ON THE SCATTERING OF SURFACE WAVES BY UNDERWATER OBSTACLES

The paper considers a 2D linear problem on scattering of the low-amplitude surface wave in an incompressible fluid that propagates over the bottom obstacle in form of a vertical rectangular wall of the finite of infinitesimal length. The bottoms of the channel and obstacle walls are absolutely rigid. The solution is found by the method of partial domains implying the subdivision of the complex geometry of the overall domain of wave field existence into the subdomains of canonical shapes. This approach allows the formal representing of the corresponding general solutions as the series with respect to eigenfunctions satisfying part of the boundary conditions in each subdomain. The unknown coefficients present in these general solutions may be found from matching conditions that postulate continuity of pressure and normal velocity fields at the boundaries of adjacent subdomains. Applying algebraization procedure to matching conditions for the corresponding general solutions leads to generation of infinite system, of linear equations with respect to the unknown coefficients. The obtained systems possess slow convergence that i, determined by the presence of velocity singularities in angular points of the obstacle. To accelerate the convergence, the method of improved reduction is applied in analyzing the infinite systems. It is based on the a priori hypotheses about the asymptotic behavior of the unknown coefficients in general solutions that is controlled by the order of field singularity in the vicinity of the corresponding angular point. The dependence of calculated energy discrepancy on the amount of considered terms in the reduced system is assessed. The method of improved reduction is shown to provide the better convergence quality at moderate number of kept terms (50 to 70), in comparison with the ordinary reduction. The use of the improved reduction also leads to some widening of the region for which the numerical error remains within acceptable limits.