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Les ondes cnoïdales sont des ondes de grav … Les ondes cnoïdales sont des ondes de gravité rencontrées sur la surface de la mer, des vagues. Elles sont solutions de l'équation de Korteweg-de Vries où interviennent les fonctions elliptiques de Jacobi notées cn, d'où le nom d'ondes « cn-oïdales ». Ce type d'onde apparaît également dans les problèmes de propagation d'onde acoustique ionique. de propagation d'onde acoustique ionique.
, In fluid dynamics, a cnoidal wave is a non … 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. The cnoidal wave solutions were derived by Korteweg and de Vries, in their 1895 paper in which they also propose their dispersive long-wave equation, now known as the Korteweg–de Vries equation. In the limit of infinite wavelength, the cnoidal wave becomes a solitary wave. The Benjamin–Bona–Mahony equation has improved short-wavelength behaviour, as compared to the Korteweg–de Vries equation, and is another uni-directional wave equation with cnoidal wave solutions. Further, since the Korteweg–de Vries equation is an approximation to the Boussinesq equations for the case of one-way wave propagation, cnoidal waves are approximate solutions to the Boussinesq equations. Cnoidal wave solutions can appear in other applications than surface gravity waves as well, for instance to describe ion acoustic waves in plasma physics.ribe ion acoustic waves in plasma physics.
, In dinamica dei fluidi, un'onda cnoidale è … In dinamica dei fluidi, un'onda cnoidale è una soluzione non lineare, esatta e periodica dell'equazione di Korteweg-de Vries. Queste soluzioni sono in termini delle funzioni ellittiche di Jacobi "cn", ed è per questo che vengono designate onde cnoidali. Vengono usate per descrivere le onde di gravità superficiali di lunghezza d'onda relativamente elevata in relazione alla profondità dell'acqua. Le soluzioni d'onda cnoidale furono derivate da e Gustav de Vries nel loro lavoro del 1895 in cui proposero anche la loro equazione di onda lunga dispersiva, ora nota come equazione di Korteweg–de Vries. Nel caso limite di lunghezza d'onda infinita, l'onda cnoidale diventa un'onda di traslazione solitaria, o solitone. L'equazione di Benjamin–Bona–Mahony ha migliorato il comportamento alle lunghezze d'onda corte in confronto all'equazione di Korteweg–de Vries, e rappresenta un altro caso di equazione d'onda unidirezionale con soluzioni di onda cnoidale. Inoltre, poiché l'equazione di Korteweg-de Vries è un'approssimazione dell'equazione di Boussinesq per la propagazione d'onda monodirezionale, le onde cnoidali sono soluzioni approssimate delle equazioni di Boussinesq. Soluzioni di onda cnoidale possono apparire anche in altre applicazioni oltre alle onde superficiali di gravità, come ad esempio per descrivere le onde acustiche ioniche nella fisica del plasma.acustiche ioniche nella fisica del plasma.
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In dinamica dei fluidi, un'onda cnoidale è … In dinamica dei fluidi, un'onda cnoidale è una soluzione non lineare, esatta e periodica dell'equazione di Korteweg-de Vries. Queste soluzioni sono in termini delle funzioni ellittiche di Jacobi "cn", ed è per questo che vengono designate onde cnoidali. Vengono usate per descrivere le onde di gravità superficiali di lunghezza d'onda relativamente elevata in relazione alla profondità dell'acqua. Soluzioni di onda cnoidale possono apparire anche in altre applicazioni oltre alle onde superficiali di gravità, come ad esempio per descrivere le onde acustiche ioniche nella fisica del plasma.acustiche ioniche nella fisica del plasma.
, In fluid dynamics, a cnoidal wave is a non … 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. Cnoidal wave solutions can appear in other applications than surface gravity waves as well, for instance to describe ion acoustic waves in plasma physics.ribe ion acoustic waves in plasma physics.
, Les ondes cnoïdales sont des ondes de grav … Les ondes cnoïdales sont des ondes de gravité rencontrées sur la surface de la mer, des vagues. Elles sont solutions de l'équation de Korteweg-de Vries où interviennent les fonctions elliptiques de Jacobi notées cn, d'où le nom d'ondes « cn-oïdales ». Ce type d'onde apparaît également dans les problèmes de propagation d'onde acoustique ionique. de propagation d'onde acoustique ionique.
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, Onde cnoïdale
, Cnoidal wave
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