Abstract:
We present a systematic methodology to develop high order accurate numerical approaches for linear advection problems. These methods are based on evolving parts of the jet of the solution in time, and are thus called jet schemes. Through the tracking of characteristics and the use of suitable Hermite interpolations, high order is achieved in an optimally local fashion, i.e. the update for the data at any grid point uses information from a single grid cell only. We show that jet schemes can be interpreted as advect-and-project processes in function spaces, where the projection step minimizes a stability functional. Furthermore, this function space framework makes it possible to systematically inherit update rules for the higher derivatives from the ODE solver for the characteristics. Jet schemes of orders up to five are applied in numerical benchmark tests, and systematically compared with classical WENO finite difference schemes. It is observed that jet schemes tend to possess a higher accuracy than WENO schemes of the same order.

Abstract:
Using high-resolution 3-D and 2-D (axisymmetric) hydrodynamic simulations in spherical geometry, we study the evolution of cool cluster cores heated by feedback-driven bipolar active galactic nuclei (AGN) jets. Condensation of cold gas, and the consequent enhanced accretion, is required for AGN feedback to balance radiative cooling with reasonable efficiencies, and to match the observed cool core properties. A feedback efficiency (mechanical luminosity $\approx \epsilon \dot{M}_{\rm acc} c^2$; where $\dot{M}_{\rm acc}$ is the mass accretion rate at 1 kpc) as small as $5 \times 10^{-5}$ is sufficient to reduce the cooling/accretion rate by $\sim 10$ compared to a pure cooling flow. This value is smaller compared to the ones considered earlier, and is consistent with the jet efficiency and the fact that only a small fraction of gas at 1 kpc is accreted on to the supermassive black hole (SMBH). We find hysteresis cycles in all our simulations with cold mode feedback: {\em condensation} of cold gas when the ratio of the cooling-time to the free-fall time ($t_{\rm cool}/t_{\rm ff}$) is $\lesssim 10$ leads to a sudden enhancement in the accretion rate; a large accretion rate causes strong jets and {\em overheating} of the hot ICM such that $t_{\rm cool}/t_{\rm ff} > 10$; further condensation of cold gas is suppressed and the accretion rate falls, leading to slow cooling of the core and condensation of cold gas, restarting the cycle. Therefore, there is a spread in core properties, such as the jet power, accretion rate, for the same value of core entropy or $t_{\rm cool}/t_{\rm ff}$. A fewer number of cycles are observed for higher efficiencies and for lower mass halos because the core is overheated to a longer cooling time. The 3-D simulations show the formation of a few-kpc scale, rotationally-supported, massive ($\sim 10^{11} M_\odot$) cold gas torus. (abstract abridged)

Abstract:
Many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature. Here a semi-implicit method is combined with a level set jet scheme to handle stiff nonlinear advection problems. The new method offers an improvement over the semi-implicit gradient augmented level set method previously introduced by requiring only one smoothing step when updating the level set jet function while still preserving the underlying methods higher accuracy. Sample results demonstrate that accuracy is not sacrificed while strict time-step restrictions can be avoided.

Abstract:
We demonstrate that at relatively low mass accretion rates, black hole candidate (BHC) X-ray binaries (XRBs) should enter `jet-dominated' states, in which the majority of the liberated accretion power is in the form of a (radiatively inefficient) jet and not dissipated as X-rays in the accretion flow. This result follows from the empirically established non-linear relation between radio and X-ray power from low/hard state BHC XRBs, which we assume also to hold for neutron star (NS) XRBs. Conservative estimates of the jet power indicate that all BHC XRBs in `quiescence' should be in this jet-dominated regime. In combination with an additional empirical result, namely that BHC XRBs are more `radio loud' than NS XRBs, we find that in quiescence NS XRBs should be up to two orders of magnitude more luminous in X-rays than BHC XRBs, without requiring any significant advection of energy into a black hole. This ratio is as observed, and such observations should therefore no longer be considered as direct evidence for the existence of black hole event horizons. Furthermore, even if BHCs do contain black holes with event horizons, this work demonstrates that there is no requirement for the advection of significant amounts of accretion energy across the horizon.

Abstract:
We study the spatial patterns formed by interacting populations or reacting chemicals under the influence of chaotic flows. In particular, we have considered a three-component model of plankton dynamics advected by a meandering jet. We report general results, stressing the existence of a smooth-filamental transition in the concentration patterns depending on the relative strength of the stirring by the chaotic flow and the relaxation properties of planktonic dynamical system. Patterns obtained in open and closed flows are compared.

