Effects of ice-floe on surface wave interaction with an irregular flexible seabed. (English) Zbl 1478.76012
Summary: The hydro-elastic response of incident wave with a horizontal floating ice-floe on a sea is studied by using linear potential theory. The lower side of the sea is bounded by an adaptable layer with small base distortion. Here, the ice-floe and adaptable bottom surface are modeled as lean uniform elastic plates. In such circumstances, there are two types of time-harmonic proliferating waves that exist in the fluid region. The waves with smaller wavenumber propagate beneath the ice-floe (ice-floe wave mode) and the other propagates along the adaptable sea-bed (adaptable base wave mode). Utilizing perturbation analysis, the initial problem is transferred to a first-order problem. The reduced problem is resolved by using the Fourier transform approach. The first-order approximations of the reflection and transmission coefficients are acquired for both the wave modes. For a particular example of a sinusoidal patch with two distinct wavenumbers is taken up to validate the results. The key benefit of the recent study is that the estimations of reflection and transmission coefficients in the case of both the wave modes are shown to establish the energy relation almost successfully.
MSC:
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 76M45 | Asymptotic methods, singular perturbations applied to problems in fluid mechanics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 86A40 | Glaciology |
| 86A05 | Hydrology, hydrography, oceanography |
Keywords:
bottom deformation; adaptable bed; floating ice plate; Fourier transform; perturbation analysis; reflection coefficient; transmission coefficientReferences:
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