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Cnoidal wave

In fluid dynamics, a cnoidal wave is a nonlinear and exact periodic wave solution of the Korteweg–de Vries equation. These solutions are in terms of the Jacobi elliptic function cn, which is why they are coined cnoidal waves. They are used to describe surface gravity waves of fairly long wavelength, as compared to the water depth.

Background, Periodic wave solutions & Direct derivation from the full inviscid-flow equations

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Overview

Background

Periodic wave solutions

Example

Solitary-wave limit

Limit of infinitesimal wave height

Direct derivation from the full inviscid-flow equations

Potential energy

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Cnoidal wave

Nodes111
Edges110
Triples75
Avg. degree1.98
Density0.018018
Components1

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Cnoidal wave

Top relations

related to Further reading · 38
Cnoidal wave → Benjamin, Bibcode, Cambridge University Press, Drazin, Encyclopedia, Fluid Mechanics, Flügge, ISBN, IX, Jager, January, Johnson, Journal, Korteweg, Laitone, Lighthill, London, Mathematical, National Bureau, On
related to Direct derivation from the full inviscid-flow equations · 11
Cnoidal wave → Benjamin, Bernoulli, Bernoulli's, Cnoidal, Following Benjamin, Further, In, Lighthill, The, They, While
related to Cnoidal waves · 10
Cnoidal wave → Boussinesq, Cnoidal, KdV, Korteweg, PhD, Rayleigh, Russell, Solitary, The, Vries
related to Phase speed · 6
Cnoidal wave → BBM, However, In, KdV, The, This
related to Example · 5
Cnoidal wave → In, KdV, Korteweg, The, Vries
related to Limit of infinitesimal wave height · 3
Cnoidal wave → Airy, First, For
is a · 1
Cnoidal wave → nonlinear and exact periodic wave solution of the Korteweg
related to Surface tension · 1
Cnoidal wave → In

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Important terminology

wave equation cnoidal waves kdv wavelength phase elliptic solutions surface long water speed height depth parameter de nonlinear also equations

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cnoidal waveis anonlinear and exact periodic wave solution of the Korteweg0.90text
Cnoidal waverelated to Cnoidal wavesThe0.60section
Cnoidal waverelated to Cnoidal wavesKdV0.60section
Cnoidal waverelated to Cnoidal wavesKorteweg0.60section
Cnoidal waverelated to Cnoidal wavesVries0.60section
Cnoidal waverelated to Cnoidal wavesPhD0.60section
Cnoidal waverelated to Cnoidal wavesSolitary0.60section
Cnoidal waverelated to Cnoidal wavesBoussinesq0.60section
Cnoidal waverelated to Cnoidal wavesRayleigh0.60section
Cnoidal waverelated to Cnoidal wavesRussell0.60section
Cnoidal waverelated to Cnoidal wavesCnoidal0.60section
Cnoidal waverelated to Direct derivation from the full inviscid-flow equationsCnoidal0.60section

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