Near-Resonance of Diffraction Waves by an Array of Plates on Shallow Water in Oblique Waves

摘要

Near-resonance of diffraction waves by an array of plates rigidly fixed on shallow water is investigated under the assumption of linear long wave theory. The plates are assumed idetnical, equally spaced along the array, and infinitely long in breadth. Near-resonant modes occur between adjacent plates at critical wavenumbers in oblique waves. Considering the relationship between this near-resonant phenomenon and an eigenvalue problem of the wave diffraction, it is shown that near-resonant phenomena occur when transmitted wave takes its maximum and reflected wave vanishes. Relationships for the near-resonance between the wave incidence angle and the wavenumber are drawn as some curves. These curves of near-resonant points are confined in particular zones. We shall refer to these zones subsequently as the resonant zones. Each resonant zone has n-1 curves representing near-resonance, where n is the number of plates. The width of resonant zone itself is independent of the number of plates but depends on the spacing of plates, wavenumber, and incidence angle. The resonant zone becomes narrow as the wavenumber or incidence angle increases and the spacing of plates decreases. The curve representing near-resonance for the largest incidence angle gives critical angles of the near-resonance in this wave diffraction problem. The amplitudes of near-resonant modes on the curves situated in both edge sides of each resonant zone, become very large without limit as the number of plates increases.