Nonlinear dynamo theory

Abstract

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

Nonlinear Dynamo in Obliquely Rotating Stratified Electroconductive Fluid in an Uniformly Magnetic Field

“…In the absence of heating ( =0) T  and of external magnetic field ( = 0) B eqs. (27)-(28) coincide with the results found in [47]. In the case of non-electroconductive fluid ( = 0)  with the temperature gradient ( 0) T   we obtain the same results as in [50].…”

“…(27)-(28) coincide with the results found in [47]. In the case of non-electroconductive fluid ( = 0)  with the temperature gradient ( 0) T   we obtain the same results as in [50]. In the limit of non-electroconductive ( = 0)  and homogeneous fluid ( =0) T  we obtain the results of [46].…”

“…The development of this large-scale instability in obliquely rotating fluid gives rise to nonlinear large-scale helical structures of Beltrami vortex type, or to localized kinks with internal helical structure. In [47] the new hydrodynamic  -effect found in [46] was generalized to the case of electroconductive fluid. The corresponding large-scale instability leads to the generation of LSVS and magnetic fields.…”

“…This method allows to construct the nonlinear theories of vortex dynamo for compressible media [40][41], as well as for convective media with a helical external force [30][31]. The asymptotic multi-scale method is used to reveal large-scale instability in the thermally stratified conductive medium in the case of helicity of small-scale velocity and magnetic fields [42][43]. Development of this large-scale instability in a convective electroconductive medium engenders the generation of both vortex and magnetic fields as well.…”

“…Development of this large-scale instability in a convective electroconductive medium engenders the generation of both vortex and magnetic fields as well. Self-consistent or nonlinear theory of magneto-vortex dynamo in a convective electroconductive medium with small-scale helicity was built in [43].…”