Faculty Publications
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Item Wave scattering by vertical porous block placed over flat and elevated seabed(Springer Science and Business Media Deutschland GmbH, 2019) Venkateswarlu, V.; Karmakar, D.The present study addresses the hydrodynamic characteristics of the incident wave through porous structure for both finite and shallow water depth. The oblique wave transformation due to the porous block over flat and elevated seabed and the submerged rigid block is presented. Analytical direct formulae are proposed to determine the wave reflection and transmission coefficient for the porous structure considering different configurations like porous block, porous block backed by wall, vertical wall away from the porous block and semi-infinite porous block at flat and elevated seabed. The analytical results for wave interaction with porous structure are presented considering the mode-coupling relation and eigenfunction expansion technique. Further, the significance of the semi-infinite porous block placed on the flat and elevated seabed is studied in detail. The analytical results obtained in the present study are validated with the numerical results available in the literature for specific cases. The significance of the critical angle and skin depth for the semi-infinite structure is explored in the wave structure interaction problems. The comparative study between various structural configurations suggests that, if the ratio of wavelength and width of the structure is greater or equal to unity (d/??1), then the structure can be regarded as semi-infinite porous block for flat and elevated seabed. The derived analytical formulae will be helpful in the preliminary design and analysis of the porous blocks. © 2019, Sociedade Brasileira de Engenharia Naval.Item Significance of seabed characteristics on wave transformation in the presence of stratified porous block(Taylor and Francis Ltd. michael.wagreich@univie.ac.at, 2020) Venkateswarlu, V.; Karmakar, D.The wave transformation due to the presence of stratified porous structure lying on flat seabed, elevated seabed, and stepped seabed is analyzed under the oblique wave incidence. The stratified porous structure in the absence and presence of the leeward wall along with the confined region is examined using the matched eigenfunction expansion technique. The direct analytical relations are obtained to examine the wave transformation for the case of long-wave approximations for multilayered porous structure lying on various types of seabed. The wave reflection coefficient, transmission coefficient, energy damping, and wave force on the vertical wall in the presence of stratified porous block are analyzed with variation in the sea-bed characteristics, porosity, friction factor, structural width, and water chamber length. The study shows that the energy damping increases with the increase in the porosity of the seaside porous layer due to the presence of high void spaces. Further, the stratified porous structure shows a considerable impact in decreasing the resonating peaks and troughs for the wave force acting on the seawall. In addition, the stepped seabed is observed to reduce the wave force on the leeward wall as compared with the uniform and elevated seabed in the presence of stratified porous block. © 2019, © 2019 Japan Society of Civil Engineers.Item Numerical investigation on the wave dissipating performance due to multiple porous structures(Taylor and Francis Ltd., 2021) Venkateswarlu, V.; Karmakar, D.Gravity wave interaction with porous structures is investigated under the assumption of linearized wave theory. Multiple porous blocks of finite thickness with finite spacing are investigated under the action of oblique ocean waves considering leeward unbounded region and confined region. The eigenfunction expansion method is employed to analyse the effect of multiple-confined regions in the trapping of oblique waves. The study outcomes are validated with numerical and experimental results available in the literature. The friction factor and the inertia effect of the porous medium are considered and different porosity conditions are adopted to determine the wave reflection coefficient, transmission coefficient, wave dissipation and wave force impact on the leeward wall. The functional efficiency of multiple fully extended porous structures is studied for different values of porosity, water chamber length, angle of incidence, friction factor and spacing between the porous blocks. The seabed is assumed to be uniform impermeable bottom and uneven bottom (step approximation is adopted). The study demonstrates that the better wave blocking is achieved with the increase in the series of porous structures and the confined regions can be used effectively for the trapping of oblique waves. The present study will be helpful in the design of porous structures for security of coastal facilities and coastal structures in offshore environment. © 2019 Indian Society for Hydraulics.Item Dissipation of Gravity Waves Due to Submerged Porous Plate Coupled With Porous Structures(American Society of Mechanical Engineers (ASME), 2023) Krishna, K.R.A.; Abdulla, K.; Karmakar, D.The present study focuses on wave trapping due to the submerged horizontal porous plate combined with the bottom-standing porous structure and surface-piercing porous structure. The submerged plate thickness is considered to be negligible as compared to the incident wavelength and water depth, and the porous structure is