber": 4.999999999999999
  }
}

Limitations and assumptions

Zero velocity shear is rejected because the finite ratio is undefined. No critical threshold or turbulence diagnosis is imposed.

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 Density Gradient Stratification Strength when you need its operation: Compute signed N² from observed density gradients with depth positive down; negative values remain instability indicators rather than an invented real Brunt–Väisälä frequency. 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: Lake Physics Tools: rLakeAnalyzer reference manual.

References

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

Similar or alternative tools

Density Gradient Stratification Strength
Compute signed N² from observed density gradients with depth positive down; negative values remain instability indicators rather than an invented real Brunt–Väisälä frequency.
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.