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2 International Journal of Applied Mechanics and Engineering

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Water wave scattering by an infinite step in the presence of an ice-cover

Ray S., De S., Mandal B. N.

International Journal of Applied Mechanics and Engineering

2019

Vol. 24, no. 4

157--168

The classical problem of water wave scattering by an infinite step in deep water with a free surface is extended here with an ice-cover modelled as a thin uniform elastic plate. The step exists between regions of finie and infinite depths and waves are incident either from the infinite or from the finite depth water region. Each problem is reduced to an integral equation involving the horizontal component of velocity across the cut above the step. The integral equation is solved numerically using the Galerkin approximation in terms of simple polynomial multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge of the step. The reflection and transmission coefficients are obtained approximately and their numerical estimates are seen to satisfy the energy identity. These are also depicted graphically against thenon-dimensional frequency parameter for various ice-cover parameters in a number of figures. In the absencje of ice-cover, the results for the free surface are recovered.

Water wave scattering by two thin symmetric inclined plates submerged in finite depth water

Gayen R., Mandal B. N.

International Journal of Applied Mechanics and Engineering

2003

Vol. 8, no 4

589-601

Water wave scattering by two thin symmetric plates submerged in water of uniform finite depth is investigated here assuming the linear theory. The problem is formulated in terms of two hypersingular integral equations involving the discontinuities in the symmetric and antisymmetric potential functions describing the motion in the fluid, across one of the plates. These are solved approximately by an expansion-cum-collocation method in which the unknown discontinuities across a plate are approximated by a finite series involving Chebyshev polynomials of the second kind. The reflection and transmission coefficients are then obtained numerically. The numerical results for the reflection coefficient are depicted graphically against the wave number for different configurations of the plates. It is observed that if the depth of submergence of the mid points of the plates below the free surface is of the order of one-tenth of the depth of the water bottom, then the deep water results effectively hold good. Also known results for two thin vertical plates, a single vertical plate are recovered as special cases.