In this paper, we find a new large scale instability which appears in obliquely rotating flow with the small scale turbulence, generated by external force with small Reynolds number. The external force has no helicity. The theory is based on the rigorous method of multi-scale asymptotic expansion. Nonlinear equations for instability are obtained in the third order of the perturbation theory. In this article, we explain in detail the nonlinear stage of the instability and we find the nonlinear periodic vortices and the vortex kinks of Beltrami type.
С использованием асимптотического метода многих масштабов построена нелинейная теория возникновения крупномасштабных структур в стратифицированной проводящей среде при наличии мелкомасштабных осцилляций поля скорости и магнитных полей. Такие стационарные мелкомасштабные осцилляции поддерживаются малыми внешними источниками при малых числах Рейнольдса. Получена нелинейная система уравнений, описывающая эволюцию крупномасштабных структур поля скорости и магнитных полей. Линейная стадия эволюции приводит к известной неустойчивости. Рассмотрены стационарные крупномасштабные структуры, возникающие при стабилизации линейной неустойчивости.Ключевые слова: стратифицированная проводящая среда, нелинейная система уравнений, неустойчивость, крупномасштабные структуры, метод многих масштабов
The objective of this study aims at using the Matlab-Simulink environment and the LabVIEW software environment to build computer models of a six-dimensional (6D) chaotic dynamic system. For the fixed system’s parameters, the spectrum of Lyapunov exponents and the Kaplan-York dimension are calculated. The presence of two positive Lyapunov exponents demonstrates the hyperchaotic behavior of the system. The fractional Kaplan-York dimension indicates the fractal structure of strange attractors. An active control method is extended to achieve global chaotic synchronization of two identical novel 6D chaotic systems with unknown system parameters. Based on the results obtained in Matlab-Simulink and LabVIEW models, a chaotic signal generator for the 6D chaotic system is implemented in the MultiSim environment. The experimental results show that the chaotic behavior simulation in the MultiSim environment is similar to those in the Matlab-Simulink and LabVIEW models. The simulation results demonstrate that the Pecora-Carroll method is a simple way of chaotic masking and signal decoding.
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