Numerical Analyses on Propagation of Nonlinear Internal Waves

Abstract

A set of nonlinear surface/internal-wave equations, which have been derived on the basis of the variational principle without any assumptions concerning wave nonlinearity and dispersion, is applied to compare numerical results with experimental data of surface/internal waves propagating through a shallow-or a deep-water region in a tank. Internal waves propagating over a submerged breakwater or a uniformly sloping beach are also simulated. The internal progressive wave shows remarkable shoaling when the interface reaches the critical level, after which physical variables including wave celerity become unstable near the wave-breaking point. In the case of the internal-wave trough reflecting at the vertical wall, the vertical velocities of water particles in the vicinity of the interface are different from that of the moving interface at the wall near the wave breaking, which means that the kinematic boundary condition on the interface of trough has been unsatisfied.

Shoaling of Nonlinear Internal Waves on a Uniformly Sloping Beach

“…In the derivation process of equations, the velocity potential is expanded into a power series of vertical position, after which the velocity potential is approximated using only several terms of the power series in numerical computation. It has been confirmed that the numerical model shows good results in comparison with experimental data over a flat seabed (Yamashita et al, 2011) when the number of terms for the velocity potential is sufficient.…”

“…Nonlinear internal wave eqations based on the variational principle are as follows (Yamashita et al, 2011): (6), (7), and (8) are rewritten to finite difference equations, after which the time development is carried out by applying implicit schemes similar to that of Nakayama and Kakinuma (2010).…”

Surface and Internal Waves due to a Moving Load on a Very Large Floating Structure

“…In the present paper, interaction of surface/internal water waves with floating platforms is discussed in consideration of both nonlinearity of fluid motion and flexibility of oscillating structure. In a multilayer fluid system, for example, Yamashita et al 6 , it is assumed that no fluids of different layers mix together; since this leads to discontinuity of several variables at interfaces, an elastic plate can be put in between two layers as shown in Figure 1. Then we can study multilayer fluids interacting with horizontally large thin plates oscillating flexibly on/below the sea surface.…”