My research interest are including (but not limited to) these topics : Surface water waves, Variational Modelling, and Finite Element Method.
My current Postdoc Project:
Our aim is to further develop a water wave model, the so-called Variational Boussinesq Model (VBM) to be more applicable for practical applications in coastal engineering such as simulating short waves, e.g. wind waves entering a harbour, as well as for long waves, e.g. tsunamis. In the previous PhD project (below), the dispersive properties of the model are improved significantly by an optimization of vertical profiles in the VBM approximation. This optimization has a consequence that the model has a tailor-made dispersion relation which makes the model more flexible for simulating very short waves as well as very long waves. Figure 1 shows an example of simulation of wind waves in the harbour of Jakarta, Indonesia.
Figure 1. Simulation of wind waves in the harbour of Jakarta, Indonesia.
In this project, we will incorporate several physical phenomena of coastal waves such as wave breaking, bottom dissipation and wind effects into the VBM. Besides that, the VBM will be extended for calculating a pressure on a ship or structure by waves.
Animation in Figure 1 can be downloaded [here] 9.7MB.
My previous Ph.D. Project:
Our aim is to further develop a water wave model, the so-called Variational Boussinesq Model (VBM) which is based on the Hamiltonian structure of gravity surface waves. In the VBM, the fluid potential in the expression of the kinetic energy is approximated by its value at the free surface plus a linear combination of the vertical potential profiles with horizontal spatially dependent functions as coefficients. The vertical potential profiles are chosen a priori and determine completely the dispersive properties of the model. For signalling problems above varying bottom, the optimization of the wave number(s) in one or more Airy functions as vertical profiles is obtained by minimizing the kinetic energy functional for a given influx signal. All expressions in the energy contain at most second order derivatives, which makes a numerical implementation with finite elements relatively easy.
The applicability of the model is investigated for coastal waves (irregular waves) entering harbours. The main interest in the coastal wave and harbour simulations is the so-called long-wave generation and resonance problems of harbours. In Figure 2, 1D simulations of the Optimized VBM are compared with experimental data from MARIN hydrodynamic laboratory for irregular waves with period 12s running over a sloping bottom. In Figure 3, we show a comparison of wave disturbance plots (normalized significant waveheight) from realistic simulations in the harbour of Jakarta, Indonesia, of a spectral code [SWAN] (left plot) and the 2D OVBM (right plot).
Figure 2. The simulated (solid) and measured (dash) signals of irregular waves with period 12s are compared at the shallow area, h=15m, after the waves running above a 1/20 slope from h=30m.
Figure 3. Wave disturbances (in percentage) of the simulations of SWAN (left plot) and the Optimized VBM (right plot) in the harbour of Jakarta, Indonesia.
An illustration how an irregular wave propagates ....
The red dot runs with the so-called phase velocity, while the yellow dot with the so-called group (energy) velocity. The biggest challenge in modelling of Boussinesq-type equations is to model these velocities correctly for higher frequency (shorter) waves.
Professional addresses (1),
Department of Applied Mathematics, University of Twente,
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