Internal Rossby Radius Deformation

Calculate two-layer internal Rossby radius c/|f| using supplied reduced gravity and signed Coriolis parameter; no latitude or coordinate transformation.

Description

The internal Rossby radius compares an internal-wave speed with rotation.

The internal Rossby radius compares an internal-wave speed with rotation. Its positive length uses the magnitude of a supplied signed Coriolis parameter.^[1]

The tool returns internalWaveSpeedMPerSecond, rossbyDeformationRadiusM. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Internal Rossby Radius Deformation

Use this for the following task: Calculate two-layer internal Rossby radius c/|f| using supplied reduced gravity and signed Coriolis parameter; no latitude or coordinate transformation. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Internal Rossby Radius Deformation and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter upperLayerDepthM, lowerLayerDepthM, reducedGravityMPerSecondSquared, signedCoriolisPerSecond according to the field table, then run the tool.
Read internalWaveSpeedMPerSecond, rossbyDeformationRadiusM. 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
upperLayerDepthM	Upper layer depth m	number	Required
lowerLayerDepthM	Lower layer depth m	number	Required
reducedGravityMPerSecondSquared	Reduced gravity m per second squared	number	Required
signedCoriolisPerSecond	Signed coriolis per second	number	Required

Supply positive layer depths and reduced gravity and a nonzero signed Coriolis parameter. Return the two-layer speed and radius.

c=sqrt(reducedGravity×upperDepth×lowerDepth/(upperDepth+lowerDepth)); radius=c/abs(Coriolis)

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

Output field	Meaning	Value type
internalWaveSpeedMPerSecond	Internal wave speed m per second	number
rossbyDeformationRadiusM	Rossby deformation radius m	number

json

{
  "input": {
    "upperLayerDepthM": 10,
    "lowerLayerDepthM": 10,
    "reducedGravityMPerSecondSquared": 0.02,
    "signedCoriolisPerSecond": -0.0001
  },
  "output": {
    "internalWaveSpeedMPerSecond": 0.31622776601683794,
    "rossbyDeformationRadiusM": 3162.277660168379
  }
}

Limitations and assumptions

Zero Coriolis is rejected rather than returning an infinite radius. Latitude, coordinate transformations and complex stratification are not inferred.

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 Internal Seiche Period Rectangular when you need its operation: Estimate the fundamental rectangular nonrotating two-layer internal seiche period 2L/c; higher harmonics are excluded as duplicated scaling variants. Choose Lake Number Inertial for the complementary 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.

Background reference: Lake Physics Tools: rLakeAnalyzer reference manual.

References

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

Similar or alternative tools

Internal Seiche Period Rectangular
Estimate the fundamental rectangular nonrotating two-layer internal seiche period 2L/c; higher harmonics are excluded as duplicated scaling variants.
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.