Propagation Of Flexural Gravity Waves Research Articles

Flexural-gravity wave dissipation under strong compression and ocean current near blocking point

Flexural-gravity wave propagation in a dissipative sea-ice under the influence of strong compressive force and ocean current is studied. The dissipation is caused by the viscous parameter introduced in the icecovered boundary condition and results in the complex dispersion relation. The complex roots are computed using the wellestablished ML method where the initial choice is made from the roots of the dispersion relation of the non-dissipative counterpart, which poses difficulties due to the wave blocking, a phenomenon where progressive wave mode collide and wave energy propagation stops. The shift in the central wavenumber of an initial Gaussian disturbance as it propagates through the dissipative compressed ice is shown following the method proposed by Muschietti and Dum (DOI:10.1063/1.860877) when the initial central wavenumber matches and/or around the blocking wavenumber. The transformation of the location and decay of maximum amplitude and group velocity over time is shown. The effects of ice thickness and in-plane compression are also demonstrated. A small decrease in central wavenumber is shown, while the group velocity increases/decreases around the primary/secondary blocking wavenumber. Further extensive research on this method is required to incorporate the effects of other modes corresponding to the frequency of the initial central wavenumber.

Simulation of Flexural-Gravity Wave Propagation for Elastic Plates in Shallow Water Using Energy-Stable Finite Difference Method with Weakly Enforced Boundary and Interface Conditions

Simulation of Flexural-Gravity Wave Propagation for Elastic Plates in Shallow Water Using Energy-Stable Finite Difference Method with Weakly Enforced Boundary and Interface Conditions

Spacetime modulation in floating thin elastic plates

We consider the propagation of flexural-gravity waves in thin elastic plates floating atop nonviscous fluids, e.g., seawater, which are governed by a partial differential equation with Laplacian and tri-Laplacian terms. We investigate the effect of time modulation as well as spacetime modulation on thin floating elastic plates and show the peculiarity of the phenomena of the $k$-band gap and the rotated $k$-band gap in the context of flexural-gravity waves. This makes possible floating plates with nonreciprocal features and behaving as elastodynamic analogs of luminal electromagnetic metamaterials, with exotic applications in enhanced control of ocean waves, such as filtering devices, unidirectional acoustic propagation, and isolation effects and energy harvesting in maritime engineering.

Parity-Time Symmetry and Exceptional Points for Flexural-Gravity Waves in Buoyant Thin-Plates

We derive and apply a transfer matrix method (M-matrix) coupling liquid surface waves and flexural-gravity waves in buoyant thin elastic plates. We analyze the scattering matrix (S-matrix) formalism for such waves propagating within a Fabry-Perot like system, which are solutions of a sixth order partial differential equation (PDE) supplied with adequate boundary conditions. We develop a parity-time (PT)-symmetry theory and its applications to thin elastic floating plates. The sixth order PDE governing the propagation of these waves leads to six by six M and S matrices, and results in specific physical properties of the PT-symmetric elastic plate systems. We show the effect of geometry and gain/loss on the asymmetric propagation of flexural-gravity waves, as well as a Fano-like line-shape of the reflection signature. Importantly, we show the possibility of obtaining coherent perfect absorber-laser (CPAL) using simple thin structures.

An investigation of the properties of flexural-gravity wave propagation in a coupled submerged and floating plate system

The propagation of flexural-gravity waves in a coupled submerged and floating plate system is studied, and the complex flexural gravity wave propagation properties are investigated in the frequency and time domain, The system exhibits two modes of propagation analogous to the surface and internal waves in a two-layer fluid. The effect of the plate properties on the phase velocities of both the faster (floating plate in general) and the slower (submerged plate in general) modes are analysed in detail. Both modes exhibit complex properties, including waves with negative kinetic energy and points of blocking at which no energy can propagate. They also show complex coupling and energy transfer in the time-domain. Furthermore, the dependency of the blocking frequency and the critical opposing current is analysed in both the shallow and deep water limits. The occurrence of blocking in the internal mode under a specific constraint is also demonstrated. As a special case, the influence of the submerged plate’s position and compressive force on the dynamics of the free surface flexural-gravity wave blocking is studied. The characteristics of the phase speed in both modes are studied, and the occurrences/non-occurrences of optima are mathematically proved. Some of the analytic results are illustrated by time-domain simulations which illustrate the complex wave propagation phenomena of this system.

