Solitary and cnoidal wave scattering by a submerged horizontal plate in shallow water

Solitary and cnoidal wave transformation over a submerged, fixed, horizontal rigid plate is studied by use of the nonlinear, shallow-water Level I Green-Naghdi (GN) equations. Reflection and transmission coefficients are defined for cnoidal and solitary waves to quantify the nonlinear wave scattering. Results of the GN equations are compared with the laboratory experiments and other theoretical solutions for linear and nonlinear waves in intermediate and deep waters. The GN equations are then used to study the nonlinear wave scattering by a plate in shallow water. It is shown that in deep and intermediate depths, the wave-scattering varies nonlinearly by both the wavelength over the plate length ratio, and the submergence depth. In shallow water, however, and for long-waves, only the submergence depth appear to play a significant role on wave scattering. It is possible to define the plate submergence depth and length such that certain wave conditions are optimized above, below, or downwave of the plate for different applications. A submerged plate in shallow water can be used as a means to attenuate energy, such as in wave breakers, or used for energy focusing, and in wave energy devices

Laminar flow around sharp and curved objects:The lattice Boltzmann method

Abstract: The lattice Boltzmann method (LBM) is a relatively new computational method to model fluid flows by tracking collision, advection, and propagation of mesoscopic fluid parti-cles. LBM originated from the cellular automata combined with kinetic theory and the Boltzmann equation. The method is used to solve the explicit finite-difference scheme lattice Boltzmann equations which are second order in space and first order in time. LBM does not attempt to solve the Navier–Stokes equations directly; however, it obeys the equations. The two-dimensional flows around square and circular cylinders are simulated with uniform and nonuniform grid structures using the LBM. The boundary layer growth and wake region phy-sics are captured with small-scale details, and the results are validated by comparison with labora-tory experiments for the Reynolds numbers between 50 and 350. Compatibility of the method in simulating flow around hydrofoil geometries and a combination of objects is also provided