The global solution of the problem of the critical inclination

The publication of the solution of the Ideal Resonance Problem (Garfinkelet al., 1971) has opened the way for a complete first-orderglobal theory of the motion of an artificial satellite, valid for all inclinations. Previous attempts at such a theory have been only partially successful. With the potential function restricted to $$V = - 1/r + J_2 P_2 (\sin \theta )/r^3 + J_4 P_4 (\sin \theta )/r^5 ,$$ the paper constructs aglobal solution of the first order in √J ₂ for the Delaunay variablesG, g, h, l and for the coordinatesr, θ, and ?. As a check, it is shown that this solution includes asymptotically theclassical limit with the critical divisor 5 cos² i?1. The solution is subject to thenormality condition $$eG^2 /(1 + \frac{{45}}{4}e^2 ) \geqslant O\left[ {\left| {\frac{1}{5}(J_2 + J_4 /J_2 )} \right|^{1/4} } \right],$$ which bounds the eccentricitye away from zero in deep resonance. A historical section orients this work with respect to the contributions of Hori (1960), Izsak (1962), and Jupp (1968).     

‘Application of a New Spectral Theory of Stably Stratified Turbulence to the Atmospheric Boundary Layer over Sea Ice’

A new spectral closure model of stably stratified turbulence is used to develop a K–ε model suitable for applications to the atmospheric boundary layer. This K–ε model utilizes vertical viscosity and diffusivity obtained from the spectral theory. In the ε equation, the Coriolis parameter-dependent formulation of the coefficient C ₁ suggested by Detering and Etling is generalized to include the dependence on the Brunt-Väisälä frequency, N. The new K–ε model is tested in simulations of the ABL over sea ice and compared with observations from BASE as simulated in large-eddy simulations by Kosovic and Curry, and observations from SHEBA.     

A generalized Biot–Gassmann model for the acoustic properties of shaley sandstones1

We obtain the wave velocities of clay-bearing sandstones as a function of clay content, porosity and frequency. Unlike previous theories, based simply on slowness and/or moduli averaging or two-phase models, we use a Biot-type three-phase theory that considers the existence of two solids (sand grains and clay particles) and a fluid. The theory, which is consistent with the critical porosity concept, uses three free parameters that determine the dependence of the dry-rock moduli of the sand and clay matrices as a function of porosity and clay content.
Testing of the model with laboratory data shows good agreement between predictions and measurements. In addition to a rock physics model that can be useful for petrophysical interpretation of wave velocities obtained from well logs and surface seismic data, the model provides the differential equation for computing synthetic seismograms in inhomogeneous media, from the seismic to the ultrasonic frequency bands.     

Low‐frequency modulation and trend of the relationship between ENSO and precipitation along the northern to centre Peruvian Pacific coast

The relationship between El Niño Southern Oscillation (ENSO) and precipitation along the Peruvian Pacific coast is investigated over 1964–2011 on the basis of a variety of indices accounting for the different types of El Niño events and atmospheric and oceanographic manifestations of the interannual variability in the tropical Pacific. We show the existence of fluctuations in the ENSO/precipitation relationship at decadal timescales that are associated with the ENSO property changes over the recent decades. Several indices are considered in order to discriminate the influence of the two types of El Niño, namely, the eastern Pacific El Niño and the central Pacific El Niño, as well as the influence of large‐scale atmospheric variability associated to the Madden and Julian Oscillation, and of regional oceanic conditions. Three main periods are identified that correspond to the interleave periods between the main climatic transitions over 1964–2011, i.e. the shifts of the 1970s and the 2000s, over which ENSO experiences significant changes in its characteristics. We show that the relationship between ENSO and precipitation along the western coast of Peru has experienced significant decadal change. Whereas El Niño events before 2000 lead to increased precipitation, in the 2000s, ENSO is associated to drier conditions. This is due to the change in the main ENSO pattern after 2000 that is associated to cooler oceanic conditions off Peru during warm events (i.e. central Pacific El Niño). Our analysis also indicates that the two extreme El Niño events of 1982/1983 and 1997/1998 have overshadowed actual trends in the relationship between interannual variability in the tropical Pacific and precipitation along the coast of Peru. Overall, our study stresses on the complexity of the hydrological cycle on the western side of the Andes with regard to its relationship with the interannual to decadal variability in the tropical Pacific. Copyright © 2014 John Wiley & Sons, Ltd.