Lake Number Inertial

Evaluate a Lake Number convention using Schmidt stability already in J/m² and water-side friction velocity; no extra gravity factor, wind-to-water conversion or universal mixing threshold.

Description

Lake Number compares stratification resistance with water-side wind forcing using basin geometry.

Lake Number compares stratification resistance with water-side wind forcing using basin geometry. Its value depends on the precise stability units and depth convention supplied.^[1]

The tool returns lakeNumber. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Lake Number Inertial

Use this for the following task: Evaluate a Lake Number convention using Schmidt stability already in J/m² and water-side friction velocity; no extra gravity factor, wind-to-water conversion or universal mixing threshold. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Lake Number Inertial and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter schmidtStabilityJPerM2, surfaceAreaM2, waterDensityKgPerM3, waterFrictionVelocityMPerSecond, thermoclineDepthM, volumeCentroidDepthM, maximumDepthM according to the field table, then run the tool.
Read lakeNumber. 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
schmidtStabilityJPerM2	Schmidt stability j per m2	number	Required
surfaceAreaM2	Surface area m2	number	Required
waterDensityKgPerM3	Water density kg per m3	number	Required
waterFrictionVelocityMPerSecond	Water friction velocity m per second	number	Required
thermoclineDepthM	Thermocline depth m	number	Required
volumeCentroidDepthM	Volume centroid depth m	number	Required
maximumDepthM	Maximum depth m	number	Required

Supply nonnegative Schmidt stability in J/m² and depths, positive area, density, friction velocity and maximum depth. Require thermocline and centroid strictly above the bottom.

Ln=S×(1−thermoclineDepth/maxDepth)/(density×frictionVelocity²×sqrt(surfaceArea)×(1−centroidDepth/maxDepth))

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

Output field	Meaning	Value type
lakeNumber	Lake number	number

json

{
  "input": {
    "schmidtStabilityJPerM2": 100,
    "surfaceAreaM2": 100,
    "waterDensityKgPerM3": 1000,
    "waterFrictionVelocityMPerSecond": 0.1,
    "thermoclineDepthM": 5,
    "volumeCentroidDepthM": 5,
    "maximumDepthM": 10
  },
  "output": {
    "lakeNumber": 0.9999999999999999
  }
}

Limitations and assumptions

No additional gravity multiplier is applied because the supplied stability already has energy units. The result has no universal mixing threshold and does not convert wind speed to water friction velocity.

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 Schmidt Stability Index when you need its operation: Compute signed Schmidt potential-energy stability from piecewise-constant layer areas/densities and depth-positive-down centers; negative values indicate an inverted profile, not positive mixing energy. Choose Wedderburn Number for the complementary 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.

Background reference: Lake Physics Tools: rLakeAnalyzer reference manual.

References

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

Similar or alternative tools

Schmidt Stability Index
Compute signed Schmidt potential-energy stability from piecewise-constant layer areas/densities and depth-positive-down centers; negative values indicate an inverted profile, not positive mixing energy.
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.