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    Reduction of hydroelastic response of a flexible floating structure by an annular flexible permeable membrane
    Selvan, SA ; Behera, H ; Sahoo, T (Springer, 2019-10-01)
    In the present study, hydroelastic response mitigation of a very large floating circular structure by an annular flexible permeable membrane is studied under the assumption of the linearized theory of water waves and small amplitude structural response. The very large floating structure is modeled based on small amplitude plate theory, while the flexible annular membrane is modeled using the two-dimensional string equation. Darcy’s law is used to model wave past the permeable annular membrane. To keep the structures in position, both the floating structures are assumed to be moored on the circular boundaries. The velocity potentials are expanded in terms of the Fourier–Bessel series in the open water, membrane-, and plate-covered regions. The solution of the physical problem is obtained using the matched eigenfunction expansion method along with the orthogonality of the vertical eigenfunctions in the open water region. On the other hand, orthogonal mode–coupling relation, satisfied by the vertical eigenfunctions in the floating flexible plate-covered region, is used when there is no spacing between the outer and the inner structures. The wave forces exerted on the inner and outer structures, deflection of the plate, and flow distribution around the inner plate are analyzed using numerical computations to understand the hydroelastic response of the inner elastic plate in the presence of the outer porous membrane. The effects of various wave and structural parameters such as wavenumber, porous-effect parameter, tensile force, width of the outer membrane, spring constants associated with the mooring joints, and the spacing between the structures are examined. The study reveals that the porous-effect parameter and the width of the annular membrane play an important role in reducing the wave forces on the inner plate. Moreover, due to the reflection and dissipation of a major part of the wave energy concentrating near the free surface, the inner floating structure experiences negligible wave loads in the case of deep water.
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    Wave Attenuation by Multiple Outer Porous Barriers in the Presence of an Inner Rigid Cylinder
    Behera, H ; Gayathri, R ; Selvan, SA (ASCE-AMER SOC CIVIL ENGINEERS, 2020-01-01)
    The wave forces acting on a rigid cylinder are investigated in the presence of multiple outer porous cylindrical barriers by assuming the linear water wave theory. A Bessel series solution is obtained for the boundary value problem by using the methods of eigenfunction expansion and least-squares approximation. Two configurations of outer porous barriers are considered, namely bottom-standing and surface-piercing. As a special case, the effect of fully extended barriers is studied. The wave loads exerted on the cylinders, free surface elevations, and flow distribution around the structures are computed and analyzed for different physical parameters. The present theory is ratified with the result available in the literature for a single fully extended outer porous barrier. The study reveals that the hydrodynamic forces exerted on the inner impermeable cylinder are reduced significantly as the number of outer porous barriers is increased. Thus, multiple outer fully extended or partial porous barriers can be set up to protect the inner rigid cylinder.
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    Wave energy dissipation by a floating circular flexible porous membrane in single and two-layer fluids
    Selvan, SA ; Behera, H (Elsevier, 2020-06-15)
    In this study, the impact of gravity wave on a circular elastic floating permeable membrane is investigated using linear water wave theory in both homogeneous and two-layer fluids. The matched eigenfunction expansion technique is employed to obtain an analytic solution of the boundary value problem. Further, the plane wave integral representation of Bessel and Hankel functions are applied to study the influence of porous structure in damping the far-field wave energy. In order to examine the effect of various physical parameters, heave force exerted on the membrane, deflection of the membrane, reflected and transmitted wave amplitudes, flow distribution around the structure and far-field energy dissipation are computed and analyzed for three different edge conditions such as (i) free edge, (ii) moored edge and (iii) clamped edge. The study reveals that the surface wave amplitude on the lee side of the structure decreases significantly in the presence of floating porous elastic membrane. Moreover, the membrane having clamped edge dissipates more wave energy as compared to that for moored and free edge conditions.
