Abstract
The research presented here investigates the interaction of oblique flexural gravity waves with a pair of asymmetric trenches. The fluid considered here is bounded above by an infinite thin uniform ice sheet of particular flexural rigidity. Velocity potential describing the motion in the fluid is obtained explicitly in terms of non-orthogonal eigenfunctions. The mode-coupling relations satisfied by the eigenfunction are given. Using matching conditions along the vertical boundaries of the trench walls the problem is transformed into a system of singular integral equations. The unknown functions involved in the integral equations are calculated numerically using multi-term Galerkin approximations involving ultraspherical Gegenbauer polynomials. The reflection and transmission coefficients are obtained numerically and depicted in the number of figures for both symmetric and asymmetric cases. The energy balance relation satisfied by the reflection and transmission coefficients is obtained. The results are analyzed for various non-dimensional parameters describing the model. The results using the present method are compared with previously published works available in the literature. It is found that a thin ice sheet of uniform flexural rigidity has a significant effect on the scattering behavior of the wave in presence of wide trenches.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
