Research Projects

The present proposal addresses an important and underexplored area in wave–structure interaction problems, with a focus on the analytical development of wave interactions with multiple flexible porous structures in a single- or two-layer fluid. While extensive analytical and numerical progress has been made for single flexible porous structures, the case of multiple such structures presents formidable analytical challenges due to their geometrical configurations and the involvement of higher-order structural boundary conditions. This proposal aims to develop new analytical methods for solving mixed boundary value problems (BVPs) related to wave interactions with multiple flexible porous structures in single- or two-layer fluids in infinite water depth. In the mathematical model, the fluid is assumed to be inviscid and incompressible, and linear water wave theory is considered. The flow past a porous structure is modelled using Darcy's law, and the Euler-Bernoulli beam equation is used to model the flexible structures. Moreover, the problem will be considered in two dimensions, and accordingly, the structure will be modeled as one-dimensional. The proposed physical problems in the upper half-plane are modelled as mixed BVPs for the Laplace equation with higher-order structural boundary conditions. To address the problem analytically, the mathematical problem in the upper half-plane will be decomposed into quarter-plane problems by introducing symmetric functions along with appropriate connections. The key innovation lies in finding suitable symmetric functions and connections in the form of integro-differential relations. Subsequently, the decomposed problem in the quarter planes will be handled by known techniques used for solving singular integral equations and the Galerkin approximation method as appropriate. This methodology is expected to yield explicit analytical expressions for hydrodynamic quantities such as reflection and transmission coefficients, as well as closed-form solutions for wave potentials and structural deflections. As special cases, wave interaction with multiple flexible vertical membranes will be investigated. Moreover, for both the flexible porous plate and the permeable membrane, appropriate edge conditions are imposed based on the specific nature of the physical problem under consideration. Besides, efforts will be made to generalize the two-dimensional problem to account for oblique waves, for which the governing equations will be reduced to modified Helmholtz equations. The utility of the developed methods will be demonstrated by analyzing a class of wave-structure interaction problems of recent interest in ocean engineering.