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High-frequency lengthwise diffraction by the curve separating soft and hard part of the surface |
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| Institution: | 1. ExxonMobil Upstream Research Company, 22777 Springwoods Village Parkway, Houston, TX, 77389, United States;2. ExxonMobil Production Company, 22777 Springwoods Village Parkway, Houston, TX 77389, United States;3. C-CORE, Captain Robert A. Bartlett Building, Morrissey Road, St. John''s, NL A1B 3X5, Canada;4. Centre for Arctic Research and Development (CARD), Dr. Jack Clark Building, Morrissey Road, St. John''s, NL A1C 3X5, Canada;5. Ian Jordaan and Associates, St. John''s, NL A1C 3X5, Canada;1. The Sixth Affiliated Hospital of Guangzhou Medical University, Qingyuan City People’s Hospital, Qingyuan 511518, Guangdong, China;2. Department of Pathophysiology, School of Basic Medical Sciences, Anhui Medical University, Hefei, Anhui, China;1. School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China;2. School of Information Science & Engineering and Shandong Provincial Key Laboratory of Laser Technology and Application, Shandong University, Jinan 250100, China |
| Abstract: | The paper examines the model problem of high-frequency diffraction by a convex surface consisting of two parts. One is soft, the other is hard. The incident wave falls at a small angle to the line which separates soft and hard parts of the surface. The change in the boundary condition provokes the field in the Fock zone to have a rapid transverse variation. This causes a special boundary-layer to be formed. The boundary value problem for the three dimensional parabolic equation is reduced to the Riemann problem solved by the factorization in the form of infinite products containing the zeros of the Airy function and zeros of its derivative. the results of this factorization appear under the sign of double Fourier integral in the representation of the field. Both numerical and asymptotic analysis of this representation is carried out and illustrates the effects of high-frequency diffraction caused by the line of the boundary condition discontinuity. |
| Keywords: | Diffraction High-frequency asymptotics Soft-hard surface Airy functions Factorization Infinite product |
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