Source: https://guthlabs.ai/docs/instruments/shallow-water-wave-speed-breaking-depth/mechanism/

instrument mechanism / verified-clean

# Shallow-Water Wave Speed & Breaking Depth mechanism

The inspectable method record for Shallow-Water Wave Speed & Breaking Depth, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The formulas are acceptable simplified approximations under explicit SI-unit and physical-domain constraints, but the specification needs review to define units, validate nonnegative inputs, state the shallow-water applicability condition, and clarify whether H is local wave height or incoming/offshore height. The honest simplified-linear-theory label is appropriate but should also mention the empirical 0.78 breaker-index limitation.

- c=√(gd) is the standard non-dispersive shallow-water wave-speed formula, but it is valid only when the water is sufficiently shallow relative to wavelength and assumes no significant current or other corrections.

- H/d≈0.78 is an empirical breaker-index rule of thumb, not a universal breaking law. The estimated breaking depth requires d_break≈H/0.78, but the spec does not explicitly state this rearrangement.

- The meaning of incoming wave height is ambiguous: using offshore incident height directly as H ignores shoaling, refraction, dissipation, and local wave-height transformation before breaking.

## Units and conventions

- Water depth d and wave height H are assumed to be in metres.

- Wave speed is reported in metres per second and estimated breaking depth in metres.

- Gravity is assumed to be g=9.81 m/s².

- The breaking criterion uses wave height H and local depth d in the same length units.

- The centimetre test case must be converted to metres before applying either formula.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "water_depth_m": 4,
    "incoming_wave_height_m": 1.2
  },
  "expected_outputs": {
    "wave_speed_m_per_s": 6.264184,
    "estimated_breaking_depth_m": 1.538462
  },
  "working": "c=√(gd)=√(9.81×4)=√39.24=6.264184 m/s. Breaking criterion H/d=0.78 gives d_break=H/0.78=1.2/0.78=1.538462 m."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The specification does not define validation for zero depth, so the division H/d can become undefined. It also leaves wave-height convention and unit handling unspecified, allowing materially different breaking-depth results.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/shallow-water-wave-speed-breaking-depth/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/shallow-water-wave-speed-breaking-depth/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/shallow-water-wave-speed-breaking-depth/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`