On the stability of particular solutions of the singly averaged Hill problem

We consider the particular solutions of the evolutionary system of equations in elements that correspond to planar and spatial circular orbits of the singly averaged Hill problem. We analyze the stability of planar and spatial circular orbits to inclination and eccentricity, respectively. We construct the instability regions of both particular solutions in the plane of parameters of the problem.     

Modes to replace transitional asymptotic ray fields in a vertically inhomogeneous earth model

Summary. Asymptotic ray theory (ART) fails in transition regions near critically reflected, bottom glancing or caustic-forming rays in a vertically inhomogeneous layered earth. These deficiencies are repaired here by replacing the transitional ray fields with guided modes plus truncation remainders. Exact ray-mode equivalences and their high-frequency asymptotic approximations are formulated, and their validity and efficiency are verified by numerical comparisons for SH motion in a two-layer earth model comprised of an inhomogeneous sediment above an homogeneous semi-infinite bedrock.     

Self-similar solutions for the blast wave problem in radiative gasdynamics,I

Similarity solutions, describing the flow of a perfect gas behind spherical shock waves, are investigated including the radiation heat flux. The shock is assumed to be propagating in a medium at rest. Shock radius varies exponentially with time and density is inversely proportional to fifth power of the shock radius immediately ahead of the shock front.     

Thermal stability of a layer with permeable boundaries and variable gravitational field

The aim of this paper is to investigate the thermal stability of a fluid layer with permeable boundaries and a variable gravitational field. It is observed that the principle of exchange of stabilities is valid when the layer is heated form below and the complex growth rate of an arbitrary oscillatory mode exists outside of a circle whose radius depends upon the permeability parameter, Prandtl number and wavelength of the mode. In the case of a layer heated from below, gravity increasing upward has a destabilizing effect whereas the permeability parameter has a stabilizing effect.     

Kinematics of stars in Kovalsky-Kapteyn figures. II

Rostov State Pedagogical Institute; All-Union Scientific Research Institute Gradient. Translated from Astrofizika, Vol. 33, No. 3, pp. 379–393, November–December, 1990.     

OTEC cold-water pipe research

Shelf-mounted Ocean Thermal Energy Conversion (OTEC) plants require installation of cold-water pipes (CWP) on slopes of40degto depths of 1000 m. In addition, tower platforms containing OTEC power systems may be located on lesser sloped terrain near shore and exposed to special environmental loading problems affecting foundation design. Shelf-mounted installations require careful attention to site selection and geotechnical considerations for foundation integrity on sloped surfaces. This paper primarily discusses research associated with cold-water pipe and foundation installations on steep slopes, although research continues on tower platforms located on the shelf. At least five nations are in various stages of development of OTEC systems for island applications. Each of their systems is either shelf mounted or land based and requires that a large diameter cold-water pipe be installed on a steep slope to provide cold water from 1000-m depths. In addition to the installation and deployment of the large cold-water pipe, the most significant problem is the design and installation of suitable foundations that will last for several decades. To date there is very little experience in the offshore industry for large installations on steep slopes. A major scale-model research project is underway on the slopes of the island of Hawaii. A section of pipe 2.4 m in diameter and 24 m long was installed using combination concrete foundations and joints. The pipe and foundations are fully instrumented to measure environmental loading forces due principally to currents and waves. Environmental measurements will also be taken in the test area. The measurement data will be used to validate available analytical models for subsequent use in aiding industry in providing more cost-effective designs for OTEC pipes and foundations.     

The exact theory of inductive conductivity sensors for oceanographic application

The results of a general theoretical investigation of three commonly used types of inductive conductivity sensors, i.e., the single transformer, the double transformer, and the double transformer with an additional loop, are presented. The resulting formulas describe the dependence of the sensor output signal not only on the conductivity of the seawater but also on the parameters of the electrical circuit, among them the permeability of the transformer core(s), which-unlike the other parameters-shifts considerably during oceanographic in situ measurements. A mathematical discussion of these formulas shows that for certain circuit configurations, the sensor output is independent of changes in permeability. Most of these configurations form the basis of existing oceanographical conductivity sensors, among them the "classical" sensors developed by H. Hinkelmann [3], [4], and by N. L. Brown [14], while some others make evident further possibilities for eliminating the unwanted effects of shifting permeability. In the era of microelectronics, the latter might lead to a reassessment, especially of the single transformer-type sensor.     

Range of validity of seismic ray and beam methods in general inhomogeneous media – I. General theory

Summary. The limitations of asymptotic wave theory and its geometrical manifestations are newly formalized and scrutinized. Necessary and sufficient conditions for the existence of acoustic and seismic rays and beams in general inhomogeneous media are expressed in terms of new physical parameters: the threshold frequency ω₀ associated with the P/S decoupling condition, the cut-off frequency ω_c associated with the radiation-zone condition, the total curvature of the wavefront and the Fresnel-zone radius.
The analysis is facilitated with the introduction of a new ancillary functional – the hypereikonal which is capable of representing ordinary as well as evanescent waves. The hypereikonal is the natural extension of the eikonal theory.
With the aid of the above new parameters, simple conditions are obtained for the decoupled far field, the decoupled near field, two point dynamic ray tracing, paraxial wavefields and Gaussian beams.