Shallow-Water Wave Speed & Breaking Depth mechanism

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

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