Abstract:
Context. We observe a solar jet at north polar coronal hole (NPCH) using SDO AIA 304 {\deg}A image data on 3 August 2010. The jet rises obliquely above the solar limb and then retraces its propagation path to fall back. Aims. We numerically model this observed solar jet by implementing a realistic (VAL-C) model of solar temperature. Methods. We solve two-dimensional ideal magnetohydrodynamic equations numerically to simulate the observed solar jet. We consider a localized velocity pulse that is essentially parallel to the background magnetic field lines and initially launched at the top of the solar photosphere. The pulse steepens into a shock at higher altitudes, which triggers plasma perturbations that exhibit the observed features of the jet. The typical direction of the pulse also clearly exhibits the leading front of the moving jet. Results. Our numerical simulations reveal that a large amplitude initial velocity pulse launched at the top of the solar photosphere produces in general the observed properties of the jet, e.g., upward and backward average velocities, height, width, life-time, and ballistic nature. Conclusions. The close matching between the jet observations and numerical simulations provides first strong evidence for the formation of this jet by a single velocity pulse. The strong velocity pulse is most likely generated by the low- atmospheric reconnection in the polar region which results in triggering of the jet. The downflowing material of the jet most likely vanishes in the next upcoming velocity pulses from lower solar atmosphere, and therefore distinctly launched a single jet upward in the solar atmosphere is observed.

Abstract:
The fact that self-confined jets are observed around black holes, neutron stars and young forming stars points to a jet launching mechanism independent of the nature of the central object, namely the surrounding accretion disc. The properties of Jet Emitting Discs (JEDs) are briefly reviewed. It is argued that, within an alpha prescription for the turbulence (anomalous viscosity and diffusivity), the steady-state problem has been solved. Conditions for launching jets are very stringent and require a large scale magnetic field $B_z$ close to equipartition with the total (gas and radiation) pressure. The total power feeding the jets decreases with the disc thickness: fat ADAF-like structures with $h\sim r$ cannot drive super-Alfv\'enic jets. However, there exist also hot, optically thin JED solutions that would be observationally very similar to ADAFs. Finally, it is argued that variations in the large scale magnetic $B_z$ field is the second parameter required to explain hysteresis cycles seen in LMXBs (the first one would be $\dot M_a$).

Abstract:
We continue our study of chaotic mixing and transport of passive particles in a simple model of a meandering jet flow [Prants, et al, Chaos {\bf 16}, 033117 (2006)]. In the present paper we study and explain phenomenologically a connection between dynamical, topological, and statistical properties of chaotic mixing and transport in the model flow in terms of dynamical traps, singular zones in the phase space where particles may spend arbitrary long but finite time [Zaslavsky, Phys. D {\bf 168--169}, 292 (2002)]. The transport of passive particles is described in terms of lengths and durations of zonal flights which are events between two successive changes of sign of zonal velocity. Some peculiarities of the respective probability density functions for short flights are proven to be caused by the so-called rotational-islands traps connected with the boundaries of resonant islands (including those of the vortex cores) filled with the particles moving in the same frame. Whereas, the statistics of long flights can be explained by the influence of the so-called ballistic-islands traps filled with the particles moving from a frame to frame.

Abstract:
The southward wind events in the Gulf of Tehuantepec generate large warm eddies and strong offshore current jets that produce entrainment of subsurface waters into the upper ocean resulting in cool (dense) water masses. Strong frontal features occur at the boundary between warm eddies and cool patches. An important fraction of the cool water is subducted beneath these eddies as intrapycnocline ‘lenses’ (eddies) within the boundary of a larger eddy. These small eddies are stable and interact with the larger one. Observational evidence of two such lenses is presented. Qualitative arguments based on observed flow and density fields, as well as vorticity arguments, confirm the existence of subduction processes. The magnitude of the subduction rate is estimated as large as 80 m d-1. A revised conceptual scheme of the eddy generating process is summarized as: a) during the event the wind-induced offshore current entrains subsurface water in the central gulf, thus establishing the initial density gradient; b) also during the event, the horizontal density gradient is maintained by horizontal warm water advection; c) after the event a coastal jet separates from the west coast reaches the central gulf and spins up to form an anticyclone; d) subduction due to intense convergence occurs where the warm coastal jet meets the cool water; e) the ‘mature’ warm eddy propagates offshore carrying a lens of cool subducted water within its boundary.

Abstract:
Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of coexistence and stability of propagating or stationary nonuniform solutions, which for the general case of far from instability onsets, is conducted using spatial dynamics and numerical continuations. The selection is determined by the boundary conditions which either preserve or destroy the translational symmetry of the model. Accordingly, we explain the criterion and the properties of stationary periodic states if the system is bounded and show that propagation of nonlinear waves (including solitary) against the advective flow corresponds to coexisting family that emerges nonlinearly from a distinct oscillatory Hopf instability. Consequently, the resulting pattern selection is qualitatively different from the symmetric finite wavenumber Turing or Hopf instabilities.