Abstract:
The three-dimensional problem involving diffraction of water wave by a finite floating rigid dock over an arbitrary bottom is
studied for two cases (1) in the absence of wall (2) in the presence of wall. The problem is handled for its solution with the aid of step
method. Here both asymmetric and symmetric arbitrary bottom profile is approximated using successive steps. Step approximation
helps to apply the matched eigenfunction expansion method, in result, system of algebraic equations are obtained which are solved to
determine the hydrodynamic quantities, namely, force experienced by rigid floating dock as well as rigid seawall, free surface elevation,
transmission and reflection coefficients associated with transmission and reflected waves respectively. The effects of various structural
and system parameters are examined on these hydrodynamics quantities. The appropriate values of length and thickness of dock, water
depth and angle of incidence provide the salient information to marine and coastal engineers to design the offshore structures and
creation of parabolic trench on the bottom. The present results are compared with known results in special case of bottom topography.
The energy balance relation is derived and checked.
