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In this paper, the propagation of water surface waves over one-dimensional periodic and random bottoms is investigated by the transfer matrix method. For the periodic bottoms, the band structure is calculated, and the results are compared to the transmission results. When the bottoms are randomized, the Anderson localization phenomenon is observed. The theory has been applied to an existing experiment (Belzons, et al., J. Fluid Mech. {bf 186}, 530 (1988)). In general, the results are compared favorably with the experimental observation.
Convection over a wavy heated bottom wall in the air flow has been studied in experiments with the Rayleigh number $sim 10^8$. It is shown that the mean temperature gradient in the flow core inside a large-scale circulation is directed upward, that c
A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface w
Metamaterials and photonic/phononic crystals have been successfully developed in recent years to achieve advanced wave manipulation and control, both in electromagnetism and mechanics. However, the underlying concepts are yet to be fully applied to t
The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken
We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply-connected fluid domain that includes stationary obstacl