Iribarren Number¶
A dimensionless surf-similarity parameter that compares a beach or structure slope with incident-wave steepness to classify breaking regimes and organize run-up, reflection, and coastal-response predictions.
Core Idea¶
The Iribarren number is tan(alpha)/sqrt(H/L0), a dimensionless comparison of slope with incident-wave steepness. It organizes breaker type, run-up, and reflection only when the wave-height, period, and response conventions match the chosen correlation. The number is only reproducible when its wave convention is stated. The number is only reproducible when its wave convention is stated.
Scope of Application¶
Use the number in coastal and hydraulic analysis only with the incident-wave definition, slope geometry, and response correlation declared. Use it for beaches, breakwaters, and dikes with slope, H convention, L0 convention, and empirical regime stated.
- Breaker classification. Organizes common breaking modes on plane slopes.
- Wave run-up. Indexes uprush correlations on beaches and defenses.
- Reflection. Relates sloping-boundary geometry to reflected-wave response.
- Breakwaters and dikes. Supports structure-specific design correlations.
- Laboratory comparison. Normalizes experiments with matched conventions.
Clarity¶
The parameter is a ratio of two geometric steepness scales, not a direct measurement of breaking. Reporting xi without alpha, H convention, period or wavelength convention, and target correlation hides the choices that make the number meaningful. The closest near miss sets the boundary: Wave steepness H/L0 is the closest near miss: it supplies the denominator's physical comparison but omits the structure or beach slope that defines surf similarity.
Manages Complexity¶
Many wave and slope variables become one similarity coordinate, enabling regime maps and empirical comparison. The compression is useful precisely because metadata remain attached; without them, unlike sea states and structures can appear falsely equivalent. The central similarity compression–definition metadata tradeoff is this: One number aids comparison but several legitimate H and T conventions exist. A second regime map–continuous behavior tension matters because Named breaker types simplify transitions that are not perfectly sharp. The laboratory correlation–field geometry tension adds that Controlled slopes support calibration while real bathymetry is irregular.
Abstract Reasoning¶
Use three linked moves: specify the beach or structure slope at the relevant face; choose offshore, breaking, or significant wave height for the intended correlation; compute the corresponding deep-water wavelength from a declared period convention. As a collapse test, the case exits when height or wavelength conventions are unstated, inconsistent units remain, or empirical thresholds are transported to another response without validation. A fourth check is to form the dimensionless ratio before consulting any regime chart. A final check is to apply only thresholds calibrated for the same definition and response.
Knowledge Transfer¶
The similarity-design logic transfers to other dimensionless engineering groups, but the Iribarren formula and breaker thresholds stay within surface-wave interaction with a slope. A numerical match does not transfer run-up behavior to a differently defined structure or wave statistic. No canonical parent prime is currently asserted; broader structural comparisons remain related-prime analogies until separately adjudicated in the DAG. The number is a dimensionless quotient of matched geometric inputs. Regime behavior is organized by a nondimensional group.
Relationships to Other Abstractions¶
Current abstraction Iribarren Number Domain-specific
Parents (1) — more general patterns this builds on
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Iribarren Number is a kind of Dimensionless Quantity Domain-specific
It is a dimensionless coastal-engineering similarity quantity.
Hierarchy path (1) — routes to 1 parentless root
- Iribarren Number → Dimensionless Quantity → Physical quantity → Measurement
Neighborhood in Abstraction Space¶
Iribarren Number sits in a sparse region of the domain-specific corpus (61st percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Domain-Specific Measurement Parameters (36 abstractions)
Nearest neighbors
- Turner angle — 0.87
- Wavenumber-frequency diagram — 0.85
- Tidal atlas — 0.85
- Atmospheric refraction — 0.85
- Rossby whistle — 0.84
Computed from structural-signature embeddings · 2026-10-08