Wave Steepness
Calculate the steepness of a wave, s = H ÷ L, dividing the wave height H by the wavelength L. The dimensionless result is the relative steepness of the wave — the taller it is for its length, the steeper. Steepness has a physical limit: deep-water waves break when s exceeds about 1/7 (0.143), as the crest becomes unstable (120° angle). Young storm waves are steep; swell that travels long distances is gentle (low steepness). Steepness governs wave stability, breaking and vessel comfort. Enter the wave height and wavelength.
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Wave steepness
The steepness of a wave is the ratio between its height and its length: s = H ÷ L. It measures how steep the wave is — a tall, short wave is steep; a low, long one is gentle. Simple as it looks, steepness governs fundamental properties. There is a physical stability limit: in deep water a wave cannot be steeper than roughly 1/7 (0.143) — the Michell criterion. Past that point the crest turns unstable (the crest angle reaches 120°), the water at the top moves faster than the wave itself, and the wave breaks (whitecapping, the 'white horses' seen in rough seas). This limit explains why, even in violent storms, open-ocean waves never exceed a certain steepness — the surplus energy is dissipated in breaking. Steepness also tells the sea states apart: young wind waves (freshly generated, still under the action of the wind) are steep, chaotic and uncomfortable for navigation; swell (mature waves that have traveled far from the storm that generated them) is gentle (low steepness), with long, regular crests and a longer period. Vessels respond very differently to the two: steep waves cause much more pitching and discomfort. Steepness also enters the calculation of forces on structures and the breaking process at the shoreline (together with the beach slope, in the Iribarren number). Enter the wave height and the wavelength.
Related Tools
Ocean Wavelength
Calculate the wavelength of an ocean wave in deep water, L = g·T² ÷ (2π), from the wave period T (s) and gravity g (9.81 m/s²). The result, in meters, is the distance between two successive crests — in deep water, it depends only on the period. Long-period waves (swell from distant storms) have much larger wavelengths than local wind waves. The wavelength sets the depth at which the wave 'feels' the bottom (about L/2), starts to refract and shoal until it breaks. It is a fundamental parameter of linear wave theory and coastal engineering. Enter the wave period.
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.
Wave Energy
Calculate the energy density of an ocean wave, E = (1 ÷ 8)·ρ·g·H², from the water density ρ (kg/m³, ~1025 for seawater), gravity g and the wave height H (m). The result, in J/m² (energy per surface area), is the sum of the wave's kinetic and potential energy — proportional to the square of the height, so large waves carry far more energy. It is the basis for calculating wave energy generation potential and the impact on coastal structures and beach erosion. Enter the water density and the wave height.
Half-Wave Dipole Length
Calculate the physical length of a half-wave dipole, L = (150 ÷ f)·VF, from the frequency f (MHz) and the velocity factor VF (typically ~0.95 for wires, correcting the end effect). The result, in metres, is the total length of the dipole antenna resonant at the desired frequency — each arm is half this value. The half-wave dipole is the most used reference antenna, with 2.15 dBi gain. The velocity factor makes the antenna slightly shorter than a half wavelength in vacuum. Enter the frequency and the velocity factor.
Wave Power
Estimate the power flux of an ocean wave per meter of wave front, P ≈ 0.5 × H² × T, from the wave height H (m) and the period T (s), in deep water (seawater). The result, in kW/m, is the power available per meter of wave front width — a key indicator of wave energy potential for converters (WECs). Coasts exposed to ocean swells (European Atlantic, Pacific) reach 30-70 kW/m, a significant renewable resource. The power grows with the square of the height and linearly with the period. Enter the wave height and period.
Wave Group Velocity
Calculate the group velocity of an ocean wave in deep water, c_g = g·T ÷ (4π), from the period T (s). The result, in m/s, is the speed at which the wave energy (and the 'envelope' of a wave group) propagates — exactly half the celerity (phase velocity) in deep water. This difference explains a curious phenomenon: within a wave group, individual crests appear at the rear, advance through the group (faster than it) and disappear at the front. The group velocity is what matters for energy transport and predicting swell arrival at the coast. Enter the wave period.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.