S.R. Manam

Bio: S.R. Manam is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Boundary value problem & Scattering. The author has an hindex of 9, co-authored 24 publications receiving 289 citations. Previous affiliations of S.R. Manam include Indian Institute of Technology Kharagpur & Indian Institute of Science.

Expansion formulae in wave structure interaction problems

Abstract: A large class of problems in the field of fluid–structure interaction involves higher-order boundary conditions for the governing partial differential equation and the eigenfunctions associated with these problems are not orthogonal in the usual sense. In the present study, mode-coupling relations are derived by utilizing the Fourier integral theorem for the solutions of the Laplace equation with higher-order derivatives in the boundary conditions in both the cases of a semi-infinite strip and a semi-infinite domain in two dimensions. The expansion for the velocity potential is derived in terms of the corresponding eigenfunctions of the boundary-value problem. Utilizing such an expansion of the velocity potential, the symmetric wave source potentials or the socalled Green’s function for the boundary-value problem of the flexural gravity wave maker is derived. Alternatively, utilizing the integral form of the wave source potential, the expansion formulae for the velocity potentials are recovered, which justifies the completeness of the eigenfunctions involved. As an application of the wave maker problem, oblique water wave scattering caused by cracks in a floating ice-sheet is analysed in the case of infinite depth.

Waves past porous structures in a two-layer fluid

Abstract: Havelock’s type of expansion theorems, for an integrable function having a single discontinuity point in the domain where it is defined, are utilized to derive analytical solutions for the radiation or scattering of oblique water waves by a fully extended porous barrier in both the cases of finite and infinite depths of water in two-layer fluid with constant densities. Also, complete analytical solutions are obtained for the boundary-value problems dealing with the generation or scattering of axi-symmetric water waves by a system of permeable and impermeable co-axial cylinders. Various results concerning the generation and reflection of the axisymmetric surface or interfacial waves are derived in terms of Bessel functions. The resonance conditions within the trapped region are obtained in various cases. Further, expansions for multipole-line-source oblique-wave potentials are derived for both the cases of finite and infinite depth depending on the existence of the source point in a two-layered fluid.

Oblique Wave Trapping by Porous Structures Near a Wall

Abstract: The current study deals with the oblique wave trapping by bottom-standing and surface-piercing porous structures of finite width placed at a finite distance from a vertical rigid wall Using the Sollitt and Cross model for wave motion within the porous structure, the problems are analyzed based on the small-amplitude water wave theory in water of finite depth The solutions of the associated boundary value problems are obtained analytically using the eigenfunction expansion method and numerically using a multidomain boundary-element method In the boundary-element method, the boundary value problems are converted into integral equations over the physical boundaries The physical boundaries are discretized into a finite number of elements to obtain a system of linear algebraic equations Various aspects of structural configurations, in trapping surface gravity waves, are analyzed from the computed results on the reflection coefficients and the hydrodynamic forces Suitable arrangements of the rigid

Gravity wave interaction with porous structures in two-layer fluid

Abstract: Oblique wave interaction with rectangular porous structures of various configurations in two-layer fluid are analyzed in finite water depth. Wave characteristics within the porous structure are analyzed based on plane wave approximation. Oblique wave scattering by a porous structure of finite width and wave trapping by a porous structure near a wall are studied under small amplitude wave theory. The effectiveness of three types of porous structures—a semi-infinite porous structure, a finite porous structure backed by a rigid wall, and a porous structure with perforated front and rigid back walls—in reflecting and dissipating wave energy are analyzed. The reflection and transmission coefficients for waves in surface and internal modes and the hydrodynamic forces on porous structures of the aforementioned configurations are computed for various physical parameters in two-layer fluid. The eigenfunction expansion method is used to deal with waves past the porous structure in two-layer fluid assuming the associated eigenvalues are distinct. An alternate procedure based on the Green’s function technique is highlighted to deal with cases where the roots of the dispersion relation in the porous medium coalesce. Long wave equations are derived and the dispersion relation is compared with that derived based on small amplitude wave theory. The present study will be of significant importance in the design of various types of coastal structures used in the marine environment for the reflection and dissipation of wave energy.