Interaction of flexural gravity wave in ice cover with a pair of bottom-mounted rectangular barriers

This paper considers the reflection and transmission of flexural gravity waves by a pair of bottom-mounted rectangular barriers of arbitrary height and width. Depth of the fluid considered here is finite but not necessarily uniform. The fluid region is bounded by an infinite long thin ice sheet of homogeneous properties. Using linearized water wave theory the velocity potential associated with the motion is formulated. Eigenfunction matching technique is used to convert the boundary value problem to a set of integral equations which are solved by using multi-term Galerkin method. The reflection and transmission coefficients are calculated and represented graphically. An expression for the energy balance relation is given and checked carefully. A model of the problem in which the fluid is bounded by a free surface is recovered. For a set of physical parameters the results are analyzed through a number of figures. The convergence and correctness of the method is confirmed by comparing the results with the one available in the literature. It is shown that a pair of thick bottom-mounted barriers have significant impact on reflected and transmitted flexural gravity waves. Resonance effects are observed and verified for different parameters of the current problem.