On the period of the periodic orbits of the restricted three body problem

We will show that the period T of a closed orbit of the planar circular restricted three body problem (viewed on rotating coordinates) depends on the region it encloses. Roughly speaking, we show that, \(2 T=k\pi +\int _\Omega g\) where k is an integer, \(\Omega \) is the region enclosed by the periodic orbit and \(g:{\mathbb {R}}^2\rightarrow {\mathbb {R}}\) is a function that only depends on the constant C known as the Jacobian constant; it does not depend on \(\Omega \). This theorem has a Keplerian flavor in the sense that it relates the period with the space “swept” by the orbit. As an application we prove that there is a neighborhood around \(L_4\) such that every periodic solution contained in this neighborhood must move clockwise. The same result holds true for \(L_5\).     

Diurnal variations of temperature as a cause of periodic variations of high-frequency geoacoustic emission

Investigated is the periodic component of geoacoustic emission within the frequency band from 2.0 to 6.5 kHz registered by the piezoceramic hydrophone installed near the bottom of Lake Mikizha in the Kamchatka Peninsula. It is revealed that the variation period is 24 hours and the maximum variation is observed in summer, when the average daily air temperature is above 10°C. In that period the close connection is revealed between the series of air temperature and geoacoustic emission. Taking into account the similar results of measurements of the ground surface slope at the observation site, the most probable reason for the diurnal variations of high-frequency geoacoustic emission is the deformation of near-surface sedimentary rocks caused by diurnal variations of temperature.     

Observations of estuarine circulation and solitary internal waves in a highly energetic tidal channel

Despite vigorous tidal and wind mixing, observations in an estuarine tidal inlet in the Wadden Sea show that during part of the tidal cycle, vertical stratification and internal waves may still develop. Acoustic Doppler current profiler (ADCP) and conductivity, temperature, depth observations, collected over the past 6 years at 13 h anchor stations (ASs), reveal that these occur especially during slack tide, when there is little wind and large freshwater discharge from nearby Lake IJssel. Measurements with a moored ADCP show that in the same tidal phase, strong cross-channel circulation develops, which may suddenly reverse circulation sense due to passing density fronts. In the vertically stratified phase that follows after the front passage, propagating mode-one solitary internal waves are observed. These are resonantly generated during decelerating tidal ebb currents when the (shear) flow passes a transcritical regime (Froude number equal to 1). A combination of photographs (including one from the International Space Station), bathymetric data, and ASs data leads to the discovery of yet another source of internal waves in this area, produced during slackening tide by propagating lee waves that develop over a deep trench. We suggest that both the cross-channel circulation as well as the (solitary) internal waves may locally be of importance for the (re)distribution and transport of sediments and nutrients and may influence tidally averaged transports.     

Applying essentially non‐oscillatory interpolation to controlled‐source electromagnetic modelling*

Modelling and inversion of controlled‐source electromagnetic (CSEM) fields requires accurate interpolation of modelled results near strong resistivity contrasts. There, simple linear interpolation may produce large errors, whereas higher‐order interpolation may lead to oscillatory behaviour in the interpolated result. We propose to use the essentially non‐oscillatory, piecewise polynomial interpolation scheme designed for piecewise smooth functions that contains discontinuities in the function itself or in its first or higher derivatives. The scheme uses a non‐linear adaptive algorithm to select a set of interpolation points that represent the smoothest part of the function among the sets of neighbouring points. We present numerical examples to demonstrate the usefulness of the scheme. The first example shows that the essentially non‐oscillatory interpolation (ENO) scheme better captures an isolated discontinuity. In the second example, we consider the case of sampling the electric field computed by a finite‐volume CSEM code at a receiver location. In this example, the ENO interpolation performs quite well. However, the overall error is dominated by the discretization error. The other examples consider the comparison between sampling with essentially non‐oscillatory interpolation and existing interpolation schemes. In these examples, essentially non‐oscillatory interpolation provides more accurate results than standard interpolation, especially near discontinuities.     

The biogeochemical sulfur cycle in the marine boundary layer over the Northeast Pacific Ocean

The major components of the marine boundary layer biogeochemical sulfur cycle were measured simultaneously onshore and off the coast of Washington State, U.S.A. during May 1987. Seawater dimethylsulfide (DMS) concentrations on the continental shelf were strongly influenced by coastal upwelling. Concentration further offshore were typical of summer values (2.2 nmol/L) at this latitude. Although seawater DMS concentrations were high on the biologically productive continental shelf (2–12 nmol/L), this region had no measurable effect on atmospheric DMS concentrations. Atmospheric DMS concentrations (0.1–12 nmol/m³), however, were extremely dependent upon wind speed and boundary layer height. Although there appeared to be an appreciable input of non-sea-salt sulfate to the marine boundary layer from the free troposphere, the local flux of DMS from the ocean to the atmosphere was sufficient to balance the remainder of the sulfur budget.     

