Thermal Wind Vertical Shear

Integrate signed thermal-wind top-minus-bottom shear from measured horizontal density-gradient profiles on positive-down depths; no absolute reference current or mapped coordinate gradients are inferred.

Description

Thermal-wind balance relates horizontal density gradients to vertical current shear.

Thermal-wind balance relates horizontal density gradients to vertical current shear. A reference current is needed to obtain absolute currents.

When to use Thermal Wind Vertical Shear

Use this tool to integrate signed thermal-wind top-minus-bottom shear from measured horizontal density-gradient profiles on positive-down depths; no absolute reference current or mapped coordinate gradients are inferred.

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 Thermal Wind Vertical Shear 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 depthsM, eastwardDensityGradientsKgPerM4, northwardDensityGradientsKgPerM4, referenceDensityKgPerM3, signedCoriolisPerSecond, gravityMPerSecondSquared using the field table and calculation rules, then run the tool.
Read eastwardTopMinusBottomMPerSecond, northwardTopMinusBottomMPerSecond. 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
depthsM	Depths m	list of number	Required
eastwardDensityGradientsKgPerM4	Eastward density gradients kg per m4	list of number	Required
northwardDensityGradientsKgPerM4	Northward density gradients kg per m4	list of number	Required
referenceDensityKgPerM3	Reference density kg per m3	number	Required
signedCoriolisPerSecond	Signed coriolis per second	number	Required
gravityMPerSecondSquared	Gravity m per second squared	number	Required

Use increasing nonnegative positive-down depths, aligned gradients, positive reference density/gravity and nonzero signed Coriolis. Integrate by trapezoids; the northward component uses minus the eastward gradient integral.^[1]

east top-minus-bottom = g/(ρf) × ∫ northward density gradient ddepth

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
eastwardTopMinusBottomMPerSecond	Eastward top minus bottom m per second	number
northwardTopMinusBottomMPerSecond	Northward top minus bottom m per second	number

json

{
  "input": {
    "depthsM": [
      0,
      10
    ],
    "eastwardDensityGradientsKgPerM4": [
      0,
      1
    ],
    "northwardDensityGradientsKgPerM4": [
      1,
      2
    ],
    "referenceDensityKgPerM3": 1000,
    "signedCoriolisPerSecond": 0.01,
    "gravityMPerSecondSquared": 1
  },
  "output": {
    "eastwardTopMinusBottomMPerSecond": 1.5,
    "northwardTopMinusBottomMPerSecond": -0.5
  }
}

Limitations and assumptions

Signs depend on the stated axes and hemisphere; no absolute current or mapped gradient is inferred.

Numbers and computed results must be finite; overflow produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Vector Average Current Components: Distinguish duration-weighted vector resultant from scalar mean current speed, retaining reversals; does not infer coordinates or drifter displacements. For a complementary task, 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.

References

Thermal Wind Vertical Shear — tool.io

Similar or alternative tools

Vector Average Current Components
Distinguish duration-weighted vector resultant from scalar mean current speed, retaining reversals; does not infer coordinates or drifter displacements.
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.