Iribarren number

Iribarren's work was further developed by Jurjen Battjes in 1974, who named the parameter after Iribarren.^[4][7][8]

The importance of this parameter for so many aspects of waves breaking on slopes appears to justify that it be given a special name. In the author's opinion it is appropriate to call it the "Iribarren number" (denoted by "Ir"), in honor of the man who introduced it and who has made many other valuable contributions to our knowledge of water waves.

— Jurjen A. Battjes, "Surf Similarity", Proceedings of the 14th International Conference on Coastal Engineering (1974)^[4]

Definition

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

${\displaystyle \xi ={\frac {\tan \alpha }{\sqrt {H/L_{0}}}},}$   with   ${\displaystyle L_{0}={\frac {g}{2\pi }}\,T^{2},}$

where ξ is the Iribarren number, ${\displaystyle {\displaystyle \alpha }}$ is the angle of the seaward slope of a structure, 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

The type of breaking wave – spilling, plunging, collapsing or surging – depends on the Iribarren number. According to

${\displaystyle \xi _{0}={\frac {\tan \alpha }{\sqrt {H_{0}/L_{0}}}}}$   or   ${\displaystyle \xi _{b}={\frac {\tan \alpha }{\sqrt {H_{b}/L_{0}}}},}$

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]

References

Footnotes