A variational approach to elastic wave propagation in anomalous layers

Summary . A unified variational approach is derived for elastic wave propagation in infinite and semi-infinite stratified media involving anomalous layers. As a specific application we provide accurate approximations to the transition matrix which appears in the so-called amplification problem in earthquake engineering.     

Meridional circulation from differential rotation in an adiabatically stratified solar/stellar convection zone

Meridional circulation in stellar convection zones is not generally well observed, but may be critical for the workings of MHD dynamos operating in these domains. Coriolis forces from differential rotation play a large role in determining what the meridional circulation is. Here, we consider the question of whether a stellar differential rotation that is constant on cylinders concentric with the rotation axis can drive a meridional circulation. Conventional wisdom says that it can not. Using two related forms of the governing equations that respectively estimate the longitudinal components of the curl of the meridional mass flux and the vorticity, we show that such differential rotation will drive a meridional flow. This is because to satisfy anelastic mass conservation, non-spherically symmetric pressure contours must be present for all differential rotations, not just ones that depart from constancy on cylinders concentric with the rotation axis. Therefore, the fluid is always baroclinic if differential rotation is present. This is because, in anelastic systems, the perturbation pressure must satisfy a Poisson type equation, as well as an equation of state and a thermodynamic equation. We support our qualitative reasoning with numerical examples, and show that meridional circulation is sensitive to the magnitude and form of departures from rotation constant on cylinders. The effect should be present in 3D global anelastic convection simulations, particularly those for which the differential rotation driven by global convection is nearly cylindrical in profile. For solar-like differential rotation, Coriolis forces generally drive a two-celled circulation in each hemisphere, with a second, reversed flow at high latitudes. For solar like turbulent viscosities, the meridional circulation produced by Coriolis forces is much larger than observed on the Sun. Therefore, there must be at least one additional force, probably a buoyancy force, which opposes the meridional flow to bring its amplitude down to observed values.     

Shock wave propagation in non-ideal fluids

Expressions for the variation of shock strength and its propagation in non-ideal fluids are presented by using the method developed by Whitham. The effects of the presence of rotation, rotation and magnetic field on the strength and propagation velocity of shock waves have been discussed separately. Finally, the effects of the presence of gravitation on the shock strength and on propagation velocity have been studied.     

A spreadsheet method of estimating best-fit hydraulic gradients using head data from multiple wells

Hydraulic gradients from planar water tables, or piezometric surfaces, and horizontal flow regimes can be quickly and conveniently calculated from data sets involving numerous wells. The matrix-solving functions of a modem spreadsheet program (Excel) were used to determine the equation of a water-table plane, Ax + By + Cz - D = 0, and the equation coefficients were then used to determine the magnitude of the hydraulic gradient, according to gradient = square root of A2 + B2/C2, and its direction, according to alpha = arctan B/A, where alpha is the angle measured from the x-axis. A pre-prepared Excel file constructed to handle data from up to 20 wells at once is available for free downloading at www.geo.ku.edu/hydro/KUHydro.html.     

Global Dynamic Model of Critical Frequency of the Ionospheric F2 Layer

Geomagnetism and Aeronomy - A global dynamic model of the F2 layer of the ionosphere GDMF2 is designed to calculate foF2 in both quiet and geomagnetically disturbed conditions. The term...     

Challenge Future – Technical Progress and Globalization

Central elements of the challenges of the future are the population, supply and disposal trap, the question of how the increasing world population will be supplied with long‐lasting and effective sources of energy, raw materials and food? How do we deal with the problems of greenhouse effect, ozone hole, forest dieback, ground erosion, desertification and other environmental threats? Driven by the dynamics of the technical progress the world is in the midst of experiencing the transition from an industrial to an information society. The process of globalization is intrinsically tied to the information society and plays a vital role in the path to a new, digital development of the world. Therefore, new challenges have been added to the traditional ecological challenges at the beginning of the 21^st century, which the world community must react swiftly to.     

Interaction of internal waves with a horizontally inhomogeneous density field area overlying a ridge

In the context of the general linear theory, we consider the propagation of an internal tide across a frontal zone overyling an oceanic ridge. For a uniformly stratified ocean, the solution was derived using Riemann's technique. The dependences of the generated internal wave amplitudes on the stratification parameters and bottom topography were determined. We have found that wave disturbances of high intensity inside and in the neighbourhood of the ridge may be concentrated in raytype areas. An increase of the horizontal density gradient in the frontal zone results in a perceptible deformation of these areas.Translated by Vladimir A. Puchkin.     

Atmospheric temperature sounding with the Fourier spectrometer

Preliminary results of a space experiment using the IKFS-2 infrared sounder (Meteor-M2 satellite) showed high-quality of measurements of spectra of the outgoing thermal radiation of the atmosphere–surface system and the adequacy of developed IR radiation atmospheric models in the 15-μm carbon gas absorption band used to recover the vertical profiles of the atmospheric temperature. Outgoing radiation spectra measured by IKFS-2 instruments make it possible to restore vertical temperature profiles with errors close to 1K in most of the 0–30 km high-altitude region, except for the lower troposphere and altitudes above 30 km, where these errors are close to 2–3K.     

A probabilistic performance‐based approach for mitigating the seismic pounding risk between adjacent buildings

Existing design procedures for determining the separation distance between adjacent buildings subjected to seismic pounding risk are based on approximations of the buildings' peak relative displacement. These procedures are characterized by unknown safety levels and thus are not suitable for use within a performance‐based earthquake engineering framework. This paper introduces an innovative reliability‐based methodology for the design of the separation distance between adjacent buildings. The proposed methodology, which is naturally integrated into modern performance‐based design procedures, provides the value of the separation distance corresponding to a target probability of pounding during the design life of the buildings. It recasts the inverse reliability problem of the determination of the design separation distance as a zero‐finding problem and involves the use of analytical techniques in order to evaluate the statistics of the dynamic response of the buildings. Both uncertainty in the seismic intensity and record‐to‐record variability are taken into account. The proposed methodology is applied to several different buildings modeled as linear elastic single‐degree‐of‐freedom (SDOF) and multi‐degree‐of‐freedom (MDOF) systems, as well as SDOF nonlinear hysteretic systems. The design separation distances obtained are compared with the corresponding estimates that are based on several response combination rules suggested in the seismic design codes and in the literature. In contrast to current seismic code design procedures, the newly proposed methodology provides consistent safety levels for different building properties and different seismic hazard conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of the geomagnetic induction tensor

The geomagnetic induction tensor is a means of summarizing the response of the earth at a given observing site to a geomagnetic variation source field. In this paper the characteristics of the tensor elements are examined, both generally and for the special cases of one-dimensional and two-dimensional geologic structure. The first-order model is taken of uniform source fields originating external to a semi-infinite half-space. Graphical ways of presenting the information contained in an induction tensor are explored, including ellipses of rotation, polar diagrams, and diagrams analogous to the Mohr circles of elasticity theory. Criteria to distinguish “two-dimensional” data from “three-dimensional” data are established. The advantages of simultaneously recording “normal” and “anomalous” variations are demonstrated in terms of the extra tensor elements which may then be estimated. The most practical way of presenting information from many stations on a map may be by drawing, for each site, arrows which summarize the response in the vertical field and quadrics which summarize the response in the horizontal field.