Waves-in-ice measurements are presented, obtained with a shipborne stereoscopic camera system in the Antarctic marginal ice zone during an extreme polar cyclone. Data show large waves, significant wave height ≈5m 45 km in from the ice edge in 100% sea-ice comprised of pancake floes (60%) and interstitial frazil ice (40%), and linear wave decay (≈0.72%km^-1). The dominant component of wave energy shifts towards longer periods as waves propagate deeper into sea ice, the spectrum becomes narrower in frequency and broader in direction. Individual waves up to 8m high are observed ≈50 km in from the sea-ice edge, the largest wave measured in 100% sea-ice, but consistent with occurrence probability predicted by linear wave theory. Measurements reveal that wave-in-ice interactions remain intense in 100% sea-ice.

The growing effects of global warming and rising sea levels have increased interest in studying the interaction between gravity waves and floating ice sheets in Polar Regions. This area of research is analogous to the interaction between surface gravity waves and very large floating structures (VLFSs) since both ice sheets and VLFSs are modeled as thin elastic plates. Examining the hydrodynamic performance of these floating structures is essential due to their widespread application in the utilisation of ocean space for both humanitarian and technical purposes. A lot of current research is focused on wave-structure interaction problems with man-made seabed structures for technical purposes. On the other hand, not as much research has been done to understand how natural features like sand ripples and bars affect flexural gravity waves. The interaction of incident progressive waves with undulated sandbars results in resonant conditions leading to the formation of triads. The multi-scale method is used to derive the envelope equations for flexural gravity waves, which are subsequently used to understand the role of detuned frequency to account for the Bragg resonance. The study reveals in the presence of a detuned frequency the occurrence of a cut-off frequency, below which wave reflection is monotonic and above which it becomes oscillatory. However, Bragg scattering occurs in the presence of multiple sinusoidal patches, having harmonic and sub-harmonic peaks in wave reflection. Subsequently, the scattering coefficients are analysed in the context of flexural gravity waves across a spectrum of physical parameters involving the floating ice sheet and sea bed configurations. Further studies are being attempted to enhance the understanding of flexural gravity wave propagation over sinusoidal beds of varied configurations.

In the present study, the linear theory for flexural gravity waves impinging obliquely on dual inverse Π-type breakwaters, which are bottom standing structures consist of a pair of thin vertical plates extending upward, is examined in finite fluid-depth. The study’s primary aim is to investigate the effect of adding two vertical thin plates with a rectangular structure beneath an ice-covered water surface. The ice cover is modeled as a thin, flexible plate of uniform thickness, assuming the Euler–Bernoulli beam equation governs its motion. To tackle this boundary value problem, a system of Fredholm-type integral equations is derived, utilizing mode-coupling relations. The multi-term Galerkin method is employed to solve the equations, effectively addressing the half singularities at the sharp submerged edges of the thin plates. Chebyshev polynomials, multiplied by associated weight functions, are selected as the basis functions for the Galerkin technique, ensuring convergence of the solution. This approach enables a detailed exploration of wave interaction with the breakwater-ice system under a variety of structural parameters. The study examines key physical quantities, including the reflection coefficient, transmission coefficient, and horizontal wave force. These quantities are computed and analyzed across various configurations to understand their behavior and sensitivity to structural changes. To ensure the accuracy and reliability of the results, comparisons are made with existing studies for several limiting cases, confirming the validity of the findings. A comparative analysis between inverse Π-type and conventional rectangular breakwaters reveals that adding thin plates on either side of a rectangular breakwater significantly enhances its wave-scattering efficiency. The study reveals that Bragg resonance effects depend on both the thickness of the ice sheet and the submergence gap between the ice-covered surface and the breakwater. The ice cover's thickness, in particular, plays a critical role in improving the breakwater’s performance: as the ice sheet thickness increases, the surface displacement amplitude in the transmitted wave region diminishes, while the wavelength remains unchanged. Furthermore, the study demonstrates that the addition of these thin plates results in a marked reduction in surface displacement amplitude within the transmitted region, thus creating an ideal tranquil zone. These results highlight the potential of dual inverse Π-type breakwaters to effectively scatter waves while offering significant benefits in coastal protection, particularly in ice-covered regions. The findings offer practical insights for the design and deployment of more effective wave-interaction structures in real-world marine environments.

This study examines the scattering of obliquely incident water waves by a horizontal floating flexible, permeable viscoelastic membrane in finite water depth and placed over variable rigid seabed topography in the context of three-dimensional linear water wave theory. The physical problem when a partially reflection vertical seawall is placed downstream of the membrane is also considered. The problem is studied under the potential water wave theory assumption, with two types of variable bottom topographies. The eigenfunction expansion-boundary element method is used to derive the different results based on different physical and structural parameters. Also, the finite difference method is coupled with the boundary element method to handle the membrane's dynamic boundary condition containing a second-order derivative. The accuracy of the numerical results is verified by deriving and using energy balance relations for water wave scattering by floating flexible porous membrane and when a vertical partial reflection wall is situated downstream of the membrane. This study examines the impact of sinusoidally varying bottom topography, membrane's damping parameter, and incident wave heading angle on the different wave transformation characteristics. The results of the present investigation indicate that the viscoelastic characteristics of the membrane contribute to extending its lifespan and can be utilized to create a calm zone on the lee side of the membrane barriers.

