A modified Green's function for the internal gravitational wave equation in a layer of a stratified medium with a constant shear flow |
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| Authors: | VV Bulatov YuV Vladimirov |
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| Institution: | 1. Department of Agricultural and Resource Economics, University of Saskatchewan, Saskatoon, Saskatchewan, Canada and formerly School of Economic Sciences, Washington State University;2. School of Economic Sciences, Washington State University, Pullman, WA 99164, United States;1. Department of Economic Analysis II, BiRE, BETS and BRiDGE, University of the Basque Country, UPV/EHU, Avda. Lehendakari Aguirre, 83, 48015 Bilbao, Spain;2. Department of Applied Economics III, BiRE and BETS, University of the Basque Country, UPV/EHU, Avda. Lehendakari Aguirre, 83, 48015 Bilbao, Spain |
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| Abstract: | The construction of a modified Green's function for the internal gravitational wave (IGW) equation in a layer of a stratified medium when there are constant mean shear flows is considered and the basic properties of the corresponding eigenvalue problems and the modified eigenfunctions and eigenvalues are investigated. It is shown that each mode of the modified Green's function consists of a sum of three terms describing (1) the IGWs that propagate from the source, (2) the effects of a time varying source, localized in a certain neighbourhood of it, and (3) the effects of the displacement of the fluid (an internal discontinuity) caused by the source. The resulting expressions are analysed out for a constant and oscillating source of the generation of IGWs in which each of the terms of Green's function is represented in the form of simple quadratures. |
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