The effect of randomness on the stability of capillary gravity waves in the presence of air flowing over water

• Autorzy: Majumder D. P. , Dhar A. K.

Identyfikatory

DOI

10.1515/ijame-2015-0054

• Języki publikacji: EN

Abstrakty

EN

A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation.

Słowa kluczowe

EN

capillary gravity waves; randomness; evolution equation; instability

PL

fala grawitacyjna; przypadkowość; niestabilność

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2015
• Tom: Vol. 20, no. 4
• Strony: 835--855
• Opis fizyczny: Bibliogr. 16 poz., tab., wykr.

Twórcy

autor

Majumder D. P.

• Department of Mathematics Bengal Engineering and Science University, Shibpur P.O. Botanic Garden, Shibpur Howrah - 711103, West Bengal, INDIA

autor

Dhar A. K.

• Department of Mathematics Bengal Engineering and Science University, Shibpur P.O. Botanic Garden, Shibpur Howrah - 711103, West Bengal, INDIA

Bibliografia

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