Alexandros Alexakis — Page 5

arXiv2005

Shell to shell energy transfer in MHD, Part II: Kinematic dynamo

We study the transfer of energy between different scales for forced three-dimensional MHD turbulent flows in the kinematic dynamo regime. Two different forces are examined: a non-helical Taylor Green flow with magnetic Prandtl number P_M=0.4, and a helical ABC flow with P_M=1. This analysis allows us to examine which scales of the velocity flow are responsible for dynamo action, and identify which scales of the magnetic field receive energy directly from the velocity field and which scales receive magnetic energy through the cascade of the magnetic field from large to small scales. Our results show that the turbulent velocity fluctuations are responsible for the magnetic field amplification in the small scales (small scale dynamo) while the large scale field is amplified mostly due to the large scale flow. A direct cascade of the magnetic field energy from large to small scales is also present and is a complementary mechanism for the increase of the magnetic field in the small scales. Input of energy from the velocity field in the small magnetic scales dominates over the energy that is cascaded down from the large scales until the large-scale peak of the magnetic energy spectrum is reached. At even smaller scales, most of the magnetic energy input is from the cascading process.

physics.flu-dyn↗

arXiv2002

Weakly non-linear analysis of wind-driven gravity waves

We study the weakly non-linear development of shear-driven gravity waves, and investigate the mixing properties of the finite amplitude solutions. Calculations to date have been restricted to the linear theory, which predicts that gravity waves are amplified by an influx of energy through the critical layer, where the velocity of the wind equals the wave phase velocity. Because of the presence of a critical layer, ordinary weakly non-linear methods fail; in this paper, we use a rescaling at the critical layer and matched asymptotics to derive an amplitude equation for the most unstable wave, under the simplifying assumption that the physical domain is periodic. These amplitude equations are solved numerically, in their quasi-steady limit, for the cases of small density ratio (applicable to oceanography), and for arbitrary density ratio but strong stratification (for more general physical/astrophysical situations). In addition to the familiar asymptotic growth found in other inviscid flow, we find that, for the air over water case (provided the maximum wind velocity is in the range of $0.2\mpers \sim 1\mpers$), the single mode transitions from exponential to algebraic growth when the amplitude of the wave is as small as $h\sim 10^{-5}λ$; hence, it may be difficult to observe the linear regime for this case in numerical simulations. We also find that the weakly non-linear flow allows for super-diffusive particle transport with an exponent $\sim 3/2$, consistent with Venkataramani's results.

physics.flu-dyn↗