Based on Fourier-Bessel series expansion of wave functions,an analytical solution to 2-D scattering ofincident plane SV waves by circular cylindrical canyons with variable depthto-width ratios is deduced in this paper...Based on Fourier-Bessel series expansion of wave functions,an analytical solution to 2-D scattering ofincident plane SV waves by circular cylindrical canyons with variable depthto-width ratios is deduced in this paper. Unlike other analytical solutions,this paper uses the asymptotic behavior of the cylindrical function to directly define the undetermined coefficients of scattered waves,thus,avoiding solving linear equation systems and the related numerical computation problems under high-frequency incident waves,thereby broadening the applicable frequency range of analytical solutions. Through comparison with existing analytical solutions,the correctness of this solution is demonstrated. Finally, the incident plane SV wave scattering effect under circular cylindrical canyons in wider frequency bands is explored.展开更多
The flow of a freely falling liquid film of low Reynolds number down a vertical long periodic sine-shaped wavy plate of small corrugations is researched theoretically. A model based on perturbation method and power se...The flow of a freely falling liquid film of low Reynolds number down a vertical long periodic sine-shaped wavy plate of small corrugations is researched theoretically. A model based on perturbation method and power series is presented. A stream function is introduced into the governing equations and two sets of equations describing the film flow separately at zeroth and first order are developed. The zeroth order equation is solved directly. The first order equations is solved at the leading approximation. Effect of parameters Re, M, λ and ε on the free surface wave of film is discussed.展开更多
基金sponsored by the National Natural Science Foundation of China (50608066)the National Science and Technology Pillar Program of China(2006BAC13B02)
文摘Based on Fourier-Bessel series expansion of wave functions,an analytical solution to 2-D scattering ofincident plane SV waves by circular cylindrical canyons with variable depthto-width ratios is deduced in this paper. Unlike other analytical solutions,this paper uses the asymptotic behavior of the cylindrical function to directly define the undetermined coefficients of scattered waves,thus,avoiding solving linear equation systems and the related numerical computation problems under high-frequency incident waves,thereby broadening the applicable frequency range of analytical solutions. Through comparison with existing analytical solutions,the correctness of this solution is demonstrated. Finally, the incident plane SV wave scattering effect under circular cylindrical canyons in wider frequency bands is explored.
基金Acknowledgement： This work is supported by Natural Science Foundation of Tianjin of China （No. 07JCYBJC01300）.
文摘The flow of a freely falling liquid film of low Reynolds number down a vertical long periodic sine-shaped wavy plate of small corrugations is researched theoretically. A model based on perturbation method and power series is presented. A stream function is introduced into the governing equations and two sets of equations describing the film flow separately at zeroth and first order are developed. The zeroth order equation is solved directly. The first order equations is solved at the leading approximation. Effect of parameters Re, M, λ and ε on the free surface wave of film is discussed.