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    Effect of imposed shear on the dynamics of a contaminated two-layer film flow down a slippery incline
    Sani, M ; Selvan, SA ; Ghosh, S ; Behera, H (AIP Publishing, 2020-10-01)
    The linear instability of a surfactant-laden two-layer falling film over an inclined slippery wall is analyzed under the influence of external shear, which is imposed on the top surface of the flow. The free surface of the flow and the interface among the fluids are contaminated by insoluble surfactants. Dynamics of the fluid layers are governed by the Navier–Stokes equations, and the surfactant transport equations regulate the motion of the insoluble surfactants at the interface and free surface. Instability mechanisms are compared by imposing the external shear along and opposite to the flow direction. A coupled Orr–Sommerfeld system of equations is derived using the perturbation technique and normal mode analysis. The eigenmodes corresponding to the Orr–Sommerfeld eigenvalue problem are obtained by employing the spectral collocation method. The numerical results imply that the stronger external shear destabilizes the interface mode instability. However, a stabilizing impact of the external shear on the surface mode is noticed if the shear is imposed in the flow direction, which is in contrast to the role of imposed external shear on the surface mode for a surfactant-laden single layer falling film. Furthermore, in the presence of strong imposed shear, the overall stabilization of the surface mode by wall velocity slip for the stratified two-fluid flow is also contrary to that of the single fluid case. The interface mode behaves differently in the two zones at the moderate Reynolds numbers, and higher external shear magnifies the interfacial instability in both zones. An opposite trend is observed in the case of surface instability. Moreover, the impression of shear mode on the primary instability is analyzed in the high Reynolds number regime with sufficiently low inclination angle. Under such configuration, dominance of the shear mode over the surface mode is observed due to the weaker impact of the gravitational force on the surface instability. The shear mode can also be stabilized by applying the external shear in the counter direction of the streamwise flow. Conclusively, the extra imposed shear on the stratified two-layer falling film plays an active role in the control of the attitude of the instabilities.
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    Surface wave scattering by multiple flexible fishing cage system
    Selvan, SA ; Gayathri, R ; Behera, H ; Meylan, MH (AMER INST PHYSICS, 2021-03-01)
    A study of the wave dynamics around a multiple cylindrical fishing cage system is carried out under the assumption of linear water wave theory and small-amplitude wave response. The Fourier–Bessel series expansion of the velocity potential is derived for the regions enclosed under the open-water and cage systems and the immediate vicinity. The scattering between the cages is accounted for by employing Graf's addition theorem. The porous flexible cage system is modeled using Darcy's law and the three-dimensional membrane equation. The edges of the cages are moored along their circumferences to balance its position. The unknown coefficients in the potentials are obtained by employing the matched eigenfunction method. In addition, the far-field scattering coefficients for the entire system are obtained by expanding the Bessel and Hankel functions in the plane wave representation form. Numerical results for the hydrodynamic forces, scattering coefficients, and power dissipation are investigated for various cage and wave parameters. The time simulation for the wave scattering from the cage system is investigated. The study reveals that wave loading on the cage system can be significantly reduced by the appropriate spatial arrangement, membrane tension, and porous-effect parameter. Moreover, the far-field results suggest that the cage system can also be used as a breakwater.
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    Hydroelastic response of a floating plate on the falling film: A stability analysis
    Selvan, SA ; Ghosh, S ; Behera, H ; Meylan, MH (ELSEVIER, 2021-07)
    The role of a floating elastic plate on the hydrodynamic instability of a gravity-driven flow down an inclined plane is examined in the linear and nonlinear regimes. Linear instability of the system with respect to infinitesimal disturbances is captured using normal-mode analysis. The critical conditions for instability are obtained analytically utilizing the small film aspect ratio. The bifurcation of the nonlinear evolution equation is analyzed using weakly nonlinear stability analysis. The time evolution of the surface elevation is analyzed using the nonlinear analysis. The Orr–Sommerfeld boundary value problem corresponding to the perturbed flow is derived, and it is solved numerically using the spectral collocation method. The behavior of the marginal stability curves and temporal growth of the unstable waves are portrayed for a range of dimensionless flow parameters. Moreover, the pressure acting on the surface are calculated and analyzed for various structural parameters, applicable to different flow configurations. The study reveals that the structural parameters such as rigidity and mass per unit length play a crucial role in suppressing and facilitating the unstable surface waves of the flow. However, the compressive force acting on the plate results in the flexural destabilization. Thus, the plate parameters are more efficient in damping the shorter wave disturbances. Numerical observations imply that the floating elastic plate assists in stabilizing the free-falling flow and dampens the high amplitude waves.