Abstract.Here we consider the linear wave diffraction due to cylindrical structures. First we formulate the diffraction problem for a large, fixed, vertical, bottom-mounted, surface-piercing cylindrical structure in water of finite depth. The analytical solution for circular cylinder is obtained in terms of Bessel and Hankel functions using the method of separation of variables. The diffraction problem for elliptical cylinder is solved using elliptical coordinates and separation of variables method. The analytical solution is obtained in terms of Mathieu and modified Mathieu functions. Also we discuss how to obtain the analytical expressions for the wave forces on those structures. As a limiting case, we show two different ways to derive the velocity potential function for circular cylinder from the velocity potential function of elliptical cylinder.

Received: January 21, 2005

AMS Subject Classification: 76B15, 35Q35, 35J05

Key Words and Phrases: wave diffraction, cylindrical structures, Mathieu function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 19
Issue: 1