Discontinuity, Nonlinearity, and Complexity
Instability Development in Shear Flow with an Inflection–Free Velocity Profile and Thin Pycnocline
Discontinuity, Nonlinearity, and Complexity 4(3) (2016) 333351  DOI:10.5890/DNC.2016.09.009
S.M. Churilov
Institute of Solar–Terrestrial Physics SB RAS, 126a Lermontov Street, Irkutsk 664033, Russia
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Abstract
Weakly stratified flows of the class under study have a wide 3D spectrum of the most unstable waves with very close growth rates and phase velocities so that their individual critical layers merge into a common one. The analysis of evolution equations for those waves has shown that throughout a weakly nonlinear stage of development their amplitudes grow explosively. During the first (threewave) phase, the most rapidly growing are lowfrequency waves whereas at the next phase, when numerous and diverse higherorder wave interactions come into play, the growth of highfrequency waves is accelerated and they overtake lowfrequency waves. The results obtained are illustrated by numerical calculations for some ensembles of waves.
Acknowledgments
The work was supported in part by RFBR Grants No. 100500094 and No. 140500080.
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