Iribarren number

Spilling breaker.

Plunging breaker.

Collapsing breaker.

Surging breaker.

Breaking wave types: free surface and bubble plumes, as redrawn from photographs taken during a wave flume experiment.^[1]

In fluid dynamics, the Iribarren number or Iribarren parameter – also known as the surf similarity parameter and breaker parameter – is a dimensionless parameter used to model several effects of (breaking) surface gravity waves on beaches and coastal structures. The parameter is named after the Spanish engineer Ramón Iribarren Cavanillas (1900–1967),^[2] who introduced it to describe the occurrence of wave breaking on sloping beaches.^[3]

For instance, the Iribarren number is used to describe breaking wave types on beaches; or wave run-up on – and reflection by – beaches, breakwaters and dikes.^[4][5][6]

Definition

The Iribarren number – often denoted as Ir or ξ – is defined as:^[5]

$\xi = \frac{\tan \alpha}{\sqrt{H/L_0}},$   with   $L_0 = \frac{g}{2\pi}\, T^2,$

where ξ is the Iribarren number, α is the bed slope, H is the wave height, L₀ is the deep-water wavelength, T is the period and g is the gravitational acceleration. Depending on the application, different definitions of H and T are used, for example: for periodic waves the wave height H₀ at deep water or the breaking wave height H_b at the edge of the surf zone. Or, for random waves, the significant wave height H_s at a certain location.

Breaker types

Breaker types.

The type of breaking wave – spilling, plunging, collapsing or surging – depends on the Iribarren number. According to Battjes (1974), for periodic waves propagating on a plane beach, two possible choices for the Iribarren number are:

$\xi_0 = \frac{\tan \alpha}{\sqrt{H_0 / L_0}}$   or   $\xi_b = \frac{\tan \alpha}{\sqrt{H_b / L_0}},$

where H₀ is the offshore wave height in deep water, and H_b is the value of the wave height at the break point (where the waves start to break). Then the breaker types dependence on the Iribarren number (either ξ₀ or ξ_b) is approximately:^[4]

breaker type	ξ0–range	ξb–range
surging or collapsing	ξ0 > 3.3	ξb > 2.0
plunging	0.5 < ξ0 < 3.3	0.4 < ξb < 2.0
spilling	ξ0 < 0.5	ξb < 0.4

References

Footnotes

1. Kjeldsen, S.P. (1968), Bølge brydning, fysisk beskrivelse [Wave breaking, physical description] (in Danish), Technical University of Denmark, M.Sc. thesis, 110 pp.
2. Real Academia de Ciencias Exactas, Físicas y Naturales (Spanish Royal Academy of Sciences) (2003), Relación de Académicos desde el Año 1847 hasta el 2003 (PDF) (in Spanish), pp. 24–25
3. Iribarren & Norales (1949)
4. Battjes (1974)
5. Holthuijsen (2007)
6. Bruun (1984)

Other

• Battjes, J.A. (1974), "Surf similarity", Proceedings 14th International Conference on Coastal Engineering, pp. 466–480, doi:10.9753/icce.v14
• Bruun, P., ed. (1984), Design and construction of mounds for breakwaters and coastal protection, Developments in geotechnical engineering 37, Elsevier, pp. xi & 39, ISBN 0-444-42391-5
• Goda, Yoshimi (2010), Random seas and design of maritime structures (3rd ed.), World Scientific, p. 213, ISBN 9814282405
• Holthuijsen, L.H. (2007), Waves in oceanic and coastal waters, Cambridge University Press, p. 242, ISBN 1139462520
• Iribarren, C.R.; Norales, C. (1949), "Protection des ports", Proceedings XVIIth International Navigation Congress, Section II, Communication 4, Lisbon, pp. 31–80