This talk explores the behavior of nonlinear hydroelastic waves in a channel with variable bottom topography. Previous studies have predominantly used linear potential flow theories to analyze flexural-gravity wave interactions with varying bathymetry, effectively predicting wave characteristics induced by small bottom obstructions. However, these theories are limited in scope when larger obstructions or complex bottom profiles are considered, highlighting the need for a nonlinear approach. In this study, we present a fully nonlinear formulation to analyze steady flow in a channel covered by an elastic sheet with a rectangular bottom obstruction. The height and length of the obstruction are varied extensively to capture a wide range of conditions. Using the integral hodograph method, we derive a nonlinear solution by constructing the fluid's complex velocity potential, which directly incorporates the velocity magnitude at the interface between the fluid and the elastic sheet. The ice sheet is modeled as a thin hyper-elastic shell using Cosserat theory, and its equilibrium with the fluid flow is ensured by matching pressures at the interface. This coupling of the elastic sheet and liquid flow dynamics leads to a system of nonlinear equations governing the velocity magnitude at the interface, solved numerically. The results reveal the interface shape and bending moments within the ice sheet, offering new insights into hydroelastic wave behavior over complex bathymetry.

In this paper, we examine the generation of flexural-gravity waves induced by a forced, time-harmonic oscillatory pressure applied to the ice-covered surface of a uniform, finite-depth ocean. Using Euler-Bernoulli's beam equation, the floating ice sheet is modeled as a thin elastic plate. The effect of in-plane compressive forces acting on the ice is also considered. Employing linear wave theory, the problem is presented as an initial boundary value problem and solved using Laplace and Fourier transforms to derive the mathematical expression for free surface elevation in terms of infinite integrals. These integrals are evaluated asymptotically for large time and distance using the stationary phase method. The deflection of the floating ice sheet is graphically presented to illustrate variations caused by key non-dimensional parameters, such as flexural rigidity, compressive force, uniform current speed, and the angular frequency of the oscillatory pressure. Additionally, the group velocity and phase velocity of flexural-gravity waves are derived from the dispersion relation and visualized through diagrams. The results reveal that compressive forces and current speed significantly influence wave amplitude, amplifying the oscillatory behavior, while the flexural rigidity of the elastic plate and the angular frequency of the applied pressure substantially affect the plate's deflection.

This study presents a dynamic analysis of viscoelastic floating membranes subjected to random wave conditions over variable bathymetry. To analyze the effect of random sea conditions, the JONSWAP wave spectrum, ideal for representing developing or rough seas with its sharper peak in wave energy distribution, is employed, while the Pierson-Moskowitz (PM) spectrum is applied as a special case when the JONSWAP shape parameter $\gamma=1$, allowing for the study of both typical and extreme sea states. The mathematical model, developed within a Cartesian coordinate framework under linear water wave theory, examines the interaction of water waves with a flexible, permeable viscoelastic membrane positioned over undulating seabed topography of varying shoal heights in finite water depth. A numerical approach coupling the finite difference method with the boundary element method is used to solve the problem, accurately handling the membrane’s dynamic boundary conditions, including second-order derivatives. The analysis explores the effects of sinusoidal seabed variations, membrane damping properties, and the spectral characteristics of the incident waves on various hydrodynamic parameters such as wave reflection, transmission, scattering, and force. Key findings highlight the significant role of proportional material damping in wave dissipation, with local peaks in viscoelastic behavior observed at natural frequencies. The results also demonstrate how the membrane’s viscoelastic properties enhance energy dissipation, particularly when interacting with complex bathymetry and realistic wave spectra, leading to the outward dispersion of incoming waves around finite membranes. The study concludes that viscoelastic floating membranes can extend their operational lifespan by improving durability while creating calm zones on the lee side, making them effective for coastal protection and wave energy dissipation. The adaptability of the membrane under varying bathymetric and wave conditions demonstrates its potential as a practical solution for managing coastal wave impacts. These findings offer valuable insights for optimizing the design of viscoelastic floating membranes in engineering applications, particularly where variable seabed topography and random wave conditions must be accounted for.

