Resonant Instability of Kink Oscillations in Magnetic Flux Tubes with Siphon Flow

We study kink oscillations of a straight magnetic tube in the presence of siphon flows. The tube consists of a core and a transitional or boundary layer. The flow velocity is parallel to the tube axis, has constant magnitude, and confined in the tube core. The plasma density is constant in the tube core and it monotonically decreases in the transitional layer to its value in the surrounding plasma. We use the expression for the decrement/increment previously obtained by Ruderman and Petrukhin (Astron. Astrophys.631, A31, 2019) to study the damping and resonant instability of kink oscillations. We show that, depending on the magnitude of siphon-velocity, resonant absorption can cause either the damping of kink oscillations or their enhancement. There are two threshold velocities: When the flow velocity is below the first threshold velocity, kink oscillations damp. When the flow velocity is above the second threshold velocity, the kink oscillation amplitudes grow. Finally, when the flow velocity is between the two threshold velocities, the oscillation amplitudes do not change. We apply the theoretical result to kink oscillations of prominence threads. We show that, for particular values of thread parameters, resonant instability can excite these kink oscillations.

A possible origin of kilohertz quasi-periodic oscillations in low-mass X-ray binaries

A possible origin of kilohertz quasi-periodic oscillations (QPOs) in low-mass X-ray binaries is proposed. Recent numerical magnetohydrodynamic simulations of accretion disks with turbulent magnetic fields of magneto-rotational instability definitely show the presence of two-armed spiral structure in the quasi-steady state of accretion disks. In such deformed disks, two-armed ($m=2$) c-mode ($n=1$) oscillations are excited by wave–wave resonant instability. Among these excited oscillations, the fundamental in the radial direction ($n_{\rm r}=0$) will be the higher kHz QPO of twin QPOs, and the first overtone ($n_{\rm r}=1$) in the radial direction will be the lower kHz QPO of the twin. A possible cause of the twin high-frequency QPOs in black hole X-ray binaries is also discussed in the final section.

Non-linear resonant instability of short surface waves as the first stage “bag-breakup” process at the air-sea interface at high winds

<p>The recent experimental study [1], [2] identify ‘‘bag breakup’’ fragmentation as the dominant mechanism by which spume droplets are generated at hurricane wind speeds. These droplets can significantly affect the exchanging processes in the air-ocean boundary layer. In order to estimate spray-mediated heat, momentum and mass fluxes we need not only reliable experimental data, but a theoretical model of this process. The “bag-breakup” fragmentation is a strongly non-linear process, and we focus only on its first stage which includes the small-scale elevation of the water surface.</p><p>Our model of the bag’s initiation is based on a weak nonlinear interaction of a longitudinal surface wave and two oblique waves propagating at equal and opposite angles to the flow as it was done in [3], [4]. All of these waves have the same critical layer where cross velocities of oblique waves become infinite making inviscid analysis invalid. So we took into account viscous effects. As a result, it has been established that for a piecewise continuous velocity profile explosive growth of wave amplitudes is possible at the wind speeds exceeding the critical one.</p><p>The present model let us find the dependency of “bag’s” transverse size on the wind speed and estimate its lifetime.</p><p> </p><p> Acknowledgements</p><p>This work was supported by the RSF project 19-17-00209 and the RFBR projects 19-05-00249, 19-35-90053, 18-05-00265.</p><p>References:</p><ol><li>Troitskaya, Y. et al. Bag-breakup fragmentation as the dominant mechanism of sea-spray production in high winds. Sci. Rep. 7, 1614 (2017).</li> <li>Troitskaya, Y. et al. The “Bag Breakup” Spume Droplet Generation Mechanism at High Winds. Part I: Spray Generation Function. J. Phys. Oceanogr., 48, 2167–2188 (2018).</li> <li>A. Craik. Non-linear resonant instability in boundary layers// Journal of Fluid Mechanics. 50, 393-413 (1971).</li> <li>A. Craik. Resonant gravity-wave interactions in a shear flow// Journal of Fluid Mechanics. 34, 531-549 (1968).</li> </ol>

On the nature of the resonant drag instability of dust streaming in protoplanetary disc

The recently discovered resonant drag instability (RDI) of dust streaming in protoplanetary disc is considered as the mode coupling of subsonic gas-dust mixture perturbations. This mode coupling is coalescence of two modes with nearly equal phase velocities: inertial wave (IW) having positive energy and a streaming dust wave (SDW) having negative energy as measured in the frame of gas environment being at rest in vertical hydrostatic equilibrium. SDW is a trivial mode produced by the bulk streaming of dust, which transports perturbations of dust density. In this way, settling combined with radial drift of the dust makes possible coupling of SDW with IW and the onset of the instability. In accordance with the concept of the mode coupling, RDI growth rate is proportional to the square root of the coupling term of the dispersion equation, which itself is proportional to mass fraction of dust, f ≪ 1. This clarifies why RDI growth rate ∝f1/2. When SDW has positive energy, its resonance with IW provides an avoided crossing instead of the mode coupling. In the high wavenumber limit RDI with unbounded growth rate ∝f1/3 is explained by the triple mode coupling, which is coupling of SDW with two IW. It coexists with a new quasi-resonant instability accompanied by bonding of two oppositely propagating low-frequency IW. The mode coupling does not exist for dust streaming only radially in a disc. In this case RDI is provided by the obscured mechanism associated with the inertia of solids.