It is really appreciable that the number of researchers working in water wave related problems has been increasing day-by-day in India. Indian researchers, experienced and young alike, have been persuading research on various topics in coastal and ocean engineering. In this context, an informal group of researchers was formed in February 2022 for discussion and dissemination of knowledge. At present, there are more than 80 members in this group. If you are interested in joining this group, please drop an email to swaroop@iitg.ac.in

UPCOMING LECTURE

August 20, 2024, 4:30 PM, Topic: On an Important aspect of Hydrodynamics and a Study of Wave Interaction with a Porous Curved Barrier

Speaker: Prof. Sudeshna Banerjea, Professor, Department of Mathematics, Jadavpur University, Kolkata

(Abstract: The talk will be delivered in three parts. In the first part an important contribution of Sir Asutosh Mookerjee, an eminent educationist, mathematician, jurist and barrister, to the basic equations of hydrodynamics for general motion of fluid will be discussed.  In the second part, numerical solution of hypersingular integral equation based on boundary element method will be presented. Finally, the effect of a circular arc shaped porous barrier with non-uniform porosity on water waves will be discussed.)

Till now, the following online talks (Ten regular and two special) have taken place:

1.  Mathematical Methods Associated with Ursell's Partially Immersed Thin Vertical Barrier Problem (June 24, 2022)

     - Prof. B.N. Mandal, Retired Professor, Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata

2. Mathematical Modeling of Oscillating Water Column Wave Energy Converter Device in Real Sea Conditions (August 25, 2022)

   - Dr. Santanu Koley, Department of Mathematics, Birla Institute of Technology and Science - Pilani, Hyderabad Campus

(Abstract: Out of various renewable energy resources available, ocean wave energy is one of the key resources in the field of green energy. If properly utilized, ocean wave energy can fulfill the demand of around 30% of world electricity in near future. Out of various wave energy converter technologies available till date, OWC-WEC (Oscillating Water Column Wave Energy Converter Device) is the most widely used device to convert the ocean wave power into electricity. Although rigorous model tests were done in this field, not much progress is made on developing appropriate numerical models to deal with the hydrodynamics of OWC-WEC devices in real sea conditions. In my talk, I will firstly discuss the BVP (boundary value problem) associated with the regular waves interaction with the OWC device. Following this, the solution methodology of the BVP using the BEM (boundary element method) will be discussed. The case of irregular incident waves and associated techniques to analyze the performance of OWC devices in regional ocean environments will be highlighted. Following this, the time-domain analysis will be discussed. In the last part of the talk, the modeling of OWC device using multiphase CFD (Computational Fluid Dynamics) based tool will be discussed.)

3. Tsunami waves -  Influence of Ocean Water Compressibility (October 14, 2022)

   - Dr. Santu Das, Physical and Computational Sciences Division, Institute of Advanced Study in Science and Technology, Guwahati

(Abstract: Coastal areas, including both land-mass and water, throughout the world have been the most significant part of human civilization as more than 600 million people live in a coastal region within 10 m of elevation, which account for 10 per cent of the world population. On top of that, approximately 2.4 billion people, around 40 per cent of total world population, live within 100 kilometers of the coastline. Any threat to the coastal region thus possesses an enormous amount of potential damage to the world population, a country's economy, natural food resources, to name a few. Among all the natural calamities, tsunamis possess a grave threat which is evident from the recent accounts of destruction caused by 2004 Indian Ocean, 2011 Tohoku Oki, 2018 Sulawesi and Palu tsunami, which are caused following submarine earthquakes. Predicting and simulating tsunami waves is of obvious importance in providing a reliable warning system. Numerical simulations play an important role, and very sophisticated models have been developed. In particular, the inclusion of compressibility allows for the simulation of acoustic gravity waves, which have been proposed as a method for early warning although the method is in dispute. However, it has also been shown that a tsunami model based on a compressible ocean is more accurate than a model with an incompressible ocean. It is also essential to simulate different kinds of motions of the ocean bottom. An appropriate model taking the water compressibility into account and that can cater to such changes in the initial time-domain displacement is of paramount importance. In this talk, we will address this issue with the help of a simplified mathematical model under the assumption of linearized water wave theory. The objective is to derive an analytical expression for ocean surface displacement in frequency domain, and utilize this solution to simulate the surface wave profile in time-domain. Due emphasis will be laid on the mathematical techniques employed.)

