Alternative Forms of Enhanced Boussinesq Equations with Improved Nonlinearity

We propose alternative forms of the Boussinesq equations which extend the equations of Madsen and Schäffer by introducing extra nonlinear terms during enhancement. Theoretical analysis shows that nonlinear characteristics are considerably improved. A numerical implementation of one-dimensional equations is described. Three tests involving strongly nonlinear evolution, namely, regular waves propagating over an elevated bar feature in a tank with an otherwise constant depth, wave group transformation over constant water depth, and nonlinear shoaling of unsteady waves over a sloping beach, are simulated by the model. The model is found to be effective

High-Order Boussinesq Equations for Water Wave Propagation in Porous Media

To accurately capture wave dynamics in porous media, the higher-order Boussinesq-type equations for wave propagation in deep water are derived in this paper. Starting with the Laplace equations combined with the linear and nonlinear resistance force of the dynamic conditions on the free surface, the governing equations were formulated using various independent velocity variables, such as the depth-averaged velocity and the velocity at the still water level and at an arbitrary vertical position in the water column. The derived equations were then improved, and theoretical analyses were carried out to investigate the linear performances with respect to phase celerity and damping rate. It is shown that Boussinesq-type models with Padé [4, 4] dispersion can be applied in deep water. A numerical implementation for one-dimensional equations expressed with free surface elevation and depth-averaged velocity is presented. Solitary wave propagation in porous media was simulated, and the computed results were found to be generally in good agreement with the measurements

Development and validation of a two-layer Boussinesq model for simulating free surface waves generated by bottom motion

In this work, a recently developed two-layer Boussinesq model with high accuracy regarding linear and nonlinear properties and interior kinematic properties from deep to shallow water is extended to include the time-varying bathymetry for modelling earthquake- and landslide-induced waves. The effect of bottom motion is taken into account by simply adding an additional term within the kinematic bottom condition. The moving shoreline is addressed by utilizing linear extrapolation through the wet–dry boundary and into the dry region. A wide range of numerical tests covering the generation, propagation and runup of dispersive waves induced by bottom motion are carried out with the vertical two-dimensional Boussinesq model. The computed results are compared against available theoretical solutions, experimental measurements and previous numerical simulations. Both the consistencies and the discrepancies are discussed

Second-harmonic generation in quaternary atomically thin layered AgInP2S6 crystals

Nonlinear effects in two-dimensional (2D) atomic layered materials have attracted increasing interest. Here, we report the observation of optical second-harmonic generation (SHG) in two-dimensional atomically thin silver indium phosphorus sulfide (AgInP2S6) crystals, with odd layer thickness. The nonlinear signal facilitates the use of thickness-dependent SHG intensity to investigate the stacking type of this material, while the crystal-orientation dependent SHG intensity of the monolayer sample reveals the rotational symmetry of the AgInP2S6 lattice in plane. Our studies expand the 2D crystal family in nonlinear effect field, which opened considerable promise to the functionalities and potential applications of 2D materials.NRF (Natl Research Foundation, S’pore)MOE (Min. of Education, S’pore)Published versio