Ekman Layer Depth
Distinguish constant-viscosity Ekman e-folding and conventional pi depth using supplied signed Coriolis, without latitude conversion; equatorial approximation is unsupported.
Description
Ekman depth conventions can refer to exponential decay or a multiple of that scale.
Ekman depth conventions can refer to exponential decay or a multiple of that scale. Both depend on viscosity and Coriolis magnitude.
Distinguish constant-viscosity Ekman e-folding and conventional pi depth using supplied signed Coriolis, without latitude conversion; equatorial approximation is unsupported.
When to use Ekman Layer Depth
Use this tool to distinguish constant-viscosity Ekman e-folding and conventional pi depth using supplied signed Coriolis, without latitude conversion; equatorial approximation is unsupported.
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 Ekman Layer Depth 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 verticalEddyViscosityM2PerSecond, signedCoriolisPerSecond using the field table and calculation rules, then run the tool.
- Read eFoldingDepthM, conventionalPiEkmanDepthM. 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 |
|---|---|---|---|
| verticalEddyViscosityM2PerSecond | Vertical eddy viscosity m2 per second | number | Required |
| signedCoriolisPerSecond | Signed coriolis per second | number | Required |
Use positive viscosity and nonzero signed f. Return both meter scales, which are unchanged by switching hemisphere sign.1
e-folding depth = sqrt(2vertical viscosity/abs(f)); conventional depth = π × e-folding depth Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| eFoldingDepthM | E folding depth m | number |
| conventionalPiEkmanDepthM | Conventional pi ekman depth m | number |
{
"input": {
"verticalEddyViscosityM2PerSecond": 0.01,
"signedCoriolisPerSecond": 0.0001
},
"output": {
"eFoldingDepthM": 14.142135623730951,
"conventionalPiEkmanDepthM": 44.42882938158366
}
}Limitations and assumptions
Constant viscosity and nonequatorial balance are assumed; no latitude conversion.
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 Ekman Spiral Surface Deflection Angle: Calculate a constant-viscosity steady Ekman current vector at depth, including hemisphere-dependent rotation and exponential decay; not a universal observed 45-degree surface rule. For a complementary task, use Ekman Pumping Wind Curl: Compute vertical curl of stress/(rho f), including the supplied beta correction for eastward stress; positive is upward and no coordinate-derived Coriolis values are inferred.
References
-
Ekman Layer Depth — tool.io
Similar or alternative tools
- Ekman Spiral Surface Deflection Angle
Calculate a constant-viscosity steady Ekman current vector at depth, including hemisphere-dependent rotation and exponential decay; not a universal observed 45-degree surface rule.
- Ekman Pumping Wind Curl
Compute vertical curl of stress/(rho f), including the supplied beta correction for eastward stress; positive is upward and no coordinate-derived Coriolis values are inferred.