Abstract

The problem of water wave scattering by a thin circular-arc-shaped plate submerged in infinitely deep water is investigated by linear theory. The circular-arc is not necessarily symmetric about the vertical through its center. The problem is formulated in terms of a hypersingular integral equation for a discontinuity of the potential function across the plate. The integral equation is solved approximately using a finite series involving Chebyshev polynomials of the second kind. The unknown constants in the finite series are determined numerically by using the collocation and the Galerkin methods. Both the methods ultimately produce very accurate numerical estimates for the reflection coefficient. The numerical results are depicted graphically against the wave number for a variety of configurations of the arc. Some results are compared with known results available in the literature and good agreement is achieved. The suitability of using a circular-arc-shaped plate as an element of a water wave lens has also been discussed on the basis of the present numerical results.

Author Keywords: Water wave scattering; Linear theory; Circular arc; Hypersingular integral equation; Reflection coefficient

Mathematical subject codes: 76 B

Article Outline

1. Introduction

2. Formulation

3. Method of solution

4. Numerical results

5. Conclusion

Acknowledgements

References