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.
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Wave energy
An ocean wave carries energy — the same energy that lifts ships, sculpts beaches, wrecks structures and that engineers want to harvest for electricity. The energy density (per unit of surface area) of a wave is E = (1/8)·ρ·g·H², where ρ is the water density, g the acceleration of gravity and H the wave height. That energy is the sum of two equal shares: the kinetic part (from the orbital motion of the water particles) and the potential part (from the water displaced above and below the mean level). The key feature of the formula is its dependence on the square of the height: doubling the wave height quadruples its energy. That is why a storm that doubles wave height does far more than twice the damage, and why coastlines with big swell hold disproportionately greater energy potential. Wave energy ultimately comes from the wind (which transfers it to the sea), which in turn comes from the sun (which heats the atmosphere unevenly) — it is a concentrated form of solar energy. Quantifying wave energy is the basis for estimating the generation potential of wave power, for sizing coastal structures (breakwaters, jetties) that must survive the impact, and for understanding beach erosion and sediment transport. Enter the water density and the wave height.
Related Tools
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.
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.
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 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.
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.
Critical Depth in Rectangular Channel
Calculate the critical depth of a rectangular channel, y_c = (q² ÷ g)^(1/3), from the unit discharge q (flow per unit width, m³/s/m) and gravity g. Critical depth is the depth at which specific energy is minimum, marking the boundary between the two open-flow regimes: above it the flow is subcritical (slow, deep, Fr < 1, downstream-controlled); below, supercritical (fast, shallow, Fr > 1, upstream-controlled); exactly at it, Fr = 1. Critical depth is central to channel and structure hydraulics: it defines the control section at spillways, weirs and flumes (Parshall), where flow passes through the critical regime stably and the stage-discharge relation is unique — allowing flow measurement from head. It also determines whether a hydraulic jump can form and guides water-surface profiles. Enter the channel's unit discharge.
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.