Correction to: Sea-state contributions to sea-level variability in the European Seas

Ocean Dynamics - A Correction to this paper has been published: https://doi.org/10.1007/s10236-020-01434-9     

Strong triple interactions in the general three-body problem

Strong three-body interactions play a decisive role in the course of the dynamical evolution of triple systems having positive as well as negative total energies. These interactions may produce qualitative changes in the relative motions of the components. In triple systems with positive or zero total energies the processes of formation, disruption or exchange of the components of binaries take place as the result of close approaches of the three single bodies or as the result of the passages of single bodies past wide or hard binaries. In the triple systems with negative energies, the strong triple interactions may result in an escape from the system as well as a formation of a hard final binary. This paper summarizes the general results of the studies of the strong three-body interactions in the triple systems with positive and negative energies. These studies were conducted at the Leningrad University Observatory by computer simulations during 1968–1989.     

The binaries and triple systems in an irregular field

The dynamical evolution of theN-body systems (N=6) has been studied by numerical simulations. The double and triple subsystems isolated from other bodies have been revealed. The processes of their formation, evolution, and disruption have been followed. At the initial stage of evolution, a common collapse of the system takes place. After that some fast triple approaches of single bodies are possible. At further stages, some physically connected triple subsystems are formed which are disrupted by the intruders or due to their own dynamical unstability. The dissipation mechanisms formulated by van Albada (1968) and Aarseth (1973) have been confirmed. At the final stage, double or hierarchical triple systems are formed.     

Measurements of Flows Over Isolated Valleys

Wind-tunnel measurements of the flow over an isolated valley both normal and at an angle (45°) to a simulated neutrally stable atmospheric boundary layer are presented. Attention is concentrated on the nature of the flow within the valley itself. The work formed part of a wider study that included detailed field measurements around an African desert valley and some limited comparisons with that work are included. A scale of about 1:1000 was used for the laboratory work, in which an appropriate combination of hot wire and particle image velocimetry was employed. For a valley normal to the upwind flow, it is shown that the upstream influence of the valley extends to a distance of at least one half of the axial valley width upstream of the leading edge, whereas differences in mean flow and turbulence could be identified well beyond two valley widths from the downwind edge. Non-normal wind angles lead to significant along-valley flows within the valley and, even at two valley heights above the valley ridge level, there remains a significant spanwise flow component. Downwind turbulence levels are somewhat lower in this case, but are still considerably higher than in the undisturbed boundary layer. At both flow angles, there are significant recirculation regions within the valleys, starting from mean separation just beyond the leading edge, but the strong spanwise flow in the 45° case reduces the axial extent of the separated zone. The flow is shown to be in some ways analogous to flow over an isolated hill. Our results usefully enhance the field data and could be used to improve modelling of saltation processes in the field.     

Polarization-mode separation and the emission geometry of pulsar 0823 + 26: A new pattern of pulsar emission?

We explore the detailed polarization behaviour of pulsar 0823 + 26 using the technique of constructing partial ‘mode-separated’ profiles corresponding to the primary and secondary polarization modes. The characteristics of the two polarization modes in this pulsar are particularly interesting, both because they are anything but orthogonal and because the secondary mode exhibits a structure seen neither in the primary mode nor in the total profile. The new leading and trailing features in the secondary mode, which appear to represent a conal component pair, are interpreted geometrically on the basis of their width and the associated polarization-angle traverse as an outer cone. If the secondary-mode features are, indeed, an outer cone, then questions about the significance of the pulsar’s postcursor component become more pressing. It seems that 0823 + 26 has a very nearly equatorial geometry, in that both magnetic poles and the sightline all fall close to the rotational equator of the star. We thus associate the postcursor component with emission along those bundles of field lines which are also equatorial and which continue to have a tangent in the direction of our sight line for a significant portion of the star’s rotation cycle. It seems that in all pulsars with postcursor components, this emission follows the core component, and all may thus have equatorial emission geometries. No pulsars with precursors in this sense — including the Crab pulsar — are known. The distribution of power between the primary and secondary modes is very similar at both 430 and 1400 MHz. Our analysis shows that in this pulsar considerable depolarization must be occurring on time scales that are short compared to the time resolution of our observations, which is here some 0.5–1.0 milliseconds. One of the most interesting features of the modeseparated partial profiles is a phase offset between the primary and secondary modes. The secondary-mode ‘main pulse’ arrives some 1.5 ± 0.1‡ before the primary-mode one at 430 MHz and some 1.3 +0.1 ‡ at 21 cm. Given that the polar cap has an angular diameter of 3.36‡, we consider whether this is a geometric effect or an effect of differential propagation of the two modes in the inner magnetosphere of the pulsar.     

The topology and polarization of subbeams associated with the 'drifting' subpulse emission of pulsar B0943+10 – V. A new look at the low-frequency burst-mode emission

This paper reports new observations of pulsar B0943+10 carried out at the Pushchino Radio Astronomy Observatory (PRAO) at the low radio frequencies of 42, 62 and 112 MHz. B0943+10 is well known for its exquisitely regular burst-mode (B-mode) drifting subpulses as well as its weaker and chaotic quiescent mode. Earlier Arecibo investigations at 327 MHz have identified remarkable, continuous changes in its B-mode subpulse drift rate and integrated-profile shape with durations of several hours. These PRAO observations reveal that the changes in profile shape during the B-mode lifetime are strongly frequency dependent – namely the measured changes in the component amplitude ratio are more dramatic at 327 and 112 MHz as compared with those at 62 and 42 MHz. The differences, however, are most marked during the first several tens of minutes after B-mode onset; after an hour or so the profile shape changes tend to be more similar at all four frequencies. We also have found that the linear polarization of the integrated profile increases continuously throughout the lifetime of the B mode, going from hardly 10 per cent just after onset to some 40–50 per cent after several hours. Pulsar B0943+10's B mode thus provides a unique new opportunity to investigate continuous systematic changes in the plasma flow within the polar flux tube. While refraction in the pulsar's magnetosphere may well play some role, we find that the various frequency-dependent effects, both between and within the two modes, can largely be understood geometrically. If the modes and B-mode decay reflect systematic variations in the carousel-'spark' radius and emission height then a specific set of profile and linear polarization changes would be expected.