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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Instability Development in Shear Flow with an Inflection–Free Velocity Profile and Thin Pycnocline

Discontinuity, Nonlinearity, and Complexity 4(3) (2016) 333--351 | 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 (three-wave) phase, the most rapidly growing are low-frequency waves whereas at the next phase, when numerous and diverse higher-order wave interactions come into play, the growth of highfrequency waves is accelerated and they overtake low-frequency 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. 10-05-00094 and No. 14-05-00080.

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