4. Blocking Dynamics of Flexural Gravity Wave and Allied Solutions Near the Blocking Points (February 24, 2023)

-- Dr. Susam Boral, Recent PhD from Department of Ocean Engineering and Naval Architecture, IIT Kharagpur

(Abstract: There has been a significant development in the investigation of surface gravity wave interaction with ice sheets or very large floating structures, referred to as the flexural gravity wave, due to its wide applicability in polar as well as cold region science and technology. Recent studies revealed that a complex phenomenon, namely wave blocking, occurs in the flexural gravity wave due to the vanishing of group velocity for certain values of compressive force and frequency under the assumption of the linearized theory of water waves and small amplitude structural response. Noticeably, the roots of the dispersion relation coalesce at the blocking points, and multiple propagating waves in the plate-covered surface mode exist based on wave frequency. Moreover, the structure is often supported on an elastic foundation for station-keeping purposes and to mitigate the structural responses. Thus, in my talk, I will mention the role of the elastic foundation in the occurrence of flexural gravity wave blocking in the presence of viscous damping. Further, I will discuss the surface gravity wave interaction with an array of floating flexible plates resting on an elastic foundation in the context of blocking dynamics. Here, emphasis will be given for understanding the impact of multiple propagating waves in plate-covered surface mode on scattering coefficients and plate deflection. On the other hand, I will speak about the wave characteristics near the blocking point in a simple case involving a plate resting on an elastic foundation, i.e., in the context of flexural wave propagation. It is observed that the amplitude of flexural wave satisfies a hyper-Airy differential equation near blocking points, whose asymptotic solution is obtained in terms of the fourth-order Airy function. Besides, the obtained analytical result is validated with linear time-domain simulation.)

5. Some Problems on Radiation and Scattering of Waves by Horizontal Flat Plates Submerged in a Multi-layered Fluid (August 11, 2023)

-- Dr. Arijit Das, Recent PhD from Department of Applied Mathematics, Calcutta University

(Abstract: In this lecture, two classes of problems will be discussed. One is a radiation problem by a circular disc submerged in the lower layer of a three-layer fluid and the other is a scattering problem by an elliptic disc submerged in a two-layer fluid. In the first problem, the three-dimensional problem of wave radiation due to the heaving motion of the disc is considered using linear water wave theory. The problem is first reduced to solving a hypersingular boundary integral equation. This integral equation is then reduced to a system of one-dimensional Fredholm integral equations of the second kind. The solution of each integral equation is associated with a radial component of the difference of potential function across the plate. The solution of these integral equations has been used to compute added mass and damping coefficient numerically.  In the second problem, an elliptic coordinate system is used to solve the three-dimensional problem analytically. The fluid region is divided into a number of subregions. By separating variables, velocity potential in each region is expressed in terms of a series of Mathieu and modified Mathieu functions of real argument. Matching conditions and eigenfunctions' orthogonal properties provide solutions for the fluid velocity potentials. Numerical results are presented for the wave-induced forces and moments. The effect of variations in the depth of submergence of the disc, angle of incidence of the incoming wave, density ratio of the fluid, and aspect ratio of the disc on these physical quantities have been analyzed. Also, I will discuss my other research work briefly.)