considered to be of finite width. The study is performed based on the eigenfunction expansion method, and the wave interaction with the combined structure is investigated using the small amplitude wave theory. The orthogonal mode-coupling relation is used to analyze the wave interaction with the combined structure. The reflection, transmission, and dissipation coefficients along with wave force on the porous structure are investigated to analyze the hydrodynamic performance of the composite porous breakwater system. Further, the effect of porosity of submerged plate and structure, submergence depth of plate and structure, angle of incidence, and the submerged plate length are investigated to analyze the effective wave dissipation by the composite breakwater. In addition, the comparative study of the numerical method is performed with the results available in the literature. The study noted that the wave damping due to the submerged porous plate backed by surface-piercing porous structure is more as compared to the submerged porous plate backed by the bottom-standing porous structure. The study performed will be helpful to scientists and engineers in the design of suitable composite breakwater systems and also assists in selecting the best structural configuration for attenuation of wave height and to protect the offshore facility from high waves in the coastal region. © 2023 American Society of Mechanical Engineers (ASME). All rights reserved.Item Hydrodynamic performance of submerged breakwater in tandem with thin-walled as submerged reef structure(SAGE Publications Ltd, 2023) Patil, S.B.; Karmakar, D.The interaction of gravity waves with submerged tandem breakwater of different structural configurations is analysed in finite water depth using the Multi-Domain Boundary Element Method (MDBEM). The wave transformation characteristics, wave forces and wave energy dissipation are analysed considering the presence of impermeable type thin-walled as reef structure in front of the primary submerged breakwater. The comparative study is performed for the submerged structures of various shapes (trapezoidal, triangular, rectangular and thin-walled) and types (rubble mound, permeable, impermeable) that are designed to function together as a tandem breakwater. The effect of varying angle of incidence, relative submergence depth, and relative gap between the reef structure and primary breakwater on wave reflection and transmission are derived for the suggested tandem breakwater models. Among all the impermeable-type models, the thin-walled as reef structure designed at a distance in front of thin-walled as a primary submerged breakwater as a tandem is observed to perform efficiently in terms of energy dissipation and also offers an optimum wave transmission for both short and long wave conditions. Further, the permeable and rubble mound type trapezoidal tandem breakwater offers higher energy dissipation in comparison with all other breakwaters. In view of the design considerations and structural stability of submerged breakwaters, the addition of a reef structure acts as a defence system for the primary breakwater and also creates an energy dissipation zone that allows the shore dynamics to be preserved, making tandem models more effective in the harbour region. © IMechE 2022.Item Wave Energy Damping due to Coupled Porous Structure and Submerged Porous Plate(Editorial Board of Journal of Harbin Engineering, 2023) Athul Krishna, K.R.; Abdulla, K.; Karmakar, D.The present study investigates the wave-damping characteristics due to the combination of bottom-standing porous structure, submerged porous plate, and fully-extended porous structure of finite width using the small amplitude wave theory. The hydrodynamic characteristics such as reflection, transmission, and dissipation coefficients are determined to analyse the wave energy dissipation by the composite breakwater using the matched eigenfunction expansion method and orthogonal mode-coupling relation. Darcy’s law is incorporated to the flow through porous media. The composite breakwater system is investigated experimentally to validate and compare the numerical results with the physical model study. The complex porous effect parameter for the submerged plate is incorporated in the numerical analysis, which represents the reactance and resistance of the porous structure. The wave forces on the submerged plate and porous structure for the composite breakwater are investigated by considering the effects of changing parameters such as structural porosity, plate submergence, angle of incidence, width of the submerged porous structure and distance between the structures. The study illustrates that the increasing width of the fully-extended porous structure improves the performance of the breakwater system. The proposed study on the composite breakwater yields an useful information for wave energy attenuation, which can be designed and implemented in coastal and harbour areas to achieve wave tranquillity. © 2023, Harbin Engineering University and Springer-Verlag GmbH Germany, part of Springer Nature.Item Hydrodynamic analysis of an H-shaped pile-restrained floating breakwater combined with a pair of vertical barriers(Elsevier Ltd, 2024) Panda, A.; Karmakar, D.; Rao, M.The present study analyses the performance of a composite breakwater consisting of an H-shaped breakwater attached with vertical/inclined barriers held from both sides using the Multi-Domain Boundary Element Method (MDBEM). The study is performed to analyse the