Wave Refraction Snells Coefficient

Apply Snell refraction on parallel depth contours and conservation of ray width, retaining signed angle; critical/nonpropagating rays error rather than clamp.

Description

Waves refract when phase speed changes across parallel depth contours.

Waves refract when phase speed changes across parallel depth contours. Ray-width conservation supplies a separate height coefficient.

Apply Snell refraction on parallel depth contours and conservation of ray width, retaining signed angle; critical/nonpropagating rays error rather than clamp.

When to use Wave Refraction Snells Coefficient

Use this tool to apply Snell refraction on parallel depth contours and conservation of ray width, retaining signed angle; critical/nonpropagating rays error rather than clamp.

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 Wave Refraction Snells Coefficient 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 referenceIncidentAngleDegrees, referencePhaseSpeedMPerSecond, localPhaseSpeedMPerSecond using the field table and calculation rules, then run the tool.
Read localRefractionAngleDegrees, refractionHeightCoefficient. 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
referenceIncidentAngleDegrees	Reference incident angle degrees	number	Required
referencePhaseSpeedMPerSecond	Reference phase speed m per second	number	Required
localPhaseSpeedMPerSecond	Local phase speed m per second	number	Required

Use positive phase speeds and reference angle strictly in (−90,90). Reject local sine magnitude at or above one. Return signed local angle and sqrt(cos(reference)/cos(local)).^[1]

sin(local angle) = sin(reference angle) × local speed/reference speed

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

Output field	Meaning	Value type
localRefractionAngleDegrees	Local refraction angle degrees	number
refractionHeightCoefficient	Refraction height coefficient	number

json

{
  "input": {
    "referenceIncidentAngleDegrees": 30,
    "referencePhaseSpeedMPerSecond": 10,
    "localPhaseSpeedMPerSecond": 5
  },
  "output": {
    "localRefractionAngleDegrees": 14.477512185929921,
    "refractionHeightCoefficient": 0.9457416090031758
  }
}

Limitations and assumptions

Critical rays are rejected; arbitrary contour geometry is not modeled.

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 Wave Dispersion Relation Root Solver: Solve finite-depth linear dispersion omega²=g k tanh(kh) by bounded dimensionless bisection, returning phase/group speeds without deep/shallow aliases. For a complementary task, use Shoaling Coefficient H H0: Transform wave height by supplied group speeds and retained energy flux on constant-width rays; no refraction or breaking correction is silently included.

References

Wave Refraction Snells Coefficient — tool.io

Similar or alternative tools

Wave Dispersion Relation Root Solver
Solve finite-depth linear dispersion omega²=g k tanh(kh) by bounded dimensionless bisection, returning phase/group speeds without deep/shallow aliases.
Shoaling Coefficient H H0
Transform wave height by supplied group speeds and retained energy flux on constant-width rays; no refraction or breaking correction is silently included.