Influence of a Finite Step on Oblique Scattering by a Plane Vertical Barrier

Article Type

Research Article

Publication Title

Quarterly Journal of Mechanics and Applied Mathematics

Abstract

The problem of water wave scattering by partially immersed thin vertical barrier with two distinct geometrical configurations in the presence of a finite step is examined. For each barrier configuration, the problem is reduced to solving an integral equation or a coupled first-kind integral equations that involve the horizontal component of velocity across the gap below the barrier and above the finite step. The integral equations are solved employing the Galerkin approximation, which involves expansion in terms of product of simple polynomials and exponential decay function multiplied by suitable weight functions whose form is dictated by the edge condition at the submerged ends of the barrier and the edge of the step. Very accurate numerical estimates for reflection and transmission coefficients are obtained and depicted graphically against the angle of incidence for the fixed wavenumbers and against wavenumbers for fixed angle of incidence. The study found that there exists a critical angle for fixed wavenumbers for both configurations at which reflection is minimum and transmission is maximum. The increase in depth ratio plays significant role in decreasing the reflection coefficient for both configurations. For lower frequencies, Configuration I has more reflection while for higher frequencies configuration II has more reflection. The wave force on the barrier has been evaluated for both configurations, and it is observed that the force is higher in Configuration II when the wave propagates from the lower depth region to the higher depth region. Furthermore, the free-surface depression has been plotted for both configurations, illustrating the distribution of wave energy across the respective regions.

DOI

10.1093/qjmam/hbaf011

Publication Date

11-1-2025

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