scholarly journals Examples of ray‐theory solutions for two‐dimensional sound speed profiles

1974 ◽  
Vol 55 (S1) ◽  
pp. S44-S44
Author(s):  
D. White
Keyword(s):  
Sound Speed ◽  
Two Dimensional ◽  
Ray Theory

scholarly journals Towards a Wave Theory Interpretation of Time-Distance Helioseismology Data

2001 ◽  
Vol 203 ◽  
pp. 180-182
Author(s):  
A. C. Birch ◽  
A. G. Kosovichev
Keyword(s):  
Spatial Scale ◽  
Born Approximation ◽  
Acoustic Waves ◽  
Sound Speed ◽  
Large Scale ◽  
Small Scale ◽  
Ray Theory ◽  
Travel Times ◽  
Large Spatial Scale ◽  
Time Distance

Time-distance helioseismology, which measures the time for acoustic waves to travel between points on the solar surface, has been used to study small-scale three-dimensional features in the sun, for example active regions, as well as large-scale features, such as meridional flow, that are not accessible by standard global helioseismology. Traditionally, travel times have been interpreted using geometrical ray theory, which is not always a good approximation. In order to develop a wave interpretation of time-distance data we employ the first Born approximation, which takes into account finite-wavelength effects and is expected to provide more accurate inversion results. In the Born approximation, in contrast with ray theory, travel times are sensitive to perturbations to sound speed which are located off the ray path. In an example calculation of travel time perturbations due to sound speed perturbations that are functions only of depth, we see that that the Born and ray approximations agree when applied to perturbations with large spatial scale and that the ray approximation fails when applied to perturbations with small spatial scale.

Effect of Guide’s Acoustic Parameters on Vertical Directivity of the Marine Ambient Noise

2014 ◽  
Vol 577 ◽  
pp. 1207-1210
Author(s):  
Chun Xia Meng ◽  
Hao Mu ◽  
Gui Juan Li
Keyword(s):  
Shallow Water ◽  
Sound Speed ◽  
Ambient Noise ◽  
Sound Propagation ◽  
Sea Water ◽  
Surface Boundary ◽  
Ray Theory ◽  
Directivity Characteristic ◽  
Acoustic Parameters ◽  
Equipment Performance

The vertical directivity characteristic of ambient noise is one inherent characteristic of the ocean in shallow water. And it includes the information of guide’s acoustic characteristic information. The marine guide is composed of sea water; seabed and surface boundary, there into, the acoustic parameters of seabed are hardly obtained exactly. In this paper, the model of vertical directivity for ambient noise is established. Based on the ray theory of sound propagation, the influence of guide’s acoustic parameters which include sound speed, density and attenuation coefficient on vertical directivity of marine ambient noise is simulated. The results are propitious to analysis and command the characteristics of ambient noise, and valuable to accelerate the exertion of acoustic equipment performance.

The evolution of thermocline waves from an oscillatory disturbance

1993 ◽  
Vol 254 ◽  
pp. 401-416 ◽  
Author(s):  
D. Nicolaou ◽  
R. Liu ◽  
T. N. Stevenson
Keyword(s):  
Finite Difference ◽  
Shear Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Ray Theory ◽  
Navier Stokes Equations ◽  
Linear Shear ◽  
Wave Shapes ◽  
The Way

The way in which energy propagates away from a two-dimensional oscillatory disturbance in a thermocline is considered theoretically and experimentally. It is shown how the St. Andrew's-cross-wave is modified by reflections and how the cross-wave can develop into thermocline waves. A linear shear flow is then superimposed on the thermocline. Ray theory is used to evaluate the wave shapes and these are compared to finite-difference solutions of the full Navier–Stokes equations.

A Numerical Modelling of Two-Phase Flow System

2008 ◽  
Author(s):  
Moon-Sun Chung ◽  
Jong-Won Kim
Keyword(s):  
Sound Speed ◽  
Two Phase Flow ◽  
Flow System ◽  
Fluid Model ◽  
Equation System ◽  
Pressure Jump ◽  
Phase Flow ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Two Phase

A two-dimensional two-fluid model for two-phase flow system is proposed. This two-dimensional model is based on the hyperbolic one-dimensional model which is improved in its mathematical property by adopting the interfacial pressure jump terms in the momentum equations. Owing to this surface-tension effect incorporated in the momentum equations, eigenvalues of the equation system can be obtained analytically and they are proved to be all real. The eigenvectors can also be obtained analytically with linearly independent form. Further, they consist of phasic convective velocities, the sound speed of gas phase, and the sound speed of liquid phase. Consequently, the governing equation system is mathematically hyperbolic with reasonable characteristic speeds by which the upwind numerical method avails. Advantages and possibility of the present model are discussed in some detail.

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