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.

Version: v1 · 2026-09-28 · History
Domain-specific #: 10142
Domain group: Applied Sciences & Engineering
Origin domain: Engineering & Design (beyond software)
Subdomain: Coastal Engineering → Engineering & Design (beyond software)

Core Idea¶

The Iribarren number condenses the interaction between an inclined boundary and incident surface-gravity waves. It divides the tangent of the beach or structure slope by the square root of wave steepness H/L0, so steeper slopes and less-steep waves produce larger values.

The number is only reproducible when its wave convention is stated. Periodic-wave studies may use deep-water height H0 or breaking height Hb; random seas may use a significant height Hs at a declared location. L0 is the deep-water wavelength, often calculated from period and gravity.

Engineers use xi to organize spilling, plunging, collapsing, and surging breakers and to correlate run-up or reflection. Those regimes are empirical uses of the ratio, not part of dimensional cancellation itself; thresholds depend on the chosen definition and setting.

Structural Signature¶

Sig role-phrases:

slope angle. Represents the seaward inclination through its tangent. Constitutive geometric input. If altered: Changing slope changes the similarity regime even for the same wave.
wave height convention. Supplies H at offshore, breaking, or statistical conditions. Constitutive declared input. If altered: Mixing H0, Hb, and Hs makes values incomparable.
reference wavelength. Supplies L0, commonly derived from period and gravity. Constitutive scale input. If altered: A local wavelength substitution changes the defined parameter.
dimensionless ratio. Combines slope and wave steepness into xi. Identity-bearing calculation. If altered: Keeping units or omitting the square root yields another quantity.
response regime. Links ranges of xi to breaker, run-up, or reflection behavior. Diagnostic interpretation. If altered: A regime label is application-dependent rather than an exact universal law.

What It Is Not¶

Not wave steepness alone. The slope tangent is essential.
Not a dimensional measurement. All units cancel in the defined ratio.
Not convention-free. H0, Hb, and Hs create different numerical variants.
Not an exact breaker law. Regime boundaries are empirical and approximate.

Scope of Application¶

Use the number in coastal and hydraulic analysis only with the incident-wave definition, slope geometry, and response correlation declared.

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.

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.

Abstract Reasoning¶

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.
Form the dimensionless ratio before consulting any regime chart.
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.

Examples¶

Canonical¶

For a periodic wave on a plane beach, an analyst uses tan(alpha), offshore H0, and L0 from the period to compute xi0 and then locates the approximate spilling-to-plunging regime on the matching chart.

Mapped back: slope angle → plane-beach alpha; wave height convention → offshore H0; reference wavelength → deep-water L0; dimensionless ratio → xi0; response regime → breaker-type chart.

Applied / In Practice¶

A dike run-up study uses significant wave height at its specified location and the corresponding period convention; it reports that definition with xi rather than borrowing an Hb-based breaker threshold.

Mapped back: slope angle → dike face; wave height convention → declared Hs; reference wavelength → period-derived L0; dimensionless ratio → run-up variant; response regime → dike run-up correlation.

Structural Tensions¶

T1: similarity compression vs. definition metadata. One number aids comparison but several legitimate H and T conventions exist. Diagnostic: Are the variants exactly aligned?

T2: regime map vs. continuous behavior. Named breaker types simplify transitions that are not perfectly sharp. Diagnostic: How sensitive is classification near a boundary?

T3: laboratory correlation vs. field geometry. Controlled slopes support calibration while real bathymetry is irregular. Diagnostic: Does the empirical domain cover the site?

Structural–Framed Character¶

The Iribarren number is structural-leaning: dimensional similarity and the formula are formal, while wave statistics and response thresholds are engineering conventions. It is non-evaluative and portable within matched coastal settings. Its character: a slope-to-wave-steepness similarity coordinate with convention-bound interpretation.

Structural Core vs. Domain Accent¶

Skeletal core. Compare a boundary's geometric rate with the square root of an incident disturbance's steepness.

Domain-bound accent. Surface-gravity waves, deep-water wavelength, beach slope, breaking, run-up, and reflection specify the mechanism.

Why not prime. Dimensionless similarity is portable, but this exact group is a coastal-hydrodynamic index.

This entry is a kind of Dimensionless Quantity.

Ratio. The number is a dimensionless quotient of matched geometric inputs.
Similarity analysis. Regime behavior is organized by a nondimensional group.
No strict parent is asserted from the frozen catalog state.

Relationships to Other Abstractions¶

Current abstraction Iribarren Number Domain-specific

Parents (1) — more general patterns this builds on

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 (61^st 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

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With¶

Wave steepness. Tell: Is slope included in the ratio?
Breaker index. Tell: Is a height-to-depth breaking criterion intended?
Surf-zone width. Tell: Is a geometric distance rather than similarity parameter measured?
Run-up height. Tell: Is the response being predicted or the dimensionless predictor itself?

References¶

Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Iribarren_number (revision 1351394757).
Preserved source candidate: http://www.rac.es/ficheros/doc/00186.pdf
Preserved source candidate: http://resolver.tudelft.nl/uuid:df203dde-6cca-4375-85d2-8b2dbce613cb

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.