T. Sahoo

Scattering of surface waves by a semi-infinite floating elastic plate

A new inner product is developed based on the Fourier analysis to study the scattering of surface waves by a floating semi-infinite elastic plate in a two-dimensional water domain of finite depth. The eigenfunctions for the plate-covered region are orthogonal with respect to this new inner product. The problem is studied for various wave and geometrical conditions. Especially, the influence of different edge conditions on the hydrodynamic behavior is investigated and compared. The edge conditions considered in the present study involve (i) a free edge, (ii) a simply supported edge, and (iii) a built-in edge. The hydrodynamic performance of an elastic plate is characterized for various conditions in terms of wave reflection and transmission, plate deflection, and surface strain. It is observed that the hydrodynamic behavior depends on the wave conditions, the geometrical settings, and the edge conditions. The built-in edge condition induces the maximum wave reflection and the minimum wave transmission. The...

Expansion formulae in wave structure interaction problems

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 so-called Greens 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.

Trapping of surface waves by porous and flexible structures

Abstract The trapping of surface waves by submerged vertical porous and flexible barriers near the end of a semi-infinitely long channel of finite depth is investigated. The barrier configurations include a bottom-touching barrier and a surface-piercing barrier. In the case of a bottom-touching barrier, the barrier is clamped at the bottom and is free at the upper end. While in the case of a surface-piercing barrier, the barrier is clamped by a structure above the free surface and is free at the lower end which is inside the water. By matching the velocity and pressure along the barrier and along the gap and using the edge conditions at the end points, systems of linear equations are obtained. In the case of a surface-piercing barrier, the deflection, slope of deflection, the bending moment and the shear force acting on the barrier are assumed to be continuous at the interaction point where the barrier and the free surface meet each other. The reflection coefficients are obtained and discussed for various wave conditions, geometrical settings, and barrier properties. The hydrodynamic force and the overturning moment on the barrier and the deflection of a flexible barrier are calculated and analysed for different cases.

Oblique Wave Trapping by Porous Structures Near a Wall

AbstractThe 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...

Oblique wave trapping by porous and flexible structures in a two-layer fluid

Trapping of obliquely incident surface waves by permeable flexible barriers placed near a vertical rigid wall in a two-layer fluid having free surface and an interface is studied for both surface-piercing and bottom-standing partial barriers. For the surface-piercing permeable flexible barrier, the barrier is assumed to be fixed near the free surface and is free at the submerged end. On the other hand, for the bottom standing permeable flexible barrier, the barrier is assumed to be fixed at the bottom and the other end is free. As special cases of the permeable flexible barrier, the results associated with surface-piercing and bottom-standing permeable membrane barriers are obtained by assuming that the two ends of the barriers are fixed. Appropriate continuity conditions are used to deal with the interface-piercing flexible/membrane barriers. The mathematical problem is handled for solution using a generalized orthogonal relation suitable for two-layer fluid along with the least square approximation meth...

Reflection of water waves by a nearly vertical porous wall

The problem of reflection of water waves by a nearly vertical porous wall has been investigated. A perturbational analysis has been applied for the first order correction to be employed to the corresponding vertical wall problem. The Greens function technique has been used to obtain the solution of the boundary value problem at hand, after utilising a mixed Fourier transform together with an idea involving the regularity of the transformed function along the real axis. The cases of fluid of finite as well as infinite depth have been taken into consideration. Particular shapes of the wall have been considered and numerical results are also discussed.

Wave Scattering by a Partial Flexible Porous Barrier in the Presence of a Step-Type Bottom Topography

A semi-analytic model is presented for oblique wave scattering by a bottom-standing or surface-piercing flexible porous barrier in water of finite depth with a step-type bottom topography. The physical problem is solved using the methods of least-squares and multimode approximation associated with the modified mild-slope equation. Effects on the wave scattering due to bed profile, structural rigidity, compressive force, angle of incidence, barrier length, porosity, and height of the step are examined. The study reveals that under some special conditions, nearly zero/full reflection may occur in the case of wave scattering by a partial flexible porous barrier in the presence of an undulated bottom topography. Further, the study predicts that the Bragg resonance may not occur in the case of wave scattering by a topography of sinusoidal profile. The present study provides insights to help understand how waves are transformed in a marine environment with/without flexible porous barriers in the presence of a bottom topography. The concept and methodology can be generalized to analyze problems of similar nature arising in ocean engineering.

Enhanced magnetoimpedance and field sensitivity in microstructure controlled FeSiCuNbB ribbons

Fe73.5Si13.5Cu1Nb3B9 and Fe77.2Si11.2Cu0.8Nb3.3B7.5 nanocomposite materials consisting of nanocrystalline phase in an amorphous matrix were obtained by heat-treatment of their precursor amorphous ribbons. The influence of structural modifications induced during the heat-treatment on soft magnetic properties and magnetoimpedance (MI) effect have been studied. The structural investigations on both these ribbons revealed the presence of two phases, fine grained Fe3Si phase and a residual amorphous phase on heat-treatment. The maximum MI ratio obtained in the present study is 95% at f = 4 MHz, for the optimized heat-treated Fe77.2Si11.2Cu0.8Nb3.3B7.5 ribbon. This is ascribed to the increase in magnetic permeability and decrease in coercive force and intrinsic resistivity. Moreover, a maximum magnetic field sensitivity (ξ) of 8.3%/Oe at f = 2.5 MHz is obtained, for the optimized nanocrystalline Fe73.5Si13.5Cu1Nb3B9 ribbon. This suggests that tailoring of the nanocrystalline microstructures induced by optimum h...

The effect of surface tension in porous wave maker problems

Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

On the Scattering of Water Waves by Porous Barriers

The problems of scattering of water waves by both partially immersed as well as completely submerged porous barriers are studied in case of water of infinite depth in the case when the porosity effect is very small by using a perturbation analysis. The first order terms of the reflection and transmission coefficients are determined by using the consistency conditions of certain singular integral equations with logarithmic kernels.