wave transformation characteristics (reflection and transmission), wave energy dissipation and horizontal wave forces due to the gravity wave-structure interaction. The hydrodynamic performance of the integrated breakwater is performed due to the effect of changing various structural properties such as porosity, width and depth of structural elements, relative spacing between breakwater and barrier, angle of incidence and the inclination of the barriers. The boundary conditions and the corresponding edge conditions are incorporated for each surface and interface and correlated with Green's function to solve the boundary value problem. The detailed study proposes the suitable dimensions of the structural elements of the breakwater for optimal performance. The application of inclined barriers over the vertical barrier in certain conditions for maximising wave reflection is presented and analysed to understand the effectiveness of the barrier inclination. The favourable barrier dimensions and the suitable relative spacing for deep water regions are discussed, and the effect of rigidity and porosity of the barriers are analysed to maximise breakwater performance in wave attenuation. On considering the suitable design parameters and structural stability, the composition of vertical/inclined barriers with an H-shaped pile-restrained floating breakwater serves as a protective component by encountering maximum wave force and dissipating considerable wave energy to provide an efficient solution in harbour protection. © 2024 Elsevier LtdItem Wave attenuation due to stratified porous structure in the presence of stepped seabed(Springer Nature, 2024) Varghese, A.; Krishna, K.R.A.; Karmakar, D.The wave transformation due to the stratified porous structures in the presence of stepped seabed at leeward side is analysed based on the small amplitude wave theory. The study is performed to analyse the effectiveness of both horizontal and vertical stratified porous structure for the wave attenuation in the nearshore regions using orthogonal mode-coupling relation and eigenfunction expansion method. The hydrodynamic coefficients such as wave reflection, transmission, dissipation, wave force acting and surface elevation are investigated for both horizontally and vertically stratified porous structures. The effect of change in the structural properties such as varying porosity, friction factor, structural width, angle of incidence and length between the porous structure and stepped seabed are examined. Thereafter, the comparative study is performed for both horizontally and vertically stratified porous structure in the presence of stepped seabed and the numerical results are validated with the results available in the literature. The present study illustrates that with the increase in step height, the wave damping efficiency is enhanced. In addition, the wave energy dissipation is observed more for horizontally stratified structure in the case of longer waves whereas vertically stratified structure is effective in dampening of shorter waves. Further, the wave reflection and transmission for vertically stratified structure is found to be more for same length between structure and stepped seabed. The stepped seabed in leeward side in combination with vertical and horizontal stratified porous structure is intended to be an effective solution for protection of coastal facility. © The Author(s), under exclusive licence to Sociedade Brasileira de Engenharia Naval 2024.Item Hydrodynamic performance of a hybrid floating breakwater-wave energy conversion system(SAGE Publications Ltd, 2025) Patil, S.B.; Karmakar, D.The study presents the hydrodynamic performance and wave energy conversion of a hybrid floating breakwater under the framework of small amplitude linear wave theory. The hybrid floating breakwater is composed of a partially liquid-filled rectangular-box type tank with built-in buoys connected to a Power Take-Off (PTO) (linear inductance generator) and is excited under regular wave conditions for (a) constrained roll motion, and (b) constrained surge, heave, and roll motion. The Boundary Element Method (BEM) is employed with the assumption of modest sloshing in the tank of the hybrid floating breakwater to estimate the hydrodynamic efficiency of the hybrid floating breakwater. Further, the experimental investigation on the Wave Energy Converter (WEC) capabilities and the hydrodynamic coefficients (wave reflection and transmission coefficients) are estimated for the excitation frequencies corresponding to nondimensional wavenumber. The present study reveals that the hybrid concept improves wave attenuation performance by 20%–35% compared to conventional floating breakwaters by increasing wave attenuation, damping and stabilizing the wave transmission coefficient (Formula presented) within (Formula presented). The experimental investigation shows that hybrid floating breakwater attaints its floating stability for the depth 15 – 25% of partially filled fluid for which the proposed design as floating breakwater as well as WEC system is achieved for a wide range of excitation frequencies. Furthermore, the hybrid floating breakwater functions as a barrier which is noted to be capable of significantly attenuating incoming progressive waves below the predetermined threshold values of wave attenuation characteristics, in addition to converting wave energy. © IMechE 2025. This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access page (https://us.sagepub.com/en-us/nam/open-access-at-sage).