Oblique flexural gravity-wave scattering due to changes in bottom topography

Abstract

Oblique flexural gravity-wave scattering due to an abrupt change in water depth in the presence of a compressive force is investigated based on the linearized water-wave theory in the case of finite water depth and shallow-water approximation. Using the results for a single step, wide-spacing approximation is used to analyze wave transformation by multiple steps and submerged block. An energy relation for oblique flexural gravity-wave scattering due to a change in bottom topography is derived using the argument of wave energy flux and is used to check the accuracy of the computation. The changes in water depth significantly contribute to the change in the scattering coefficients. In the case of oblique wave scattering, critical angles are observed in certain cases. Further, a resonating pattern in the reflection coefficients is observed due to change in the water depth irrespective of the presence of a compressive force in the case of a submerged block.

Interaction of gravity waves with bottom-standing submerged structures having perforated outer-layer placed on a sloping bed

“…Similar results are observed in Rhee [36] and Karmakar et al [37]. This may be due to physical processes such as wave run up and wave overtopping which are not addressed in the present model.…”

Flexural gravity wave over a floating ice sheet near a vertical wall

“…They constructed a numerical solution of the nonlinear problem and compared the results with the analytic solution. Karmakar et al [37,38] applied the eigenfunction expansion and the corresponding mode coupling relations to investigate the flexural gravity wave propagation through multiple articulated floating elastic plates and the scattering of flexural gravity waves by abrupt changes in the bottom topography.…”

Comments on a class of orthogonality relations relevant to fluid-structure interaction

“…A similar OR was noted by Kaplunov et al [10]. Subsequent to the publication of [5], a number of authors utilised this approach to address a wide range of problems involving elastic plates or ice sheets floating on water of finite depth [11]- [18]. Further ORs of this class have been presented for waveguides in which one boundary comprises an elastic plate and the other a membrane or free surface [19,20].…”

“…Such ORs find application in a wide range of applications involving wave propagation in 2D (and lately 3D [27]- [29]) ducts or channels in the fields of both hydrodynamics and acoustics. The author has included a selection of references that demonstrate the versatility of the theory: wave propagation in structure/ice-covered water [11]- [18]; the study of acoustic silencers [21]- [23] and problems involving layers of distinct acoustic/fluid media [21]- [26]. The list of references is extensive but far from exhaustive.…”

“…The OR for the "drum-like" silencer [22,23] of figure 2 (b) is similar in structure: (18) in this case, of course, every occurrence of Y m (a) is replaced by Y m (d) since the membrane lies along y = d. Hydrodynamic applications that involve layered fluids [24,25] and submersed plates [26] have also been addressed. Interestingly, the article by Mohapatra et al [25] considers a boundary value problem which is very similar to that of [1,2] and uses the same OR.…”