title: Magnetic field line random walk in models and simulations of reduced magnetohydrodynamic turbulence

authors: Snodin, A. P.

subjects: diffusion

abstract: The random walk of magnetic ﬁeld lines is examined numerically and analytically in the context of reduced magnetohydrodynamic (RMHD) turbulence, which provides a useful description of plasmas dominated by a strong mean ﬁeld, such as in the solar corona. A recently developed non-perturbative theory of magnetic ﬁeld line diffusion is compared with the diffusion coefﬁcients obtained by accurate numerical tracing of magnetic ﬁeld lines for both synthetic models and direct numerical simulations of RMHD. Statistical analysis of an ensemble of trajectories conﬁrms the applicability of the theory, which very closely matches the numerical ﬁeld line diffusion coefﬁcient as a function of distance z along the mean magnetic ﬁeld for a wide range of the Kubo number R. This theory employs Corrsin’s independence hypothesis, sometimes thought to be valid only at low R. However, the results demonstrate that it works well up to R = 10, both for a synthetic RMHD model and an RMHD simulation. The numerical results from the RMHD simulation are compared with and without phase randomization, demonstrating a clear effect of coherent structures on the ﬁeld line random walk for a very low Kubo number.

text: Magnetic field line random walk in models and simulations of reduced magnetohydrodynamic turbulence The random walk of magnetic ﬁeld lines is examined numerically and analytically in the context of reduced magnetohydrodynamic (RMHD) turbulence, which provides a useful description of plasmas dominated by a strong mean ﬁeld, such as in the solar corona. A recently developed non-perturbative theory of magnetic ﬁeld line diffusion is compared with the diffusion coefﬁcients obtained by accurate numerical tracing of magnetic ﬁeld lines for both synthetic models and direct numerical simulations of RMHD. Statistical analysis of an ensemble of trajectories conﬁrms the applicability of the theory, which very closely matches the numerical ﬁeld line diffusion coefﬁcient as a function of distance z along the mean magnetic ﬁeld for a wide range of the Kubo number R. This theory employs Corrsin’s independence hypothesis, sometimes thought to be valid only at low R. However, the results demonstrate that it works well up to R = 10, both for a synthetic RMHD model and an RMHD simulation. The numerical results from the RMHD simulation are compared with and without phase randomization, demonstrating a clear effect of coherent structures on the ﬁeld line random walk for a very low Kubo number.

year: 2013

title: A Review of the Dynamics and Oscillations of the Atmosphere

authors: Ross, Joseph

subjects: fluid dynamics

abstract: The atmosphere is a complex, dynamic system and the weather depends on its state. There are many different phenomena that affect the state of the atmosphere - some only involve the atmosphere, others involve the interaction between the atmosphere and the ocean. These phenomena can be modelled using many equations originating from fluid dynamics and thermodynamics, and many of them are considered here. Energy travels around the atmosphere in the form of waves, such as Kelvin waves and Rossby waves. It is possible for a triad of Rossby waves to interact with each other in a way such that resonance occurs. A computer simulation investigating the sensitivity of such waves to turbulence was completed, and it was found that the energetic dominance of the resonant triad does not persist, and the greater the turbulence added to the Rossby triad, the earlier in the integration the instabilities occur.

text: A Review of the Dynamics and Oscillations of the Atmosphere The atmosphere is a complex, dynamic system and the weather depends on its state. There are many different phenomena that affect the state of the atmosphere - some only involve the atmosphere, others involve the interaction between the atmosphere and the ocean. These phenomena can be modelled using many equations originating from fluid dynamics and thermodynamics, and many of them are considered here. Energy travels around the atmosphere in the form of waves, such as Kelvin waves and Rossby waves. It is possible for a triad of Rossby waves to interact with each other in a way such that resonance occurs. A computer simulation investigating the sensitivity of such waves to turbulence was completed, and it was found that the energetic dominance of the resonant triad does not persist, and the greater the turbulence added to the Rossby triad, the earlier in the integration the instabilities occur.

year: 2012

title: Te mātauranga whakatere waka

authors: Tuaupiki, Jackie Whetumarama

abstract: Hei tēnei tuhinga e whai ake nei, ka tirohia te hangarau waka a ngā tūpuna o Te Moana nui a Kiwa i whakawhiti ai rātou ki ō rātou moutere tae atu ki te mātauranga whakatere waka me te arotahi o te titiro ki te whakatinanatanga o aua mātauranga. Ka tāmutu i konā, ka pūhia te titiro i runga i ngā huarere o Poronīhia e kite ai tātou i ngā āhuatanga o Tāwhirimātea i ōna moutere me ngā wero ki te whakatere waka i ērā huarere.

text: Te mātauranga whakatere waka Hei tēnei tuhinga e whai ake nei, ka tirohia te hangarau waka a ngā tūpuna o Te Moana nui a Kiwa i whakawhiti ai rātou ki ō rātou moutere tae atu ki te mātauranga whakatere waka me te arotahi o te titiro ki te whakatinanatanga o aua mātauranga. Ka tāmutu i konā, ka pūhia te titiro i runga i ngā huarere o Poronīhia e kite ai tātou i ngā āhuatanga o Tāwhirimātea i ōna moutere me ngā wero ki te whakatere waka i ērā huarere.

year: 2017