Co- and counter-helicity interaction between two adjacent laboratory prominences

The interaction between two side-by-side solar prominence-like plasmas has been studied using a four-electrode magnetized plasma source that can impose a wide variety of surface boundary conditions. When the source is arranged to create two prominences with the same helicity (co-helicity), it is observed that helicity transfer from one prominence to the other causes the receiving prominence to erupt sooner and faster than the transmitting prominence. When the source is arranged to create two prominences with opposite helicity (counter-helicity), it is observed that upon merging, prominences wrap around each other to form closely spaced, writhing turns of plasma. This is followed by appearance of a distinct bright region in the middle and order of magnitude higher emission of soft x rays. The four-electrode device has also been used to change the angle of the neutral line and so form more pronounced S-shapes

Evaporating Falling Drop

There-dimensional numerical simulations are carried out to investigate the dynamics of a drop undergoing evaporation and falling due to gravity. In order to accurately capture the interfacial phenomena dynamic adaptive grid refinement has been incorporated. The results are presented in terms of spatio-temporal evolution of the shape of the drop, along with the contours of the vapour concentration generated due to evaporation. This study has implications in natural phenomena, such as rainfall, dew formation and several industrial applications undergoing phase change. A parametric study of this phenomenon will be presented at the conference

Why a falling drop does not in general behave like a rising bubble

Is a settling drop equivalent to a rising bubble? The answer is known to be in general a no, but we show that when the density of the drop is less than 1.2 times that of the surrounding fluid, an equivalent bubble can be designed for small inertia and large surface tension. Hadamard's exact solution is shown to be better for this than making the Boussinesq approximation. Scaling relationships and numerical simulations show a bubble-drop equivalence for moderate inertia and surface tension, so long as the density ratio of the drop to its surroundings is close to unity. When this ratio is far from unity, the drop and the bubble are very different. We show that this is due to the tendency for vorticity to be concentrated in the lighter fluid, i.e. within the bubble but outside the drop. As the Galilei and Bond numbers are increased, a bubble displays underdamped shape oscillations, whereas beyond critical values of these numbers, over-damped behavior resulting in break-up takes place. The different circulation patterns result in thin and cup-like drops but bubbles thick at their base. These shapes are then prone to break-up at the sides and centre, respectivel

Dynamics of an initially spherical bubble rising in quiescent liquid

The beauty and complexity of the shapes and dynamics of bubbles rising in liquid have fascinated scientists for centuries. Here we perform simulations on an initially spherical bubble starting from rest. We report that the dynamics is fully three-dimensional, and provide a broad canvas of behaviour patterns. Our phase plot in the Galilei–Eötvös plane shows five distinct regimes with sharply defined boundaries. Two symmetry-loss regimes are found: one with minor asymmetry restricted to a flapping skirt; and another with marked shape evolution. A perfect correlation between large shape asymmetry and path instability is established. In regimes corresponding to peripheral breakup and toroid formation, the dynamics is unsteady. A new kind of breakup, into a bulb-shaped bubble and a few satellite drops is found at low Morton numbers. The findings are of fundamental and practical relevance. It is hoped that experimenters will be motivated to check our predictions

Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter

In this work we study the following nonlocal problem \begin{equation*} \left\{ \begin{aligned} M(\|u\|^2_X)(-\Delta)^s u&= \lambda {f(x)}|u|^{\gamma-2}u+{g(x)}|u|^{p-2}u &&\mbox{in}\ \ \Omega, u&=0 &&\mbox{on}\ \ \mathbb R^N\setminus \Omega, \end{aligned} \right. \end{equation*} where $\Omega\subset \mathbb R^N$ is open and bounded with smooth boundary, $N>2s, s\in (0, 1), M(t)=a+bt^{\theta-1},\;t\geq0$ with $\theta>1, a\geq 0$ and $b>0$. The exponents satisfy $1<\gamma<2<{2\theta<p<2^*_{s}=2N/(N-2s)}$ (when $a\neq 0$) and $2<\gamma<2\theta<p<2^*_{s}$ (when $a=0$). The parameter $\lambda$ involved in the problem is real and positive. The problem under consideration has nonlocal behaviour due to the presence of nonlocal fractional Laplacian operator as well as the nonlocal Kirchhoff term $M(\|u\|^2_X)$, where $\|u\|^{2}_{X}=\iint_{\mathbb R^{2N}} \frac{|u(x)-u(y)|^2}{\left|x-y\right|^{N+2s}}dxdy$. The weight functions $f, g:\Omega\to \mathbb R$ are continuous, $f$ is positive while $g$ is allowed to change sign. In this paper an extremal value of the parameter, a threshold to apply Nehari manifold method, is characterized variationally for both degenerate and non-degenerate Kirchhoff cases to show an existence of at least two positive solutions even when $\lambda$ crosses the extremal parameter value by executing fine analysis based on fibering maps and Nehari manifold

Laboratory simulations of astrophysical jets and solar coronal loops: new results

An experimental program underway at Caltech has produced plasmas where the shape is neither fixed by the vacuum chamber nor fixed by an external coil set, but instead is determined by self-organization. The plasma dynamics is highly reproducible and so can be studied in considerable detail even though the morphology of the plasma is both complex and time-dependent. A surprising result has been the observation that self-collimating MHD-driven plasma jets are ubiquitous and play a fundamental role in the self-organization. The jets can be considered lab-scale simulations of astrophysical jets and in addition are intimately related to solar coronal loops. The jets are driven by the combination of the axial component of the J×B force and the axial pressure gradient resulting from the non-uniform pinch force associated with the flared axial current density. Behavior is consistent with a model showing that collimation results from axial non-uniformity of the jet velocity. In particular, flow stagnation in the jet frame compresses frozen-in azimuthal magnetic flux, squeezes together toroidal magnetic field lines, thereby amplifying the embedded toroidal magnetic field, enhancing the pinch force, and hence causing collimation of the jet