Parametric instabilities of the radial motions of non-linearly viscoelastic shells under pulsating pressures

The parametric excitation of transverse and Langmuir waves by an externally-driven electromagnetic field of frequency (ω0 > 2ωp) in a warm and collisional plasma is studied, using the fluid equations. By an application of the multiple- time-scale perturbation method, the threshold intensity and the growth rate above threshold are obtained. The results are compared with those of Goldman (1969) and Prasad (1968), both of whom worked with a kinetic model.The theory of parametric instabilities in plasmas has been the subject of numerous investigations in recent years. Broadly speaking, the instabilities can be grouped into two categories: those for which the excited waves are purely electrostatic (see e.g. DuBois & Goldman 1965, 1967; Silin 1965; Lee & Su 1966; Jackson 1967; Nishikawa 1968; Kaw & Dawson 1969; Tzoar 1969; Sanmartin 1970; McBride 1970; Perkins & Flick 1971; Fejer & Leer 1972a, b; Bezzerides & Weinstock 1972; DuBois & Goldman 1972), and those for which one of the excited waves is electromagnetic (see e.g. Goldman & Dubois 1965; Montgomery & Alexeff 1966; Chen & Lewak 1970; Bodner & Eddleman 1972; Fejer & Leer 1972b; Lee & Kaw 1972; Forslund et al. 1972).

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The occurrence of parametric instabilities in finite-amplitude internal gravity waves

Journal of Fluid Mechanics ◽

10.1017/s0022112076002735 ◽

1976 ◽

Vol 78 (04) ◽

pp. 763 ◽

Cited By ~ 82

Author(s):

Richard P. Mied

Keyword(s):

Gravity Waves ◽

Internal Gravity Waves ◽

Finite Amplitude ◽

Parametric Instabilities

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Stability of growing viscoelastic shells with finite flexure

Soviet Applied Mechanics ◽

10.1007/bf01959818 ◽

1989 ◽

Vol 25 (9) ◽

pp. 924-929

Author(s):

V. D. Potapov

Keyword(s):

Viscoelastic Shells

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On parametric instabilities of finite-amplitude internal gravity waves

Journal of Fluid Mechanics ◽

10.1017/s0022112082001396 ◽

1982 ◽

Vol 119 ◽

pp. 367-377 ◽

Cited By ~ 44

Author(s):

J. Klostermeyer

Keyword(s):

Gravity Wave ◽

Internal Gravity Wave ◽

Maximum Growth ◽

Numerical Approach ◽

Internal Gravity Waves ◽

Resonant Interaction ◽

Finite Amplitude ◽

Interaction Diagram ◽

Parametric Instabilities ◽

Boussinesq Fluid

The equations describing parametric instabilities of a finite-amplitude internal gravity wave in an inviscid Boussinesq fluid are studied numerically. By improving the numerical approach, discarding the concept of spurious roots and considering the whole range of directions of the Floquet vector, Mied's work is generalized to its full complexity. In the limit of large disturbance wavenumbers, the unstable disturbances propagate in the directions of the two infinite curve segments of the related resonant-interaction diagram. They can therefore be classified into two families which are characterized by special propagation directions. At high wavenumbers the maximum growth rates converge to limits which do not depend on the direction of the Floquet vector. The limits are different for both families; the disturbance waves propagating at the smaller angle to the basic gravity wave grow at the larger rate.

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