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.
Description
A steady constant-viscosity Ekman model predicts rotating, decaying currents with depth.
A steady constant-viscosity Ekman model predicts rotating, decaying currents with depth. Rotation changes with the sign of Coriolis.
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.
When to use Ekman Spiral Surface Deflection Angle
Use this tool to 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.
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 Spiral Surface Deflection Angle 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 eastwardWindStressNPerM2, northwardWindStressNPerM2, waterDensityKgPerM3, verticalEddyViscosityM2PerSecond, signedCoriolisPerSecond, depthBelowSurfaceM using the field table and calculation rules, then run the tool.
- Read eastwardCurrentMPerSecond, northwardCurrentMPerSecond, speedMPerSecond. 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 |
|---|---|---|---|
| eastwardWindStressNPerM2 | Eastward wind stress n per m2 | number | Required |
| northwardWindStressNPerM2 | Northward wind stress n per m2 | number | Required |
| waterDensityKgPerM3 | Water density kg per m3 | number | Required |
| verticalEddyViscosityM2PerSecond | Vertical eddy viscosity m2 per second | number | Required |
| signedCoriolisPerSecond | Signed coriolis per second | number | Required |
| depthBelowSurfaceM | Depth below surface m | number | Required |
Use positive density and viscosity, nonnegative depth and nonzero signed f. Apply depth-dependent sine/cosine rotation to the signed wind-stress vector and return east, north and speed.1
e-fold depth = sqrt(2viscosity/abs(f)); vector decays by exp(−depth/e-fold depth) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| eastwardCurrentMPerSecond | Eastward current m per second | number |
| northwardCurrentMPerSecond | Northward current m per second | number |
| speedMPerSecond | Speed m per second | number |
{
"input": {
"eastwardWindStressNPerM2": 1,
"northwardWindStressNPerM2": 0,
"waterDensityKgPerM3": 1000,
"verticalEddyViscosityM2PerSecond": 0.5,
"signedCoriolisPerSecond": 1,
"depthBelowSurfaceM": 0
},
"output": {
"eastwardCurrentMPerSecond": 0.001,
"northwardCurrentMPerSecond": -0.001,
"speedMPerSecond": 0.0014142135623730952
}
}Limitations and assumptions
The ideal model is not a universal observed 45° surface-current rule.
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 Layer Depth: Distinguish constant-viscosity Ekman e-folding and conventional pi depth using supplied signed Coriolis, without latitude conversion; equatorial approximation is unsupported. For a complementary task, use Vector Average Current Components: Distinguish duration-weighted vector resultant from scalar mean current speed, retaining reversals; does not infer coordinates or drifter displacements.
References
-
Ekman Spiral Surface Deflection Angle — tool.io
Similar or alternative tools
- Ekman Layer Depth
Distinguish constant-viscosity Ekman e-folding and conventional pi depth using supplied signed Coriolis, without latitude conversion; equatorial approximation is unsupported.
- Vector Average Current Components
Distinguish duration-weighted vector resultant from scalar mean current speed, retaining reversals; does not infer coordinates or drifter displacements.