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Nonlinear Theory of Low‐Frequency Instabilities

 

作者: Thomas H. Dupree,  

 

期刊: Physics of Fluids(00319171)  (AIP Available online 1968)
卷期: Volume 11, issue 12  

页码: 2680-2694

 

ISSN:0031-9171

 

年代: 1968

 

DOI:10.1063/1.1691875

 

出版商: AIP

 

数据来源: AIP

 

摘要:

It is proposed that the dominant nonlinear effect of low‐frequency instabilities is an incoherent scattering of particle orbits by waves. The scattering is considered to be incoherent even when only a single mode is present. Because it is incoherent, one can include wave scattering in the theory just as collisional scattering is included in the linear wave theory. A nonlinear dispersion relation is obtained from the linear dispersion relation simply by adding wave scattering terms to the collisional scattering terms. The wave scattering causes particle diffusion over the transverse wavelength and in the theory appears as an enhanced viscosity. This wave induced viscosity can be computed from the amplitude of the wave. Waves which are linearly unstable grow until the enhanced scattering causes their nonlinear growth rates to vanish. Theoretically computed values of density fluctuations, phase shifts, and flux are in good agreement with experimental values in the cases considered.

 

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