- Dr. Koushik Kanti Barman, Post-Doctoral Research Fellow, Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung, Taiwan

(Abstract: The main objective of this talk is to investigate the two-layer wave propagation and interaction with various structures by considering various bottom profiles in a two-layer fluid within the framework of linear water wave theory. The first part explains the two-layer wave propagation in the context of practical ocean waves. In various bottom cases, the water wave flow is analysed by comparing it with realistic situations as far as possible, and the effectiveness of the present model is discussed for ocean engineering problems. The next part considers wave interaction with a few geometric structures with various configurations, e.g., (i) a single-chamber porous structure, (ii) a two-chamber structure with different porosity and friction, etc. The subsequent study explores the wave interaction problem and illustrates various hydrodynamic coefficients. This talk establishes a physical-mathematical connection between physical oceanography and ocean engineering.)

- Dr. Vijay KG, Assistant Professor, Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai

(Abstract: A detailed investigation is essential to ensure the integrity of any engineering work. Both the numerical and experimental studies are mandated for a variety of reasons such as the overall project cost, novelty of the concept, stochastic nature, uncertainty quantification, etc. As we know to demonstrate any proof of concept and to implement it in a real field, we must pass the required Technology Readiness Level (TRL). Numerical analysis comes with a certain set of advantages and disadvantages, and so is experimental analysis. In this talk, we discuss various water wave problem analyses using the boundary integral equation (BIE). The leverage and shortfall of using linear potential flow theory are taken up. Besides, the recent experimental investigations and the associated challenges are discussed.)

8. Advancing Coastal Engineering: Recent Insights into Water Wave Scattering by Various Structures (April 19, 2024)

- Dr. Biman Sarkar, Assistant Professor, Department of Mathematics, Swami Vivekananda University, Barrackpore, Kolkata

(Abstract: The key objective of the talk is to explore recent studies on water wave scattering by various structures, including permeable walls, porous barriers, and bottom-standing breakwaters. In this talk, we delve into four recent studies on water wave scattering, each offering unique insights into wave-structure interactions and their implications for coastal engineering. First, we explore the scattering of surface waves by permeable vertical walls with differing apertures, where a multi-term Galerkin technique is employed to approximate solutions and numerical estimates for reflection and transmission coefficients are obtained. Moving on, we investigate oblique wave scattering by thin multiple surface-piercing porous barriers, considering the influence of barrier permeability and bottom surface thickness on wave behaviour. Next, we delve into a breakwater model analyzing wave propagation over an asymmetric rectangular trench, employing eigenfunction expansion and Galerkin techniques to solve integral equations and validate numerical results against existing literature. Finally, we examine the scattering of normal incident waves by single and dual inverse type bottom standing breakwaters, focusing on the comparison of breakwater configurations and the effects of profile geometry on hydrodynamic quantities such as reflection and transmission coefficients. Through this comprehensive overview, we aim to provide valuable insights for the design and application of coastal structures, addressing challenges and advancing our understanding of wave-structure interactions.)

9. Analyzing Wave-Structure Interaction: Numerical Approaches and Challenges (May 17, 2024)

- Dr. K. Panduranga, Assistant Professor, Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology - Andhra Pradesh

(Abstract: The talk focuses on a class of wave-structure interaction problems that arise in the ocean and coastal engineering, with particular emphasis on
 1. developing various numerical tools to deal with surface gravity wave interaction with porous and flexible structures under the assumption of linearized wave-structure interaction theory,
 2. investigating various physical phenomena associated with wave scattering by porous and flexible structures for a variety of wave and structural parameters.

The class of physical problems analyzed in the present study are handled for solutions using the boundary element method, integral equation techniques (closed form
 solution), coupled boundary element finite difference method, etc. These solution methodologies are very effective and efficient to deal with structures having complex shapes and configurations.                     Further, in some instances, the effect of bottom undulations on the wave scattering is analyzed. For the undulated bottom case, major emphasis is placed on analyzing the occurrences of Bragg resonance phenomena. Further, the effect of structural porosity, viscoelastic damping parameter, and shape parameters of the seabed on shifting the resonance band away from the primary and
secondary Bragg values is analyzed. For wave scattering by thick and thin porous structures, the scattering coefficients, such as the reflection, transmission, and dissipation coefficients, are analyzed                      to study the effectiveness of these structures in dissipating the incoming wave energy. Further, a detailed analysis is carried out to mitigate the wave forces on the caisson breakwater using multiple                          slatted screens placed in front of the breakwater. Efforts are put into the optimum number of slatted screens and optimal positioning of slatted screens with respect to the position of the
breakwater. For floating flexible plates, the effect of in-plane compressive force on the structural deflection and buckling phenomena is analyzed. Moreover, the effect of the viscoelasticity of the floating                     plate to dissipate the incoming wave energy is discussed. In all the problems, energy balance relations are derived and are used to analyze the amount of wave energy dissipation by the porous and                           viscoelastic structures. Moreover, numerical convergence of the BEM-based solutions is provided, and certain computational results are validated with experimental and  analytical results available in the literature.

