Iribarren Number
Calculate the Iribarren number (surf similarity parameter), ξ = tan(β) ÷ √(H ÷ L), from the beach slope tan(β), the wave height H and the wavelength L. The dimensionless result classifies the wave breaking type and runup: ξ < 0.5 indicates spilling breakers (flat beaches); 0.5 < ξ < 3.3, plunging (the wave 'barrels'); ξ > 3.3, surging/collapsing (steep beaches). It is widely used in coastal engineering to predict runup, structure overtopping and riprap stability. Enter the beach slope, wave height and wavelength.
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Iribarren number
The Iribarren number (ξ, also called the surf similarity parameter) ranks among the most useful dimensionless numbers in coastal engineering, since it combines, in a single value, the beach slope and the wave steepness to predict how a wave will break and how far it will climb the beach: ξ = tan(β) ÷ √(H ÷ L), where tan(β) is the bottom or beach slope, H the wave height and L the wavelength. The value of ξ classifies the breaker type, which any beachgoer recognises intuitively. ξ < 0.5: spilling breaker - typical of flat beaches and steep waves, the wave breaks gradually from the crest downward, with foam sliding down the face (the gentle, foamy waves of shallow beaches). 0.5 < ξ < 3.3: plunging breaker - the classic wave that forms a barrel, curling into a cylinder of water that crashes ahead of itself, spectacular and dangerous, beloved by surfers (beaches of moderate slope). ξ > 3.3: surging or collapsing breaker - on very steep beaches the wave hardly breaks at all, climbing the face as a wall of water and reflecting. Beyond classifying the breaker, the Iribarren number predicts run-up (how high the water climbs the beach or structure once it has broken), overtopping (water passing over a breakwater or dike, critical for setting the crest level), wave reflection and rock armour stability (the stone weight a breakwater needs to resist the waves). It is, therefore, a central tool in coastal defence design and flood forecasting. Enter the beach slope, the wave height and the wavelength.
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