Nonlinear saturation of Rayleigh‐Taylor instability in the presence of time‐dependent equilibrium

Abstract

Abstract. The nonlinear evolution and the saturation of the collisional Rayleigh-Taylor instability in the presence of a time-dependent ambient density gradient are studied by using a local, two-dimensional nonlinear theory. A set of nonlinear equations that describes coupling of the initial unstable mode with its various harmonics, which are selfconsistently generated by the dominant nonlinearity, is derived and then solved to find the saturated amplitudes and the power spectrum of the density fluctuations. In the saturated state the density spectrum is dominated by the fluctuations that are linearly damped but are nonlinearly excited and that have spatial variations only along the direction of the ambient density gradient. It is shown that the time-dependent (increasing) density gradient enhances the saturated amplitude of the dominant modes by a factor of 2 or more, depending on the altitude of the bottomside F layer at sunset. Analysis also shows that the collisional diffusion damping leads to a two-component density fluctuation spectrum with a shallow slope at long scalelengths (> 1 km) and a steep slope at shorter scalelengths. The calculated values of the spectral index p, for a power law of the form k• p, are p • 2.0 for the shallow slope and p •-3.0 for the steep slope, and they are close to the values determined from the one-dimensional measurements.

Equatorial spread and dynamics in the F layer over West Africa from ionogram analysis, during the declining solar flux year 1994–1995

“…Extended spread F irregularity power maps from the Jicamarca radar (Woodman and La Hoz, 1976) and scintillation studies (Das Gupta et al, 1981;Koster and Huang, 1993;McClure et al, 1998;Basu, 1999;Kumar et al, 2000) have complemented the pioneer results (Hanson and Sanatani, 1973;McClure et al, 1977). Focusing on the multi-instability source region, close to the magnetic equator, "Guara" NASA rocket campaign with ground probes in Brazil (La Belle et al, 1997) and the long-period ionogram series (Abdu et al, 1981(Abdu et al, , 1992Mc Daniell and Hysell, 1997;Whalen, 2000) have greatly improved our understanding of the ESF dynamics.…”

Stability criteria of Rayleigh ‐ Taylor modes in magnetized plasmas

“…There is a large amount of literature on theoretical and numerical studies of the RT instability [1][2][3][4][5][6][7][8][9][10][11] and also some experimental observations [12][13][14][15]. Development of the RT instability in a uniform external field has been treated by Chandrasekhar [15].…”