A New Parabolic Approximation to the Helmholtz Equation

Parabolic or forward scattering approximations are often used to investigate acoustic or electromagnetic wave propagation in inhomogeneous media. Recently there has been an intensified interest in these approximations traceable in large measure to the work of Tappert1 and Claerbout2. Tappert’s work, reviewed in context in 1 applies the Leontovich-Fock (LF) approximation with considerable success to the study of underwater acoustics. Claerbeut has applied these approximations in a geophysical context. The LF parabolic approximation is very well suited to the study of sound propagation in model oceans that have range independent sound speeds. It has also been used to study propagation in fiber optics material,3 as well as in the study of laser propagation in the atmosphere.</p

Time reversal methods in acousto-elastodynamics

The aim of the article is to solve an inverse problem in order to determine the presence and some properties of an elastic “inclusion” (an unknown object, characterized by elastic properties discriminant from the surrounding medium) from partial observa- tions of acoustic waves, scattered by the inclusion. The method will require developing techniques based on Time Reversal methods. A finite element method based on varia- tional acousto-elastodynamics formulation will be derived and used to solve to solve the forward, and then, the time reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help use to construct images of the inclusions to be determined. Our approach will be applied to configurations modeling breast cancer detection, using simulated ultrasound waves

Measurement of the Enstrophy and the Vorticity Vector in a Plane Cylinder Wake using a Spectral Method

A method to determine derivative moments using only two slanted hot-wires and a spectral method has been employed for a complete determination of the enstrophy and the vorticity vector. The general idea behind the method is to minimize the measuring volume by use of only two hot-wires and to post-process the measured data. All measurements were conducted in the far wake of a cylinder at a Reynolds number of 1840. Comparisons between the spectral method and conventional measuring techniques are made, and the results justifies the approximation between enstrophy and dissipation. For the vorticity vector it was found that the components of the normal and lateral directions were considerably larger than the stream-wise ones