Algebraic Method for Approximate Solution of Scattering of Surface Waves by Thin Vertical Barrier Over a Stepped Bottom Topography

Abstract

A study on interaction of surface water waves by thin vertical rigid barrier over a step type bottom topography is analysed. The associated mixed boundary value problem is solved using the eigenfunction expansion of the velocity potential. The resulting system of equations, avoiding the traditional approach of employing application of orthogonality relations, is solved using algebraic least squares method giving rise the numerical values of the reflection and transmission coefficients by the barrier over step. The energy balance relation for the given problem is derived and verified numerically ensuring the correctness of the present results. The present results are also compared with the data available in the literature for the validation purpose. The effect of step height, length of the barrier and angle of incidence on the reflection coefficient and the non-dimensional horizontal force on the barrier have been investigated through different plots. It is observed that barrier along with step works as an effective barrier to reflect more incident waves causing calm zone along the leeside.

Application of Clifford Algebra on Group Theory

“…Specifically, David Hesten and Elie Cartan are notable contributors to the progress and development of Clifford algebra. Elie Cartan presented the idea of the spinor in 1913 and in 1938 the idea of the pure spinor and he defined Clifford algebra's as algebras of matrices and found that 8 has a periodicity inside these algebraic structures, for more info, refer [8]. David Hesten extended the concept of "Clifford Algebra" to devise a formalism and calls it Geometric Algebra [6].…”