The phenomena of Bragg reflection were first observed while analyzing the diffraction of x-rays by crystals in solid-state physics. An analogous phenomenon was observed due to the interaction of surface gravity waves with multiple periodic sea bed undulations formed due to sandbars, submerged breakwaters, or trenches. Various theoretical and experimental studies on gravity wave interaction with sinusoidal sea beds, including sandbars, demonstrate that the maximum Bragg reflection occurs when the length of the undulating sea bed/structures is half the wavelength of the normally incident waves. Various types of periodic bottom bed profiles, such as submerged breakwater/trenches, are proposed to create a tranquillity zone in the marine environment or reduce the wave loads on coastal infrastructures. The scattering coefficients are obtained numerically to examine the wave characteristics for various problems, as very few problems could be handled analytically for solutions. In the present study, the gravity wave dispersion relation in finite water depth is solved analytically and used to examine the Bragg scattering of surface gravity waves over an array of submerged trapezoidal breakwaters. Here, a closed-form solution is obtained for the Ye equation associated with the physical problem, which is used to investigate the wave scattering by a single trapezoidal breakwater. Subsequently, the matrix transfer method is used to obtain an analytic expression for the scattering coefficients linked to Bragg scattering by the array of submerged trapezoidal breakwaters. Various physical parameters, such as the scattering coefficients and free surface elevation, are computed for different parametric values of breakwater configurations and wave parameters. Additionally, time-dependent simulations of free surface elevation are exhibited for a better understanding of the wave transformation. The present approach is being generalized to study Bragg scattering of surface waves by membrane/ice-covered free surface over submerged breakwaters. This research contributes a foundational analytical framework for future studies in the field, offering insight into the application of Bragg reflection in Ocean Engineering and advancing the understanding of wave-seabed interaction dynamics.

Antarctic sea ice is crucial to Earth's climate, mediating exchanges between the atmosphere and ocean. The size and shape of sea ice floes influence ice concentration, albedo, and wave propagation through ice-covered waters. However, the remoteness and extreme weather of the Antarctic marginal ice zone (MIZ) limit in-situ observations, restricting our understanding of its mechanical and thermodynamic processes. To address this knowledge gap, we developed the Ocean-Sea Ice-Atmosphere (OSIA) Underway Observatories, initially deployed as a prototype on the South African icebreaker S.A. Agulhas II and now installed aboard the RSV Nuyina. This system employs arrays of cameras with various optical sensors to continuously monitor extensive sea ice regions, providing high-resolution spatial and temporal data. We used computer vision techniques for the segmentation of sea ice to extract ice concentration and floe size distribution from the images. Various automated segmentation methods, including traditional algorithms and advanced deep learning models, were evaluated. Their effectiveness was assessed by comparing their results to a manually segmented benchmark. Applying these methodologies, we examined the distributions of floe size from three expeditions across the Southern Ocean during the austral winters of 2017, 2019, and 2022 aboard the S.A. Agulhas II. Despite all expeditions occurring in the same season, significant interannual variability was observed in sea ice characteristics. The ice went through a process of formation, merging, breakup, and re-merging. A comparison with the wave height statistical framework supports the observed sea ice variability. During the initial phases of ice formation, the floe size distributions mirror the wave heights, but they diverge when larger merged floes are present. Our results show that sea ice imagery combined with advanced segmentation techniques can reveal details about the Antarctic MIZ, improving our understanding of its variability and underlying processes.

This study uses linear stability analysis in the two-dimensional Cartesian coordinate system to analyze the flow dynamics underneath a large floating elastic plate over a slippery surface in the presence of external shear. For both viscous and inviscid flows, the Orr–Sommerfeld equation and the Rayleigh equation, respectively, are obtained using normal mode analysis. The Chebyshev collocation method is incorporated to solve both equations numerically. Analysis of the growth rate and energy distributions is performed to understand the flow instability at various flow and structural parameters. The study reveals that the flow below the floating elastic plate dampens for larger uniform mass and structural rigidity in the viscous fluid. On the other hand, structural rigidity has no effect on flow stability in the case of inviscid flow. However, the plate of larger uniform mass stabilizes the growing disturbance generated due to the externally imposed shear at the surface of the plate. The present study is analogous to the simple geographical model of external shearing on the surface of a large ice cover zone caused by atmospheric air. This study can be extended to understand the flow stability below other large floating structures like a floating island and a floating airport.

The problem of submerged body motion in a frozen channel is considered. The fluid in the channel is assumed to be inviscid and incompressible. Fluid flow is the potential. The ice cover has non-uniform compression along the principal coordinates. The damping of hydroelastic waves generated by the motion of submerged body is modeled by taking into account porosity of ice. The submerged body is modeled as a dipole, the potential of which is determined using mirror images from the channel walls. The main problem of the submerged body motion at constant speed along the central line of the channel is considered. Two subproblems are addressed: comparison of damping effects of the porosity and viscosity of ice and investigation of effects of symmetrically variable ice thickness relative to the central line of the channel. It was found that the most important compressive stress is the stress in the direction of the motion of the submerged body. The speed of the body, which was subcritical for uncompressed ice, may become critical or supercritical. Compressive stresses perpendicular to the direction of motion do not qualitatively change the character of the ice response. These stresses, in combination with compressive stresses along the direction of motion, strengthen the effect of the latter, making the transition from subcritical to supercritical regime faster.