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.     

A transformation of the two-body problem

A transformation of the differential equations of motion of the two-body problem in the spherical coordinates to oscillator form is derived. It is shown that the independent variable transformation dt/ds=r² is a transformation which makes the oscillator form possible.     

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.     

Axial convergence in a well-mixed estuary

Transverse secondary circulations involving surface convergence, observed in a well-mixed estuary in North Wales, are made visible by the collection of surface material along an axial line which extends continuously for many kilometres through the estuary. The circulation and axial convergence, however, are seen only during the flood phase of the tide and no similar behaviour has been observed during the ebb phase.Convergent circulations in the estuary are associated with small but steady transverse density gradients in the cross-section, produced by non-uniform advection of the longitudinal gradient through the channel. A diagnostic model, using measured mean distributions of cross-sectional density, indicates surface transverse velocities (～0.1 ms^?1) similar to those observed in the estuary. The model further predicts appreciable transverse divergent currents at a fractional depth of 0.75: a prediction which has been tested in the estuary using a vertical array of accurately resolving current direction indicators.