Physics
Scientific paper
Dec 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008agufmsm23a1682m&link_type=abstract
American Geophysical Union, Fall Meeting 2008, abstract #SM23A-1682
Physics
2724 Magnetopause And Boundary Layers, 2784 Solar Wind/Magnetosphere Interactions, 4415 Cascades, 4485 Self-Organization, 4490 Turbulence (3379, 4568, 7863)
Scientific paper
The spatial degree of freedom in actual situations, for example, at the magnetopause, is much larger than box size of usual numerical simulations of the Kelvin-Helmholtz instability (KHI). If one allowed a larger simulation size, not only the fastest growing mode (the fundamental mode), but also the subharmonic modes start to grow. Eventually, the longest wave mode dominates the system and a large scale vortex appears [Wu, 1986; Miura, 1999]. In general, the subharmonic modes are initialized by seed perturbations with constant amplitudes and random phases among modes. However, 2-D simulations of the HD and MHD KHI showed that the growth of the subharmonic modes is sensitive to the initial perturbations: when the phases among modes are coherently set, the subharmonic mode saturates at larger amplitude [Patnaik et al., 1976; Baty et al., 2003]. In this study, we focus on sensitivities of the KHI to the initial perturbations in terms of phase and a spectrum power index. MHD simulations were conducted to examine how the initial perturbations determined the fate of the KHI through competitive processes of the subharmonic modes and the secondary instabilities. First, we examined two cases focusing on the initial phase difference of the perturbations. 3-D MHD simulations of the KHI show that when the phase difference between the first subharmonic (m=1) and the fastest growing (m=2) modes is zero, the energy of the mode m=2 is inversely cascaded to the mode m=1, resulting an emergence of a 2-D large scale vortex. The vortex paring inhibits the growth of the secondary MRI [Matsumoto and Seki, 2007]. When the phase of the m=1 is shifted by 0.5π, the secondary instability grows inside each KH vortex and the system undergoes a transition to a turbulent state even under the strong magnetic field (β=1.0). In addition to the phase difference, we have also examined the effect of a spectrum power index of initial perturbations. This has been examined by 2-D MHD simulations by comparing the growth rates of the subharmonic modes. Initially, we added 8 modes (m=4 is the fastest growing mode) whose amplitudes are related to the spectrum power index of α ranging from -1 to +1.5, while the phases are randomly shuffled. We found much faster appearance of the largest vortex (m=1) for the case α=1.5 than for α=-1 in which we observed growth of m=1 mode as expected from the linear theory. The maximum growth rate of the mode m=1 reached three times as large as the one from the linearly theory. In this presentation, we also show a possible mechanism of rapid formation of a broad mixing layer by a combination of the secondary R-T instability (direct cascade) [Matsumoto and Hoshino, 2006] and the fast appearance of the large scale vortex (inverse cascade).
Matsumoto Yosuke
Seki Kazuhiko
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