Dripping instability of a two-dimensional liquid film under an inclined plate

It is known that the dripping of a liquid film on the underside of a plate can be suppressed by tilting the plate so as to cause a sufficiently strong flow. This paper uses two-dimensional numerical simulations in a closed-flow framework to study several aspects of this phenomenon. It is shown that, in quasi-equilibrium conditions, the onset of dripping is closely associated with the curvature of the wave crests approaching a well-defined maximum value. When dynamic effects become significant, this connection between curvature and dripping weakens, although the critical curvature remains a useful reference point as it is intimately related to the short length scales promoted by the Rayleigh–Taylor instability. In the absence of flow, when the film is on the underside of a horizontal plate, the concept of a limit curvature is relevant only for small liquid volumes close to a critical value. Otherwise, the drops that form have a smaller curvature and a large volume. The paper also illustrates the peculiarly strong dependence of the dripping transition on the initial conditions of the simulations. This feature prevents the development of phase maps dependent only on the governing parameters (Reynolds number, Bond number, etc.) similar to those available for film flow on the upper side of an inclined plate.

Relaxation of the Boussinesq system and applications to the Rayleigh–Taylor instability

We consider the evolution of two incompressible fluids with homogeneous densities $$\rho _{-}<\rho _+$$ ρ - < ρ + subject to gravity described by the inviscid Boussinesq equations and provide the explicit relaxation of the associated differential inclusion. The existence of a subsolution to the relaxation allows one to conclude the existence of turbulently mixing solutions to the original Boussinesq system. As a specific application we investigate subsolutions emanating from the classical Rayleigh-Taylor initial configuration where the two fluids are separated by a horizontal interface with the heavier fluid being on top of the lighter. It turns out that among all self-similar subsolutions the criterion of maximal initial energy dissipation selects a linear density profile and a quadratic growth of the mixing zone. The subsolution selected this way can be extended in an admissible way to exist for all times. We provide two possible extensions with different long-time limits. The first one corresponds to a total mixture of the two fluids, the second corresponds to a full separation with the lighter fluid on top of the heavier. There is no motion in either of the limit states.

Solar Prominence Bubble and Plumes Caused By an Eruptive Magnetic Flux Rope

Prominence bubbles and plumes often form near the lower prominence–corona boundary. They are believed to play an important role in mass supply and evolution of solar prominences. However, how they form is still an open question. In this Letter we present a unique high-resolution Hα observation of a quiescent prominence by the New Vacuum Solar Telescope. Two noteworthy bubble–plume events are studied in detail. The two events are almost identical, except that an erupting mini filament appeared below the prominence–bubble interface in the second event, unlike the first one or any of the reported bubble observations. Analysis of the Hα and extreme-ultraviolet data indicates that the rising magnetic flux rope (MFR) in the mini filament is the cause of bubble expansion and that the interaction between the prominence and MFR results in plume formation. These observations provided clear evidence that emerging MFR may be a common trigger of bubbles and suggested a new mechanism of plumes in addition to Rayleigh–Taylor instability and reconnection.

A Turbulent Heliosheath Driven by the Rayleigh–Taylor Instability

The heliosphere is the bubble formed by the solar wind as it interacts with the interstellar medium (ISM). The collimation of the heliosheath (HS) flows by the solar magnetic field in the heliotail into distinct north and south columns (jets) is seen in recent global simulations of the heliosphere. However, there is disagreement between the models about how far downtail the two-lobe feature persists and whether the ambient ISM penetrates into the region between the two lobes. Magnetohydrodynamic simulations show that these heliospheric jets become unstable as they move down the heliotail and drive large-scale turbulence. However, the mechanism that produces this turbulence had not been identified. Here we show that the driver of the turbulence is the Rayleigh–Taylor (RT) instability produced by the interaction of neutral H atoms streaming from the ISM with the ionized matter in the HS. The drag between the neutral and ionized matter acts as an effective gravity, which causes an RT instability to develop along the axis of the HS magnetic field. A density gradient exists perpendicular to this axis due to the confinement of the solar wind by the solar magnetic field. The characteristic timescale of the instability depends on the neutral H density in the ISM and for typical values the growth rate is ∼3 years. The instability destroys the coherence of the heliospheric jets and magnetic reconnection ensues, allowing ISM material to penetrate the heliospheric tail. Signatures of this instability should be observable in Energetic Neutral Atom maps from future missions such as the Interstellar Mapping and Acceleration Probe (IMAP). The turbulence driven by the instability is macroscopic and potentially has important implications for particle acceleration.