Shallow Water Wave Celerity
Calculate the celerity of a wave in shallow water, c = √(g·h), from the water depth h (m) and gravity g. The result, in m/s, is the propagation speed when the depth is much smaller than the wavelength — a situation in which the wave 'feels' the bottom and its speed depends only on depth, no longer on the period. This is why waves refract as they approach the coast (the deeper part travels faster) and why tsunamis travel at hundreds of km/h in the deep ocean and slow down (piling up energy) as they reach the coast. Enter the water depth.
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Celeridade em águas rasas
Quando uma onda chega a águas rasas (profundidade muito menor que o comprimento de onda), algo muda radicalmente: a onda passa a 'sentir' o fundo, e sua velocidade deixa de depender do período e passa a depender só da profundidade: c = √(g·h). Quanto mais rasa a água, mais lenta a onda. Essa simples fórmula explica fenômenos dramáticos. A refração: como a parte da onda em água mais funda viaja mais rápido que a parte em água mais rasa, a frente de onda curva, tendendo a se alinhar paralela à costa — por isso as ondas quase sempre chegam quase de frente para a praia, mesmo vindas de ângulos oblíquos. Os tsunamis: no oceano profundo (h ~4000 m), um tsunami viaja a c = √(9,81 × 4000) ≈ 200 m/s (700 km/h!), tão rápido quanto um jato, mas com altura de poucas dezenas de centímetros — imperceptível para navios; ao chegar à costa rasa, desacelera drasticamente, e como a energia se conserva, a onda empilha em altura, podendo atingir dezenas de metros. A focalização de energia em pontas e baías, e a quebra das ondas. A fórmula c = √(gh) é a base da hidrodinâmica costeira e da modelagem de inundação por tsunami e maré meteorológica. Informe a profundidade da água.
Related Tools
Deep Water Wave Celerity
Calculate the celerity (phase velocity) of an ocean wave in deep water, c = g·T ÷ (2π), from the period T (s) and gravity g. The result, in m/s, is the speed at which the wave crest propagates. In deep water, longer-period waves travel faster — a phenomenon called dispersion, which makes long-period swell reach the coast before the short waves generated by the same storm. The celerity is half the group velocity (at which energy travels) in deep water. It is a base concept of wave hydrodynamics. Enter the wave period.
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 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.