Flexural-gravity wave motion in the presence of shear current: Wave blocking and negative energy waves

Flexural-gravity wave propagation under the action of a compressive force and in the presence of flow vorticity is studied under the framework of linear water wave theory. The occurrences of wave blocking which is analogous to the free surface gravity wave propagation against an opposing current as well as light wave propagation in curved space-time near a black hole are shown to exist. Moreover, negative energy waves that are responsible for making the total energy of the fluid flow less than that without the waves are also analyzed. The effects of compressive force, Froude number, and vorticity on the existence of negative energy waves as well as the occurrence of flexural-gravity wave blocking are graphically illustrated. The variation in group velocity for different flow parameters such as the vorticity, the Froude number, and the compressive force is analyzed. Time-dependent simulations of the propagation of wave packets are calculated.

Dynamics of flexural gravity waves: from sea ice to Hawking radiation and analogue gravity.

The propagation of flexural gravity waves, routinely used to model wave interaction with sea ice, is studied, including the effect of compression and current. A number of significant and surprising properties are shown to exist. The occurrence of blocking above a critical value of compression is illustrated. This is analogous to propagation of surface gravity waves in the presence of opposing current and light wave propagation in the curved space-time near a black hole, therefore providing a novel system for studying analogue gravity. Between the blocking and buckling limit of the compressive force, the dispersion relation possesses three positive real roots, contrary to an earlier observation of having a single positive real root. Negative energy waves, in which the phase and group velocity point in opposite directions, are also shown to exist. In the presence of an opposing current and certain critical ranges of compressive force, the second blocking point shifts from the positive to the negative branch of the dispersion relation. Such a shift is known as the Hawking effect from the analogous behaviour in the theory of relativity which leads to Hawking radiation. The theory we develop is illustrated with simulations of linear waves in the time domain.

Wave interaction with multiple articulated floating elastic plates

Flexural gravity wave scattering by multiple articulated floating elastic plates is investigated in the three cases for water of finite depth, infinite depth and shallow water approximation under the assumptions of two-dimensional linearized theory of water waves. The elastic plates are joined through connectors, which act as articulated joints. In the case when two semi-infinite plates are connected through a single articulation, using the symmetric characteristic of the plate geometry and the expansion formulae for wave-structure interaction problem, the velocity potentials are obtained in closed forms in the case of finite and infinite water depths. On the other hand, in the case of shallow water approximation, the continuity of energy and mass flux are used to obtain a system of equations for the determination of the full velocity potentials for wave scattering by multiple articulations. Further, using the results for single articulation and assuming that the articulated joints are wide apart, the wide-spacing approximation method is used to obtain the reflection coefficient for wave scattering due to multiple articulated floating elastic plates. The effects of the stiffness of the connectors, length of the elastic plates and water depth on the propagation of flexural gravity waves are investigated by analysing the reflection coefficient.

Interaction of flexural gravity waves with shear current in shallow water

In the present study, the effect of shear current on the propagation of flexural gravity waves is analyzed under the assumptions of linearized shallow-water theory. Explicit expressions for the reflection and transmission coefficients associated with flexural gravity wave scattering by a step discontinuity in both water depth and current speed are derived. Further, trapping and scattering of flexural gravity waves by a jet-like shear current with a top-hat profile are examined and certain limiting conditions for the waves to exist are derived. The effects of change in water depth, current speed, incident wavelength and the angle of incidence on the group and phase velocities as well as on the reflection and transmission characteristics are analyzed through different numerical results.

Scattering of flexural gravity waves by abrupt change in water depth

AbstractThe surface gravity waves originated in the open sea interact with floating flexible structures and penetrates into the region covered by the flexible structures to generate flexural gravity waves. In the recent decades, there is a significant interest in analyzing the propagation of flexural gravity waves which find applications in both marine technology for ocean space utilization and polar engineering in the marginal ice zone (see Chen et al. (2006), and Porter and Porter (2004)). In the present paper, the scattering of flexural gravity waves due to an abrupt change in ocean depth is analyzed in case of finite depth in the linearized theory of water waves. In the present paper, Timoshenko‐Mindlin equation for the plate equation is used to include shear and inertia effect in the plate equation. The generalized expansion formulae along with the corresponding orthogonal mode‐coupling relations are used to obtain the velocity potential for the boundary value problem associated with the physical problem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Some features of flexural-gravity wave propagation in the presence of a crack in sheet ice

The effect of a crack in an ice sheet on the propagation of surface flexural-gravity waves in a basin of constant depth is analyzed. The ice sheet is simulated by two floating semi-infinite fragments of a thin elastic isotropic plate. As the boundary-contact conditions on the line of contact between the parts of the plate the conditions of continuity of displacements for arbitrary slopes simulating one ice-floe overlying on another and free-edge conditions (crack) are considered. The dependence of the amplitude characteristics of the perturbations on the thickness of the ice, its degree of compression, the incident wave frequency, the depth of the basin, and the form of the boundary-contact conditions is investigated. Problems of wave diffraction on inhomogeneities of an elastic plate were solved in [1, 2], and on a crack in the ice sheet in [3, 4].