 Keywords: Boundary element method; Abel integral equation; Surface gravity waves; Flexible structure; Porous structures; Viscoelastic plate; Wave scattering; Bragg resonance.)

10. The Solution of a Hypersingular Integral Equation over an Elliptic Disc and Applications to Water Wave Problems (July 8, 2024)

- Dr. Rupanwita Gayen, Associate Professor, Department of Mathematics, IIT Kharagpur

(Abstract: Often in scattering and radiation theories, two-dimensional singular integrals arise over circular or elliptic regions. So far, formulas either for evaluating Cauchy principal value integrals over circular and elliptic regions or for computing hypersingular integrals over circular regions are available. This has motivated us to derive a formula that evaluates the dominant part of a hypersingular integral equation that appears in a variety of physical problems involving an elliptic disc in terms of trigonometric and associated Legendre functions $P_ν^μ$. Then we have proposed a spectral method for the solution of a class of hypersingular integral equations over an elliptic disc. Using these results we have investigated the problems of the radiation and scattering by an elliptic disc submerged in infinite-depth water. Initially, we have validated the formulation against published results for a circular disc. Once it is found satisfactory, we have conducted a rigorous parametric study to investigate the impact of the submerged depth and the geometry of the disc on several physical quantities such as added mass, damping coefficient, surface elevation, differential cross-section, and exciting forces.)

GUEST TALKS:

1. Negative energy waves in hydrodynamics (September 22, 2022)

   - Prof. Yury Stepanyants, School of Mathematics, Physics and Computing, University of Southern Queensland, Australia

(Abstract: The concept of “negative energy waves” (NEWs) is discussed in application mostly to the waves in fluids. Historically, the existence of oscillators with negative energy was noted first by H. Lambin his work of 1907. A process involving NEWs was described by W. Heisenberg in his PhD Thesis of 1923. L. Chu was the first who explicitly introduced the term NEWs in 1951 in electronics. Later, this concept has been introduced in hydrodynamics (B. Benjamin, 1963) and plasma physics (Kadomtsev et al., 1964). It is also used in quantum field theory (after Dirac’s discovery of positrons in 1928) and general relativity (after Hawkings’s discovery in 1974 of specific radiation from black holes). In essence, NEWs can exist in non-equilibrium media capable to release energy in the form of waves. In hydrodynamics and acoustics, the most common source of such waves is a fluid flow that can potentially be unstable.

 In this presentation, the concept of NEWs will be briefly outlined. An explanation will be given of how NEWs can lead to instabilities due to dissipation or coupling with waves of positive energy. Specific problems include wave generation in shear flows due to dissipative instability and radiative instability when internal waves are radiated from a shear flow due to coupling with NEWs. Nonlinear phenomena related to NEWs will be also considered, including the explosive instability in a resonant wave triplet and amplification of solitary waves. A few hydrodynamic laboratory experiments involving NEWs will be described. Some estimates in application to oceanic waves will be given.)

2. Time-dependent problems for floating plates (September 23, 2022)

   - Prof. Mike Meylan, School of Information and Physical Sciences, The University of Newcastle, Australia

(Abstract: Two different time-dependent problems for floating elastic plates will be discussed
. The forcing will be due to a point force or incident wave, and the solution will be found by the superposition of the frequency domain solutions. Various solutions will be presented.)