First-order Reflection Coefficients Research Articles

Surface wave propagation over small bottom undulations in the presence of a submerged flexible porous barrier

The problems of scattering of surface gravity waves over an undulated bottom in the presence of either a porous vertical elastic plate or a tensioned porous membrane are addressed. A simplified perturbation technique is employed to split the governing boundary value problem into a series of problems involving the zeroth and the first-order potential functions. The solution to the problem associated with zeroth-order potential is obtained by reducing it to a Fredholm integral equation with the help of Havelock’s theorems. An approximate solution of the integral equation is obtained by applying the multi-term Galerkin technique. Application of Green’s integral theorem leads to finding the first-order reflection and transmission coefficients in terms of integrals involving the shape function representing the bottom deformation and the solution of the zeroth-order problem. The accuracy of the present results is established by generating some previous results for the case of an elastic plate submerged in water with bottom deformation. From the graphical presentation of the results it is observed that at certain values of frequency related to the ripple wavenumber, the first-order reflection coefficient exhibits resonant nature, whereas the net reflection is affected by the flexibility characteristics as well as the porosity of the structure.

Scattering of interface wave by bottom undulations in the presence of thin submerged vertical wall with a gap

In this paper, the problem of interface wave scattering by bottom undulations in the presence of a thin submerged vertical wall with a gap is investigated. The thin vertical wall with a gap is submerged in a lower fluid of finite depth with bottom undulations and the upper fluid is of infinite height separated by a common interface. In the method of solution, we use a simplified perturbation analysis and suitable applications of Green’s integral theorem in the two fluid regions produce first-order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom undulations and solution of the scattering problem involving a submerged vertical wall present in the lower fluid of uniform finite depth. For sinusoidal bottom undulations, the first-order transmission coefficient vanishes identically. The corresponding first-order reflection coefficient is computed numerically by solving the zero-order reflection coefficient and a suitable application of multi-term Galerkin approximations. The numerical results of the zero-order and first-order reflection coefficients are depicted graphically against the wave number in a number of figures. An oscillatory nature is observed of first-order reflection coefficient due to multiple interactions of the incident wave with bottom undulations, the edges of the submerged wall and the interface. The first-order reflection coefficient has a peak value for some particular value of the ratio of the incident wavelength and the bottom wavelength. The presence of the upper fluid has some significant effect on the reflection coefficients.

Water wave scattering by bottom undulations in the presence of a thin partially immersed barrier

The problem of water wave scattering by bottom undulations in the presence of a partially immersed thin vertical barrier is investigated here by employing a simplified perturbation analysis. The first-order reflection and transmission coefficients are obtained in terms of integrals involving the shape function describing the bottom undulations and the solution of the scattering problem involving the barrier present in uniform finite depth water. For sinusoidal undulations of bottom symmetric about the plane of the barrier, the first-order transmission coefficient vanishes identically. The corresponding first-order reflection coefficient is computed numerically and the numerical results are depicted graphically against the wave number. Resonant interaction of the incident wave with the bottom undulations is seen to occur for a particular value of the ratio of the surface wavelength to sinusoidal wavelength. As the depth of the lower edge of the barrier tends to zero, the curve for this reflection coefficient almost coincides with the same for the reflection coefficient for the scattering problem involving sinusoidal bottom undulations only.

The small slope approximation reflection coefficient for scattering from a "Pierson-Moskowitz" sea surface

First- and second-order reflection coefficients are presented for the small slope approximation. The first-order reflection coefficient is identical to the Kirchhoff, or physical optics, result, and the second-order reflection coefficient reduces to those of perturbation theory and the Kirchhoff approximation in the appropriate limits. Numerical results are obtained for acoustic or TE-polarized electromagnetic scattering from one-dimensional, Pierson-Moskowitz sea surfaces at low grazing angles. Comparison with exact integral equation results shows that the second-order small slope approximation is extremely accurate and better than both the perturbation and Kirchhoff methods. >

First-order reflection coefficient of surface acoustic waves from thin-strip overlays

The problem of surface-wave reflection at thin-strip overlays occurs frequently in signal-processing devices. Grooved array reflectors employ strip overlays of the same material as the substrate, while metallic transducers incorporate strips of a material different from the substrate. A simple model for calculating the reflection coefficient of thin overlays is described, based on the normal-mode analysis developed by Auld. Calculated values are in close agreement with reported experimental values for grooves in ST-X quartz and Y-Z lithium niobate, and for aluminum on ST-X quartz.

Scattering of Rayleigh waves from topographic irregularities at oblique incidence

Several theoretical treatments now exist in the literature for scattering of Rayleigh waves from topograhic features which are parallel to the incident wave front. These treatments, however, are not applicable to a large class of signal-processing devices in which the surface waves are scattered by inclined reflectors. A perturbational approach, similar to the earlier treatments but applicable to oblique incidence and to all perturbation orders, is presented. The first-order reflection coefficient of a Rayleigh wave from an inclined groove is computed. It is shown that an angle similar to a ’’Brewster’’ angle exists for which the surface wave reflection coefficient is zero. A prescription for applying the theory to anisotropic media is suggested. A clarification of the applicability of this and prior theories to steep-walled structures is given.

A New Impedance-Matched Wide-Band Balun and Magic Tee

A new wide-band microwave balun particularly attractive for microstrip circuitry is described in which the normally balanced line is in the form of a pair of equal-amplitude and antiphase unbalanced lines. This novel method of input-output coupling allows a coplanar arrangement of input and output microstrip lines. Often the balanced and unbalanced line impedances in a balun are unequal, necessitating an impedance-matching network. A first-order reflection coefficient theory that mutually considers the impedance effects of the balun cavity, a compensating stub, and a quarter-wave transformer is used to design wide-band impedance-matched baluns. Curves of VSWR versus bandwidth are presented for several balanced-to-unbalanced line-impedance ratios. Experimental results are given for an octave-band impedance-matched balun with a balanced-to-unbalanced impedance ratio of 2:1. The new wide-band balun is adaptable to a microstrip magic tee. A proposed magic tee that relies on circuit symmetry for operation has multioctave bandwidth potential.