Abstract:
We consider the two-dimensional formulation of the problem on an oblique surface wave for an obstacle in the shape of a submerged strip-barrier. If the barrier is vertical, the discrete spectrum of the problem is empty, but for an inclined barrier there appear an eigenvalue below the threshold of the continuous spectrum and the corresponding trapped mode which decays exponentially in the direction, perpendicular to the obstacle. The asymptotics of the eigenvalue is found in the case of a small inclination angle.
Key words and phrases:trapped mode, water-wave, discrete spectrum, asymptotic behaviour of eigenvalues.