Both physical oceanographic processes and marine geological features in the continental shelf can cause the medium properties to have lateral heterogeneity, so horizontal refraction of sound can occur and produce significant three-dimensional (3-D) sound propagation effects. The long-term goals of this project are targeted on understanding the 3-D acoustic effects caused by the environmental fa...

Topological concepts have been introduced into electronic, photonic, and phononic systems, but have not been studied in surface-water-wave systems. Here we study a one-dimensional periodic resonant surface-water-wave system and demonstrate its topological transition. By selecting three different water depths, we can construct different types of water waves - shallow, intermediate and deep water...

We present an efficient method that uses particles to solve the 2D shallow water equations. These equations describe the dynamics of a body of water represented by a height field. Instead of storing the surface heights using uniform grid cells, we discretize the fluid with 2D SPH particles and compute the height according to the density at each particle location. The particle discretization off...

We consider the shallow water equations for flows through channels with arbitrary cross-section. The system forms a hyperbolic set of balance laws. Exact steady-state solutions are available and are controlled by the relation between the bottom topography and the channel geometry. We use a Roetype upwind scheme for the system. Considerations of conservation, near steady-state accuracy, velocity...

We present new models to describe shallow water flows over non smooth topographies. The water waves problem is formulated as a system of two equations on surface quantities in which the topography is involved in a Dirichlet-Neumann operator. Starting from this formulation and using the joint analyticity of this operator with respect to the surface and the bottom parametrizations, we derive a no...

Goals include the development of models and methods that explain observed material and acoustic properties of different physical types of shallow-ocean mud sediments. Other goals are to assess prior data relating to the acoustic properties of mud and to provide guidance in the development and interpretation of experiments. A related goal is to construct models that will guide inversion techniqu...

We consider the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water. The difficulty in this system comes from the coupling terms involving some derivatives of the unknowns that make the system nonconservative, and eventually nonhyperbolic. Due to these terms, a numerical scheme obtained by performing an arbitrary schem...