Wind Stress Mixing Depth Estimate

Screen mixing depth by supplied useful wind work against the rho·N²·h³/12 energy of uniform linear stratification; wind-work velocity/efficiency require calibration, not universal turbulent mixing.

Description

Wind can supply energy that erodes a lake’s density stratification.

Wind can supply energy that erodes a lake’s density stratification. A uniform linear density gradient gives a cubic depth dependence for the potential-energy cost of mixing.^[1]

The tool returns availableMixingEnergyJPerM2, unboundedMixingDepthM, depthLimitedMixingDepthM, bottomLimited. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Wind Stress Mixing Depth Estimate

Use this for the following task: Screen mixing depth by supplied useful wind work against the rho·N²·h³/12 energy of uniform linear stratification; wind-work velocity/efficiency require calibration, not universal turbulent mixing. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Wind Stress Mixing Depth Estimate and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter windStressPa, windWorkVelocityMPerSecond, durationSeconds, mixingEfficiency, waterDensityKgPerM3, initialBuoyancyFrequencySquaredPerSecondSquared, maximumWaterDepthM according to the field table, then run the tool.
Read availableMixingEnergyJPerM2, unboundedMixingDepthM, depthLimitedMixingDepthM, bottomLimited. 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
windStressPa	Wind stress pa	number	Required
windWorkVelocityMPerSecond	Wind work velocity m per second	number	Required
durationSeconds	Duration seconds	number	Required
mixingEfficiency	Mixing efficiency	number	Required
waterDensityKgPerM3	Water density kg per m3	number	Required
initialBuoyancyFrequencySquaredPerSecondSquared	Initial buoyancy frequency squared per second squared	number	Required
maximumWaterDepthM	Maximum water depth m	number	Required

Supply nonnegative stress, work velocity and duration; efficiency in [0,1]; and positive density, initial N² and maximum depth. Calculate available work, an unbounded depth and its bottom-limited value.

useful energy=stress×work velocity×duration×efficiency; h=cbrt(12×energy/(density×N²))

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

Output field	Meaning	Value type
availableMixingEnergyJPerM2	Available mixing energy j per m2	number
unboundedMixingDepthM	Unbounded mixing depth m	number
depthLimitedMixingDepthM	Depth limited mixing depth m	number
bottomLimited	Bottom limited	boolean

json

{
  "input": {
    "windStressPa": 1,
    "windWorkVelocityMPerSecond": 1,
    "durationSeconds": 1,
    "mixingEfficiency": 1,
    "waterDensityKgPerM3": 1000,
    "initialBuoyancyFrequencySquaredPerSecondSquared": 0.012,
    "maximumWaterDepthM": 2
  },
  "output": {
    "availableMixingEnergyJPerM2": 1,
    "unboundedMixingDepthM": 1,
    "depthLimitedMixingDepthM": 1,
    "bottomLimited": false
  }
}

Limitations and assumptions

Wind-work velocity and mixing efficiency require calibration. bottomLimited is true only if the unbounded depth strictly exceeds the bottom; this uniform-stratification screen does not simulate turbulent mixing.

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 Wedderburn Number when you need its operation: Evaluate W=g′h²/(u*²L) from caller two-layer density contrast, upper thickness, friction velocity and fetch; no universal upwelling or turnover criterion. Choose Density Gradient Stratification Strength for the complementary operation: Compute signed N² from observed density gradients with depth positive down; negative values remain instability indicators rather than an invented real Brunt–Väisälä frequency.

Background reference: Lake Physics Tools: rLakeAnalyzer reference manual.

References

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

Similar or alternative tools

Wedderburn Number
Evaluate W=g′h²/(u*²L) from caller two-layer density contrast, upper thickness, friction velocity and fetch; no universal upwelling or turnover criterion.
Density Gradient Stratification Strength
Compute signed N² from observed density gradients with depth positive down; negative values remain instability indicators rather than an invented real Brunt–Väisälä frequency.