Nonlinear Dispersive Model Research Articles

An approximate analytical solution for the nonlinear inverse axial dispersion model

An analytical solution for diffusion with homogenous n the order nonlinear chemical reaction in laminar flow of a Newtonian fluid through tubular reactor with unknown boundary conditions is presented. The results of the new solution have been compared with previously published numerical solutions and shown to be accurate.

The numerical modelling of long wave propagation in the framework of non-linear dispersion models

The work is devoted to the questions of numerical modelling of long wave propagation, in particular tsunami waves, in the framework of non-linear dispersion models of the Boussinesq and Korteweg-de Vries type. The first part of the work includes a classification of some known mathematical models, in terms of dispersion correlation, phase and group velocities. Problems arising on the construction of finite-difference approximations of non-linear dispersion models are discussed in the second part of the work, special attention is given to the questions of constructing discrete boundary conditions. In the conclusion the results obtained in the course of numerical experiments and estimation of specifics of finite-difference models, and the contribution of non-linear dispersion effects in the process of wave propagation in the coastal zone, are discussed. The results of calculations of tsunami wave propagation in a wave tube with real bathymetry, are given.

Modelling criteria for long water waves

Model equations which describe the evolution of long-wave initial data in water of uniform depth are tested to determine explicit criteria for their applicability. We consider linear and nonlinear, dispersive and non-dispersive equations. Separate criteria emerge for the leading wave and trailing oscillations of the evolving wave train. The evolution of the leading wave depends on two parameters: the volume (non-dimensional) of the initial data and an Ursell number based on the amplitude and length of the initial data. The magnitudes of these two parameters determine the appropriate model equation and its time of validity. For the trailing oscillatory waves, a local Ursell number based on the amplitude of the initial data and the local wavelength determines the appropriate model equation. Finally, these modelling criteria are applied to the problem of tsunami propagation. Asymptotic ( t → ∞) linear dispersive theory does not appear to be applicable for describing the leading wave of tsunamis. If the length of the initial wave is approximately 100 miles, the leading wave is described by a linear non-dispersive model from the source region until shoaling occurs near the coastline. For smaller lengths (∼ 40 miles) a linear dispersive (but not asymptotic) model is applicable. The longer-period oscillatory waves following the leading wave, which can induce harbour resonance, apparently require a nonlinear dispersive model.