An Improved Approach for Parameterizing Surface-Layer Turbulent Transfer Coefficients in Numerical Models

Based on classic iterative computation results, new equations to calculate the surface turbulent transfer coefficients are proposed, which allow for large ratios of the momentum and heat roughness lengths. Compared to the Launiainen scheme, our proposed scheme generates results closer to classical iterative computations. Under unstable stratification, the relative error in the Launiainen scheme increases linearly with increasing instability, even exceeding 15%, while the relative error of the present scheme is always less than 8.5%. Under stable stratification, the Launiainen scheme uses two equations, one for 0 < Ri _B ≤ 0.08 and another for 0.08 < Ri _B ≤ 0.2, and does not consider the condition that Ri _B > 0.2, while its relative errors in the region 0 < Ri _B ≤ 0.2 exceed 31 and 24% for momentum and heat transfer coefficients, respectively. In contrast, the present scheme uses only one equation for 0 < Ri _B ≤ 0.2 and another equation for Ri _B > 0.2, and the relative error of the present scheme is always less than 14%.     

Estimation of the effect of protective piers on wind wave parameters in the Sevastopol Bay

An effectiveness of the storm wave attenuation by protective piers in the Sevastopol Bay of the Black Sea is studied on the basis of numerical simulation using the SWAN spectral model. Analyzed are the parameters of waves generated by winds of four main directions as well as by the southern cyclone during the storm on November 11, 2007. It is obtained that waves from the northwest part of the Black Sea penetrate most intensively into the Sevastopol Bay in case of western wind and, to a lesser degree, in case of northern and southern winds. A protective effect of the piers is observed in the west part of the bay only and the wave attenuation near the southern coast is more significant than near the northern one. The area of the southern coast directly behind the southern pier is completely protected from the storm waves and, as moving away from the pier, the danger of intensive wave effect on the coast is kept.     

Sources of the Late Mesozoic magmatic associations in the northeastern part of the Amurian microcontinent

Based on generalization of available geochronological data, Late Mesozoic magmatic associations in the northeastern part of the Amurian microcontinent are divided into three groups: 142–125, 124–115, and <110 Ma. The age of these associations decreases with approaching the Pacific margin of Asia. In the same direction, they show a change in sources of their parental melts: continental crust (142–125 Ma) → continental crust + PREMA (DM) (124–115 Ma) → continental crust + PREMA (DM) + EMII (<110 Ma). Isotope-geochemical (Sr-Nd) study indicates that intrusive and volcanic rocks of the Late Mesozoic magmatic associations in the northeastern part of the Amurian microcontinent were originated in geodynamic settings that provided access of enriched mantle sources to magma formation. The most probable of these settings are as follows: (1) plate sliding accompanying by the formation of slab window beneath continental margin; (2) passage of the Asian margin over the East Asian mantle hot field in the Late Mesozoic; (3) asthenospheric upwelling due to delamination of the lower crust during closure of the Mongolian-Okhotsk ocean caused by collision between the Amurian microcontinent, Dzhugdzhur-Stanovoy, and Selenga-Stanovoy superterranes in the Central Asian fold belt.     

Statistical Modeling of Monthly Anomalies of Atmospheric Precipitations for the Region of the Ukraine and Black Sea

The data array accumulated for the period 1946–1995 is used to select the most significant predictor of monthly anomalies of precipitation in the region of the Ukraine and Black Sea, namely, a large-scale circulation in a sector covering the North Atlantic and Europe. Three large-scale predictors (geopotential at a level of 500GPa, sea-level pressure, and the difference between the geopotentials at levels of 500 and 1000GPa) give almost identical results: their correlation with anomalies of precipitation is equal to 0.7–0.8 in winter and 0.4–0.5 in summer. The predominant mechanism of the influence of circulation on precipitations at low frequencies is the response of the trajectories of European cyclones to changes in the upper-tropospheric jet currents in the Atlantic-European sector described as the superposition of the North-Atlantic oscillation and the Eurasian mode. The decomposition of the fields of precipitations and circulation in the eigenmodes of the canonical correlation analysis opens a possibility of direct computation of the monthly average fields of precipitations for the entire territory of the Ukraine and Black Sea region according to the large-scale geopotential fields.     

Radio Emission of Flares and Coronal Mass Ejections

We review recent progress on our understanding of radio emission from solar flares and coronal mass ejections (CMEs) with emphasis on those aspects of the subject that help us address questions about energy release and its properties, the configuration of flare?–?CME source regions, coronal shocks, particle acceleration and transport, and the origin of solar energetic particle (SEP) events. Radio emission from electron beams can provide information about the electron acceleration process, the location of injection of electrons in the corona, and the properties of the ambient coronal structures. Mildly relativistic electrons gyrating in the magnetic fields of flaring loops produce radio emission via the gyrosynchrotron mechanism, which provides constraints on the magnetic field and the properties of energetic electrons. CME detection at radio wavelengths tracks the eruption from its early phase and reveals the participation of a multitude of loops of widely differing scale. Both flares and CMEs can ignite shock waves and radio observations offer the most robust tool to study them. The incorporation of radio data into the study of SEP events reveals that a clear-cut distinction between flare-related and CME-related SEP events is difficult to establish.