Numerical Investigation into the Effects of a Viscous Fluid Seabed on Wave Scattering with a Fixed Rectangular Obstacle
Abstract
:1. Introduction
2. Model Development
2.1. Assumptions and Simplifications
2.2. Numerical Model
2.3. Model Validation
2.3.1. Surface Obstacle above a Solid Bed
2.3.2. Bottom Obstacle on a Solid Bed
2.3.3. Submerged Obstacle above a Solid Bottom
2.3.4. Waves over a Layer of Viscous Fluid Mud
3. Results and Discussions
3.1. Surface Obstacle
3.2. Bottom Obstacle
3.3. Submerged Obstacle
4. Concluding Remarks
- Surface obstacle: Section 3.1
- Incident and transmitted wave components show an amplitude attenuation rate similar to the case of waves over a muddy bed without any obstacles. Reflected waves have a much stronger damping rate.
- For incident, reflected, and transmitted wave components, the largest damping rates all occur at .
- The pattern of the velocity distribution is mainly controlled by the obstacle with modulation in magnitude and wavelength contributed by the muddy bed.
- In terms of the dimensionless vertical wave force exerted on the obstacle surface, a larger phase difference was observed for the case of a thicker mud layer.
- Bottom obstacle: Section 3.2
- The effect of bottom obstacle on mud-induced amplitude attenuation is only considerable for the reflected wave components.
- The largest wave damping of each wave component was observed when the mud layer thickness was .
- The impact of viscous fluid bed on the flow pattern in the vicinity of the obstacle was not obvious. However, a phase shift and increase in wavelength are both more evident.
- A thicker mud layer causes a larger phase lag in the dimensionless vertical wave force on the obstacle surface.
- Submerged obstacle: Section 3.3
- Due to the vortex generated in the lee of the obstacle of the obstacle, a significantly larger decrease in wave amplitude is shown for transmitted wave component. This is very different from the behaviors observed in the cases of surface or bottom obstacles.
- The largest amplitude attenuation rate occurs at for every wave component.
- With the consideration of a viscous fluid mud bed, the size of the vortex core is considerably smaller and the phase difference on the formation of the vortex can also be observed.
- The case with shows a larger decrease in the dimensionless vertical wave force on the obstacle surface. However, the phase shift is more substantial for a thicker layer with .
Author Contributions
Funding
Conflicts of Interest
References
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Zheng, K.-Y.; Chang, C.-W.; Chan, I.-C. Numerical Investigation into the Effects of a Viscous Fluid Seabed on Wave Scattering with a Fixed Rectangular Obstacle. Mathematics 2022, 10, 3911. https://doi.org/10.3390/math10203911
Zheng K-Y, Chang C-W, Chan I-C. Numerical Investigation into the Effects of a Viscous Fluid Seabed on Wave Scattering with a Fixed Rectangular Obstacle. Mathematics. 2022; 10(20):3911. https://doi.org/10.3390/math10203911
Chicago/Turabian StyleZheng, Kuan-Yu, Chen-Wei Chang, and I-Chi Chan. 2022. "Numerical Investigation into the Effects of a Viscous Fluid Seabed on Wave Scattering with a Fixed Rectangular Obstacle" Mathematics 10, no. 20: 3911. https://doi.org/10.3390/math10203911
APA StyleZheng, K.-Y., Chang, C.-W., & Chan, I.-C. (2022). Numerical Investigation into the Effects of a Viscous Fluid Seabed on Wave Scattering with a Fixed Rectangular Obstacle. Mathematics, 10(20), 3911. https://doi.org/10.3390/math10203911