Shih-Chun Hsiao

Observations on the evolution of wave modulation

A series of laboratory experiments on the long-time evolution of nonlinear wave trains in deep water was carried out in a super wave flume (300×5.0×5.2 m) at Tainan Hydraulics Laboratory of National Cheng Kung University. Two typical wave trains, namely uniform wave and imposed sideband wave, were generated by a piston-type wavemaker. Detailed discussions on the evolution of modulated wave trains, such as transient wavefront, fastest growth mode and initial wave steepness effect, are given and the results are compared with existing experimental data and theoretical predictions. Present results on the evolution of initial uniform wave trains cover a wide range of initial wave steepness () and thus, greatly extend earlier studies that are confined only to the larger initial wave steepness region (). The amplitudes of the fastest growth sidebands exhibit a symmetric exponential growth until the onset of wave breaking. At a further stage, the amplitude of lower sideband becomes larger than the carrier wave and upper sideband after wave breaking, which is known as the frequency downshift. The investigations on the evolution of initial imposed sideband wave trains for fixed initial wave steepness but different sideband space indicate that the most unstable mode of initial wave train will manifest itself during evolution through a multiple downshift of wave spectrum for the wave train with the smaller sideband space. It reveals that the spectrum energy tends to shift to a lower frequency as the wave train propagates downstream due to the sideband instability. Experiments on initial imposed sideband wave trains with varied initial wave steepness illustrate that the evolution of the wave train is a periodic modulation and demodulation at post-breaking stages, in which most of the energy of the wave train is transferred cyclically between the carrier wave and two imposed sidebands. Meanwhile, the wave spectra show both temporal and permanent frequency downshift for different initial wave steepness, suggesting that the permanent frequency downshift induced by wave breaking observed by earlier researchers is not permanent. Additionally, the local wave steepness and the ratio of horizontal particle velocity to linear phase velocity at wave breaking in modulated wave group are very different from those of Stokes theory.

NONLINEAR WATER WAVES OVER A THREE-DIMENSIONAL POROUS BOTTOM USING BOUSSINESQ-TYPE MODEL

Nonlinear water waves propagating over a three-dimensional submerged porous bottom are investigated using depth-integrated model developed by Hsiao et al. In particular, the case of waves over porous submerged trapezoidal mounds is discussed and the results are compared with the experimental data of Cruz et al. The overall comparisons are reasonably good, suggesting that the model equations used in this study can describe diffraction, reflection and refraction effects well.

Oscillatory Flows over a Permeable Wavy Boundary

In this paper viscous boundary layer flows above and inside a permeable wavy bed are studied. The flow motions are driven by an oscillatory horizontal velocity just outside the Stokes boundary layer above the bed. Analytical and numerical solutions are obtained for both the oscillatory velocity component and the steady streaming inside the permeable bed, the Stokes boundary layer and the outer boundary layer. Two specific situations are examined: (1)Weak oscillatory motions over a wavy bed with finite slope and (2) strong oscillatory motions over a small wavy slope. In both situations, the slip (tangential) velocity and the normal velocity do not vanish on the wavy surface because of the permeability. The magnitude of the bed shear stress decreases as the permeability increases. The permeability can also affect significantly the steady streaming patterns; they could change from having two pairs of recirculating cells above an impervious wavy bed to one pair of recirculating cells above a wavy permeable bed.

The Porous Effect on the Bottom Instability Under Partially Standing Waves

In this paper, we extended Blondeaux [1], Liu, et al. [2] and Mei and Yus [3] theories to study the porous effect on instability of rippled bed under the partially standing surface waves. Comparisons are made with both Blondeaux and Mei & Yus theoretical predictions and experimental data performed by many other authors. We found that based on the linear instability analysis and the parameter regimes we explored the percolation effect can change the threshold conditions by 10 ∼ 20 percent and the seepage force is negligible up to O(∈). Furthermore, the steady streamings with or without porous effect show the considerable difference in intensities at the same locations and it might change the sediment transport rate especially the suspended load.

Numerical Study on the Solitary Wave Propagating over the Density-Stratified Fluid in a Submarine Trench

The induced density-stratified fluid motion for a solitary wave past a submarine trench is investigated numerically by means of the three-dimensional Navier-Stokes (N-S) solver named Truchas. The Volume of Fluid (VOF) method is used to trace the free surface and the transport of the lower fluid (homogeneous/dense fluid) within the trench. The numerical results were validated by comparing the computed results with laboratory experiments of Chang et al. (2011) for solitary wave induced flow motion. The model is then used to examine the transport processes of the various dense fluids within the trench. Particular attentions are paid to the evolution of vortex induced by solitary wave. Specifically, the effects of various amplitudes of the incident solitary wave on flow field characteristics are examined.

Boussinesq-Type Equations for Water Wave Propagation in Porous Media

A new set of Boussinesq-type model equations based on the perturbation method similar to Hsiao et al. (2002) is derived for describing water waves propagating in porous media. The resistance forces including the linear/nonlinear drag force and the turbulence effect suggested by Sollitt and Cross (1972) are incorporated. The approach by Chen (2006) to eliminate the depth-dependent terms in momentum equation is adopted. The applicable range of water depths of new model equations is examined by comparing with the linear wave theory. Furthermore, the nonlinear properties of model equations are also numerically validated against the weakly nonlinear theory of Liu and Wen (1997). Fairly good agreements are achieved, suggesting that the present model equations can be applied to the simulation of nonlinear wave propagation in a porous structure.