WAVE PROPAGATION ON A LIQUID SURFACE IN THE PRESENCE OF A THICK RECTANGULAR BLOCK FLOATING ABOVE AN INFINITE STEP
R. Chakraborty1, M. Majhi2, B.N. Mandal3
1Diamond Harbour Women’s University, Diamond Harbour, India
2Chakdaha College, Chakdaha, India
3Indian Statistical Institute, Kolkata, India
Keywords: surface wave propagation, rectangular block, infinite step, Galerkin method, hydrodynamic characteristics
Abstract
The problem of surface wave propagation in the presence of a thick rectangular block floating above an infinite step is studied within the framework of linear theory. The block is located entirely in the region of finite depth. An eigenfunction expansion method is used to construct the velocity potential describing the fluid motion in the finite- and infinite-depth regions. From the pressure continuity conditions in the gaps above the step corner and below the two corners of the block, three integral equations of the first kind are derived for the horizontal velocity components in these gaps. The integral equations are solved using the Galerkin method, the basis functions are chosen as simple polynomials multiplied by exponentially decaying functions, and the weight functions are determined taking into account the edge conditions. We perform the numerical calculations of the hydrodynamic characteristics-the reflection and transmission coefficients and the components of the wave force acting on the block. The dependences on the wave number are obtained and analyzed.
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