The Variational Boussinesq Model (VBM) for waves above a layer of ideal fluid conserves mass, momentum, energy, and has decreased dimensionality compared to the full problem. It is derived from the Hamiltonian formulation via an approximation of the kinetic energy, and can provide approximate dispersion characteristics. Having in mind a signalling problem, we search for optimal dispersive properties of the 1D model over flat bottom and, using a finite element numerical code, investigate its quality. The dispersive properties in VBM are completely determined by the vertical potential profile. Especially for broad-band wave fields, we optimize a superposition of one or a few Airy hyperbolic vertical potential profiles, characterized by their wavenumber. The optimal wavenumbers are obtained by a new optimization principle that minimizes the kinetic energy for the given initial signal. We obtained good results for realistic test cases of focusing wave groups with broad spectra, compared to data from real-life experiments at MARIN hydrodynamic laboratory. In this paper we show results of comparing VBM calculations with one and two optimized vertical profiles with experimental data and simulations with other codes.
- Variational Boussinesq Model
- Kinetic energy optimization
- Optimized dispersion
- Surface waves
Lakhturov, I., Adytia, D., & van Groesen, E. W. C. (2012). Optimized Variational 1D Boussinesq Modelling for broad-band waves over flat bottom. Wave motion, 49(2), 309-322. https://doi.org/10.1016/j.wavemoti.2011.11.004