Baroclinic Rossby Wave Speed
Calculate dispersive beta-plane baroclinic Rossby-wave phase/frequency from supplied deformation radius and wave numbers; distinct from an existing lake deformation-radius inversion.
Description
Baroclinic Rossby waves have a westward beta-plane phase speed modified by wave numbers and deformation radius.
Baroclinic Rossby waves have a westward beta-plane phase speed modified by wave numbers and deformation radius. Frequency retains the zonal wave-number sign.
Calculate dispersive beta-plane baroclinic Rossby-wave phase/frequency from supplied deformation radius and wave numbers; distinct from an existing lake deformation-radius inversion.
When to use Baroclinic Rossby Wave Speed
Use this tool to calculate dispersive beta-plane baroclinic Rossby-wave phase/frequency from supplied deformation radius and wave numbers; distinct from an existing lake deformation-radius inversion.
Gather the water, wave, current or profile observations and any supplied calibration constants. Confirm units and the stated coordinate and pressure conventions.
How to use Baroclinic Rossby Wave Speed and understand its results
- Gather the water, wave, current or profile observations and any supplied calibration constants. Confirm units and the stated coordinate and pressure conventions.
- Enter betaPerMeterSecond, deformationRadiusM, zonalWaveNumberPerM, meridionalWaveNumberPerM using the field table and calculation rules, then run the tool.
- Read zonalPhaseSpeedMPerSecond, angularFrequencyPerSecond. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| betaPerMeterSecond | Beta per meter second | number | Required |
| deformationRadiusM | Deformation radius m | number | Required |
| zonalWaveNumberPerM | Zonal wave number per m | number | Required |
| meridionalWaveNumberPerM | Meridional wave number per m | number | Required |
Use positive beta and radius with signed wave numbers. Return negative zonal speed and signed angular frequency, including zero frequency at zero zonal wave number.1
zonal phase speed = −beta/(k² + l² + 1/radius²); frequency = speed × k Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| zonalPhaseSpeedMPerSecond | Zonal phase speed m per second | number |
| angularFrequencyPerSecond | Angular frequency per second | number |
{
"input": {
"betaPerMeterSecond": 0.001,
"deformationRadiusM": 10,
"zonalWaveNumberPerM": 0.1,
"meridionalWaveNumberPerM": 0
},
"output": {
"zonalPhaseSpeedMPerSecond": -0.04999999999999999,
"angularFrequencyPerSecond": -0.004999999999999999
}
}Limitations and assumptions
The supplied radius is not inferred and no global dispersion relation is solved.
Numbers and computed results must be finite; overflow produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Western Boundary Intensification Width: Compare Munk lateral-viscosity and Stommel linear-drag boundary scales under supplied positive beta; these are alternative ideal balances, not a combined current-width solution. For a complementary task, use Sverdrup Interior Transport: Compute signed Sverdrup interior transport per width and supplied strip transport; assumes steady linear vorticity balance, not a western boundary current or global circulation prediction.
References
-
Baroclinic Rossby Wave Speed — tool.io
Similar or alternative tools
- Western Boundary Intensification Width
Compare Munk lateral-viscosity and Stommel linear-drag boundary scales under supplied positive beta; these are alternative ideal balances, not a combined current-width solution.
- Sverdrup Interior Transport
Compute signed Sverdrup interior transport per width and supplied strip transport; assumes steady linear vorticity balance, not a western boundary current or global circulation prediction.