Gravity wave interaction with an articulated submerged plate resting on a Winkler foundation

• Published in: Applied mathematical modelling Vol. 113; pp. 416 - 438
• Main Authors: Boral, S., Sahoo, T., Meylan, M.H.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.01.2023
• Subjects: Energy balance relation; Reflection and transmission coefficients; Submerged articulated plate; Time domain simulation; Wave blocking; Wave scattering; Wave blocking; Submerged articulated plate; Time domain simulation; Reflection and transmission coefficients; Energy balance relation; Wave scattering
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2022.09.007

•When a plate is submerged in a fluid, no wave blocking occurs in the plate mode irrespective of compressive force.•Multiple propagating modes occur due to wave blocking when a submerged plate rest on a Winker foundation.•In wave scattering by articulated submerged plate, energy relation depends on wave amplitude and the energy transfer rate.•Discontinuities in the reflection and transmission coefficients occur at blocking and saddle points in wave scattering.•Irregularities in plate deflection occur due to the superposition of multiple propagating waves within blocking frequencies. Surface gravity wave interaction with an articulated flexible submerged plate in the presence of lateral compressive force is investigated within the framework of blocking dynamics, assuming that the submerged plate is resting on a uniform Winkler foundation. The problem is studied considering small-amplitude plate response and linearised water wave theory in finite water depth. The loci of the dispersion relation reveal the occurrence of wave blocking in the submerged plate mode for a range of wave frequency and compressive force when the submerged plate is resting on a Winker foundation. However, in the absence of the Winkler foundation, no wave blocking occurs in the plate mode irrespective of the values of compressive force, and plane wave propagation in plate mode does not happen for particular values of compressive force. Four propagating wavenumbers exist within the blocking frequencies, of which one is in the surface mode, and others are in the submerged plate mode. Thus, to account for the four propagating wave modes, the existing solution approach for a pair of propagating wave modes is modified in an appropriate manner within the limit of blocking frequencies. Consequently, the energy relation is obtained using Green’s identity, in which the reflection and transmission coefficients are a combination of the amplitudes of different reflected and transmitted wave modes and the associated energy transfer rates. The reflection coefficient in the submerged plate mode jumps from one to zero for very small values of frequency due to the introduction of the Winkler foundation in the presence of compressive force. In addition, zero wave reflection occurs for a higher frequency range with an increase in the values of the Winkler constant. Removable discontinuities are observed at the blocking and saddle points, whilst jump discontinuities occur in the reflection and transmission coefficients due to the change of incident wave mode within the blocking frequencies. Linear time-dependent displacements in surface and submerged plate modes are presented prior to the blocking limit.