Universal Journal of Physics and Application Vol. 8(2), pp. 129 - 141
DOI: 10.13189/ujpa.2014.020211
Reprint (PDF) (782Kb)

Weakly Nonlinear Stage of Instability Development in a Sharply Stratified Shear Flow with an Inflection-Free Velocity Profile

Semyon Churilov ^*
Institute of Solar Terrestrial Physics SB RAS, 126a Lermontov Street, Irkutsk 664033, Russia

ABSTRACT

The distinctive property of the class of shear flows under study is that in a large part of the instability domain the phase velocities of waves are so close that their individual critical layers merge into a common one. Throughout a weakly nonlinear stage of perturbation development, this is the layer in that the most intensive and diverse wave interactions operate which determine scenario of perturbation evolution. Analysis of these interactions allows us, first, to reveal two stages of the evolution, three-wave one, when three-wave interactions dominate, and post-three-wave when numerous nonlinear interactions of different orders come into play, and, second, to determine which of the higher-order interactions are competitive. On this basis, we have found the structure of nonlinear evolution equations, substantiated that the nonlinear growth of wave amplitudes is explosive, and calculated growth indexes for both nonlinear stages. It is found that during the three-wave stage the most rapidly growing are low-frequency waves whereas at the next stage the growth of high-frequency waves is accelerated, and to the end of the weakly nonlinear stage all the waves have amplitudes of the same order. The results obtained are illustrated by numerical calculations for some ensembles of waves.

KEYWORDS
Shear Flow with an Inflection-free Velocity Profile, Sharp Density Stratification, Nonlinear Wave Interactions, Critical Layer

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Semyon Churilov , "Weakly Nonlinear Stage of Instability Development in a Sharply Stratified Shear Flow with an Inflection-Free Velocity Profile," Universal Journal of Physics and Application, Vol. 8, No. 2, pp. 129 - 141, 2014. DOI: 10.13189/ujpa.2014.020211.

(b). APA Format:
Semyon Churilov (2014). Weakly Nonlinear Stage of Instability Development in a Sharply Stratified Shear Flow with an Inflection-Free Velocity Profile. Universal Journal of Physics and Application, 8(2), 129 - 141. DOI: 10.13189/ujpa.2014.020211.