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.

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), who introduced it to describe the occurrence of wave breaking on sloping beaches.

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.

Definition

The Iribarren number – often denoted as Ir or ξ – is defined as:

$\xi = \frac{\tan \alpha}{\sqrt{H/L_0}},$   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.

Further information: breaking wave

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:

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