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REFLECTION OF OBLIQUE INCIDENT WAVES BY PERFORATED CAISSONS WITH TRAVERSE WALL

Journal of Hydrodynamics 2005年第3期17卷 257-268页

作者： LIYu-cheng LIUHong-jie DONGGuo-hai StateKeyLaboratoryofCoastalandOffshoreEngineering DalianUniversityofTechnologyDalian116023China ZhejiangProvincialPlanDesignandResearchInstituteofCommunications Hangzhou310006China

The interaction of oblique incident waves with infinite number of perforated caissons is investigated. The fluid domain is divided into infinite sub-domains by the caissons, and eigen-function expansion is applied to expand velocity potentials in each domain. A phase relation is introduced for wave oscillation in each caisson, and the structure geometry is considered in constructing the models of reflection waves. The reflected waves with the present analysis include all of the waves traveling in different directions when incident wave period is short. Numerical examinations show that velocities at the inner and outer sides of the front walls of caissons ase close to each other, and reflection coefficients satisfy the energy conservation relation very well when porous effect parameter is infinite. Numerical results show that the reflection coefficients of oblique incident waves are smaller for shorter caissons at low frequency, and decrease with the increase of wave incident angle.

关键词： wave reflection oblique incident wave traverse wall perforated caisson eigen-function expansion

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Analytical Solutions to Definite Integrals for Combinations of Legendre, Bessel and Trigonometric functions Encountered in Propagation and Scattering Problems in Spherical Coordinates

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Journal of Applied Mathematics and Physics 2022年第9期10卷 2690-2697页

作者： Farhad Azadi Namin Department of Electrical Engineering Amirkabir University of Technology (Tehran Polytechnic) Tehran Iran

Mie theory is a rigorous solution to scattering problems in spherical coordinate system. The first step in applying Mie theory is expansion of some arbitrary incident field in terms of spherical harmonics fields in terms of spherical which in turn requires evaluation of certain definite integrals whose integrands are products of Bessel functions, associated Legendre functions and periodic functions. Here we present analytical results for two specific integrals that are encountered in expansion of arbitrary fields in terms of summation of spherical waves. The analytical results are in terms of finite summations which include Lommel functions. A concise analytical expression is also derived for the special case of Lommel functions that arise, rendering expensive numerical integration or other iterative techniques unnecessary.

关键词： Mie Theory Vector Spherical Wave function eigen-function expansion Spherical Harmonics Special functions

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