A combined EOF/variational approach for mapping radar-derived sea surface currents

A technique for reconstruction of the 2d surface velocity field from radar observations is proposed. The method consecutively employs two processing techniques: At the first stage raw radial velocity data are subject to EOF analysis, which enables to fill gaps in observations and provides estimates of the noise level and integral parameters characterizing small-scale variability of the sea surface circulation. These parameters are utilized at the second stage, when the cost function for variational interpolation is constructed, and the updated radial velocities are interpolated on the regular grid.Experiments with simulated and real data are used to assess the method's skill and compare it with the conventional 2d variational (2dVar) approach. It is shown that the proposed technique consistently improves performance of the 2dVar algorithm and becomes particularly effective when a radar stops operating for 1–2 days and/or a persistent gap emerges in spatial coverage of a basin by the HFR network.     

Asymptotic approximation of long-time solution for low-temperature filtration combustion

There is a renewed interest in using combustion for the recovery of medium viscosity oil. We consider the combustion process when air is injected into the porous medium containing some fuel and inert gas. Commonly the reaction rate is negligible at low temperatures, hence the possibility of oxygen breakthrough. In this case, the oxygen gets in contact with the fuel in the downstream zone leading to slow reaction. We focus on the case when the reaction is active for all temperatures, but heat losses are negligible. For a combustion model that includes heat and mass balance equations, we develop a method for calculating the wave profile in the form of an asymptotic expansion and derive its zero- and first-order approximations. This wave profile appears to be different from wave profiles analyzed in other papers, where only the reaction at the highest temperatures was taken into account. The combustion wave has a long decaying tail. This tail is hard to observe in the laboratory because heat losses must be very small for the long tail to form. Numerical simulations were performed in order to validate our asymptotic formulae.     

On some exceptional cases in the integrability of the three-body problem

We consider the Newtonian planar three-body problem with positive masses m ₁, m ₂, m ₃. We prove that it does not have an additional first integral meromorphic in the complex neighborhood of the parabolic Lagrangian orbit besides three exceptional cases ∑m _i m _j /(∑m _k )² = 1/3, 2³/3³, 2/3² where the linearized equations are shown to be partially integrable. This result completes the non-integrability analysis of the three-body problem started in papers [Tsygvintsev, A.: Journal für die reine und angewandte Mathematik N 537, 127–149 (2001a); Celest. Mech. Dyn. Astron. 86(3), 237–247 (2003)] and based on the Morales–Ramis–Ziglin approach.     

Bimodal Distribution of Magnetic Fields and Areas of Sunspots

We applied automatic identification of sunspot umbrae and penumbrae to daily observations from the Helioseismic Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) to study their magnetic flux density (B) and area (A). The results confirm an already known logarithmic relationship between the area of sunspots and their maximum flux density. In addition, we find that the relation between average magnetic flux density ( $B_{\rm avg}$ ) and sunspot area shows a bimodal distribution: for small sunspots and pores (A≤20 millionth of solar hemisphere, MSH), $B_{\rm avg} \approx 800~\mbox{G}$ (gauss), and for large sunspots (A≥100 MSH), $B_{\rm avg}$ is about 600 G. For intermediate sunspots, average flux density linearly decreases from about 800 G to 600 G. A similar bimodal distribution was found in several other integral parameters of sunspots. We show that this bimodality can be related to different stages of sunspot penumbra formation and can be explained by the difference in average inclination of magnetic fields at the periphery of small and large sunspots.     

Global Solar Free Magnetic Energy and Electric Current Density Distribution of Carrington Rotation 2124

Solar eruptive phenomena, like flares and coronal mass ejections (CMEs), are governed by magnetic fields. To describe the structure of these phenomena one needs information on the magnetic flux density and the electric current density vector components in three dimensions throughout the atmosphere. However, current spectro-polarimetric measurements typically limit the determination of the vector magnetic field to only the photosphere. Therefore, there is considerable interest in accurate modeling of the solar coronal magnetic field using photospheric vector magnetograms as boundary data. In this work, we model the coronal magnetic field for global solar atmosphere using nonlinear force-free field (NLFFF) extrapolation codes implemented to a synoptic maps of photospheric vector magnetic field synthesized from the Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) as boundary condition. Using the resulting three-dimensional magnetic field, we calculate the three-dimensional electric current density and magnetic energy throughout the solar atmosphere for Carrington rotation 2124 using our global extrapolation code. We found that spatially, the low-lying, current-carrying core field demonstrates a strong concentration of free energy in the active-region core, from the photosphere to the lower corona (about 70 Mm). The free energy density appears largely co-spatial with the electric current distribution.     

Smoothing supernova data to reconstruct the expansion history of the Universe and its age

We propose a non-parametric method of smoothing supernova data over redshift using a Gaussian kernel in order to reconstruct important cosmological quantities including   H ( z )  and   w ( z )  in a model-independent manner. This method is shown to be successful in discriminating between different models of dark energy when the quality of data is commensurate with that expected from the future Supernova Acceleration Probe ( SNAP ). We find that the Hubble parameter is especially well determined and useful for this purpose. The look-back time of the Universe may also be determined to a very high degree of accuracy (≲0.2 per cent) using this method. By refining the method, it is also possible to obtain reasonable bounds on the equation of state of dark energy. We explore a new diagnostic of dark energy – the ' w -probe'– which can be calculated from the first derivative of the data. We find that this diagnostic is reconstructed extremely accurately for different reconstruction methods even if Ω_{0 m} is marginalized over. The w -probe can be used to successfully distinguish between Λ cold dark matter and other models of dark energy to a high degree of accuracy.     

Evolution and Fragmentation of Wide-Angle Wind Driven Molecular Outflows

We present two dimensional cylindrically symmetric hydrodynamic simulations and synthetic emission maps of a stellar wind propagating into an infalling, rotating environment. The resulting outflow morphology, collimation and stability observed in these simulations have relevance to the study of young stellar objects, Herbig-Haro jets and molecular outflows. Our code follows hydrogen gas with molecular, atomic and ionic components tracking the associated time dependent molecular chemistry and ionization dynamics with radiative cooling appropriate for a dense molecular gas. We present tests of the code as well as new simulations which indicate the presence of instabilities in the wind-blown bubble’s swept-up shell.     

The turbulent dispersion of surface drifters by water waves: experimental study

Ocean Dynamics - Dispersion of a passive tracer by water waves is of significant importance for many scientific and technological problems including bio-diversity of marine life, ecological impact...     

Multi-scale variability of circulation in the Gulf of Tonkin from remote sensing of surface currents by high-frequency radars

Ocean Dynamics - The sea surface velocity measurements obtained during the period of 2014–2016 using two high-frequency radars (HFR), which were installed on the northern coast of Vietnam,...