S. S. Vinogradov

Scattering of an E-Polarized Plane Wave by Two-Dimensional Airfoils

Abstract This article presents the implementation of the rigorous method of regularization to the scattering of an E-polarized plane wave by the classical airfoil described by the Zhukovski transform. The accurate computation of the scattering patterns and the radar cross-section are performed in a wide frequency band for different incident angles.

Regularization of the Dirichlet Problem for Laplace's Equation: Surfaces of Revolution

Abstract Based on the idea of analytical regularization, a mathematically rigorous and numerically efficient method to solve the Laplace equation with a Dirichlet boundary condition on an open or closed arbitrarily shaped surface of revolution is described. To improve the convergence of the series for the single-layer density, we extracted and evaluated in an explicit form the singularity of the density at the surface edge. Numerical investigations of canonical structures, such as the open prolate spheroid and the open surface obtained by the rotation of “Pascals Limaçon” or the “Cassini Oval,” exhibit the high accuracy and wide applicability of the method.

Evaluation of the Northern Gulf of Mexico Littoral Initiative Model Based On the Observed Temperature and Salinity In the Mississippi Bight

Temperature and salinity measurements from the Northern Gulf of Mexico Littoral Initiative (NGLI) survey during August 30 - September 14, 2000 reveal a high level of temporal and spatial variability in the Mississippi Bight. To support scientific studies using a numerical model, a three-dimensional hydrodynamic Estuarine and Coastal Ocean Model (ECOM) is implemented in the Mississippi Bight. The ECOM is run with realistic topography, stratification and meteorological forcing to hindcast circulation on a shallow and highly variable shelf of the Mississippi Bight. The results of the model are compared with observation to evaluate the ECOM performance on different temporal scales. Based on the area oceanography and data availability, three temporal scales are chosen for model/data comparison: fine scale (less than an hour), diurnal, and large scale (a two-week period). Limitations of the ECOM application on each scale are discussed. The model is capable to reproduce observed water masses, describe spatial distribution of water properties, and simulate areas with high horizontal gradient such as freshwater plumes. However, delayed response to meteorological forcing, overestimated mixing rates and uncertainties in computation of river discharges result in statistically significant bias in the simulations. Along with traditional linear correlations from all observational points and spectral analysis over the diurnal cycle, a new technique of model validation is introduced. The technique is a new application of an existing variational interpolation method. Detailed description of the method and numerical procedure allow one to apply this technique to any oceanographic data with prescribed data variances for model/data comparison.

Analytical regularization based analysis of a spherical reflector symmetrically illuminated by an acoustic beam

A mathematically accurate and numerically efficient method of analysis of a spherical reflector, fed by a scalar beam produced by a complex source-point feed, is presented. Two cases, soft and hard reflector surface, are considered. In each case the solution of the full-wave integral equation is reduced to dual series equations and then further to a regularized infinite-matrix equation. The latter procedure is based on the analytical inversion of the static part of the problem. Sample numerical results for 50-lambda reflectors demonstrate features that escape a high-frequency asymptotic analysis.

Diffraction of H-polarized Plane Wave by Cylindrical Cavities of Arbitrary Shape

The diffraction problem for an arbitrary shaped cylindrical cavity excited by a H-polarized plane wave is rigorously solved by the Method of Regularization. Along with the previously solved analogous problem for E-polarization this rigorous solution completes the construction of a reliable and highly efficient analytic-numerical technique for the analysis of diffraction problems for metallic cylinders of an arbitrary cross-section. Both problems are reduced to the numerical solution of a well-conditioned infinite system of linear algebraic equations of Fredholm type. Its numerical solution is effected by a truncation method. The computational accuracy only depends on truncation number. The effectiveness of this approach is demonstrated by examples of wave scattering problems for two-dimensional airfoils and engine intakes of various shapes. The combination of well-known approximate techniques with the developed approach has been exploited for studies of wave scattering problems for elongated cylinders of arbitrary cross-section.

Physical oceanography and acoustic propagation during LADC experiment in the Gulf of Mexico in 2001

The Littoral Acoustic Demonstration Center (LADC) deployed three environmental and acoustic moorings in a downslope line just off the Mississippi River Delta in the northern Gulf of Mexico in an area of a large concentration of sperm whales in July 2001. The measurement of whale vocalizations and, more generally, ambient noise, were the objectives of the experiment. Each mooring had a single hydrophone autonomously recording Environmental Acoustic Recording System (EARS) obtained from the U.S. Naval Oceanographic Office and modified to recorded signals up to 5859 Hz continuously for 36 days. Also, self‐recording, environmental sensors were attached to the moorings to obtain profiles of time series data of temperature and salinity. Satellite imagery and NOAA mooring data were gathered for an analysis of eddy formations and movement in the Gulf. This paper will discuss the possible environmental impact of two events that occurred during the experiment: the passage of Tropical Storm Barry and the movement of...

Accurate simulation of a spherical reflector antenna by the complex point source-dual series approach

In a previous paper (see IEEE Trans. Antennas and Propagation, vol.43, no.8, p.793-801, 1995), we considered a circular-cylindrical reflector fed by complex-point E and H-polarized line sources. Dual series equations (DSE) were formulated in terms of the trigonometric functions, with the static part analytically inverted based on the Riemann-Hilbert problem solution. The resulting matrix equation was of the Fredholm 2nd kind. A remarkable feature of this equation is that it can be solved numerically with a guaranteed accuracy and small CPU time expenditures. The present study is similar but deals with a more practical model of a 3-D spherical reflector fed by a complex point source. The solution is obtained, via the DSE, in terms of the associated Legendre functions, with the static part inversion based on the Abel integral equation technique. We consider here two scalar problems of the hard and soft reflector surface, but keep in mind the vector electromagnetic problem as an ultimate goal.

Coupling and scattering from axisymmetric bodies, open and closed: Regularisation methods

An accurate and numerically efficient solution is developed for the scalar wave diffraction problem from an arbitrary shaped body of revolution, either closed or having an aperture. The Dirichlet boundary condition is considered. Based on analytical regularization, the method transforms the standard surface integral equation to an algebraic system that may be truncated to well-conditioned system that produces solutions of prescribed and guaranteed accuracy.

Diffraction from Arbitrarily Shaped Open Shells of Revolution: Dynamic Case

A mathematically rigorous and numerically efficient approach is developed for solving the Laplace equation with Dirichlet boundary condition on a closed or open arbitrary shaped surface of revolution. Although important in itself, the problem also provides a first step towards the solution of the related wave scattering problem. The generalized method of analytical regularization transforms the problem to a well-conditioned infinite system of linear algebraic equations of the second kind. This provides a robust numerical solution with any desired accuracy.

Gulf of Mexico oceanography and acoustic‐pulse propagation across the DeSoto Canyon

To investigate the feasibility of monitoring the movements of the large eddies that dominate circulation in the deep waters of the Gulf of Mexico, acoustic‐propagation studies are made using historic and ocean dynamic model data for sound‐speed profiles representing the distinctions among the various water masses inside and outside these eddies. The propagation work concentrates on a slice across the DeSoto Canyon in the northeast Gulf from the shelf break off the Mississippi Delta to the Florida shelf—a region in which a deep sound channel exists. The objective for the study of this slice is to determine the potential for monitoring the movement and evolution of eddies as they enter DeSoto Canyon. Two frequency bands of a pulse source (400–600 and 900–1100 Hz) and deep water source placements near the sound‐channel axis (900 m) and a vertical array of receivers are used in modeling. Details of the temporal structure in the arrivals show significant variations for the different waters of the order of 0=2E...