Author

# S. Zhang

Bio: S. Zhang is an academic researcher. The author has contributed to research in topics: Mathieu function & Free surface. The author has an hindex of 1, co-authored 1 publications receiving 22 citations.

Topics: Mathieu function, Free surface, Diffraction, Surface wave

##### Papers

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TL;DR: The diffraction of small-amplitude surface waves by a horizontally submerged disk of elliptic cross section located at a finite depth beneath the free surface is investigated analytically in this article.

Abstract: The diffraction of small-amplitude surface waves by a horizontally submerged disk of elliptic cross section located at a finite depth beneath the free surface is investigated analytically. The fluid domain is divided into three regions, two internal regions, one above and one beneath the disk, and an external region extending to infinity in the horizontal plane. The theoretical formulation leads to solutions for the fluid velocity potentials in each region in terms of series of Mathieu and modified Mathieu functions of real argument. Numerical results are presented for the wave-induced forces and moments, and the variation of water surface elevation in the vicinity of the disk for a range of wave and structural parameters. In particular, the results for the hydrodynamic loads show significant differences from the corresponding estimates for a circular disk, while the results for the water surface elevation clearly show the effect of wave focusing around the rear of the disk.

25 citations

##### Cited by

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TL;DR: In this paper, it was shown that the added-mass coefficient becomes negative for a range of frequencies when the disc is sufficiently close to the free surface of deep water, and the resulting integral equation is a generalization of Love's integral equation for the electrostatic field of a parallel-plate capacitor.

Abstract: A thin rigid plate is submerged beneath the free surface of deep water. The plate performs small-amplitude oscillations. The problem of calculating the radiated waves can be reduced to solving a hypersingular boundary integral equation. In the special case of a horizontal circular plate, this equation can be reduced further to one-dimensional Fredholm integral equations of the second kind. If the plate is heaving, the problem becomes axisymmetric, and the resulting integral equation has a very simple structure; it is a generalization of Love's integral equation for the electrostatic field of a parallel-plate capacitor. Numerical solutions of the new integral equation are presented. It is found that the added-mass coefficient becomes negative for a range of frequencies when the disc is sufficiently close to the free surface.

82 citations

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TL;DR: In this paper, the hydrodynamic performance of a modified two-layer horizontal-plate breakwater is examined by means of the matched eigenfunction expansion method, and a linear analytical solution is developed for the interaction of water waves with the structure.

79 citations

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TL;DR: In this paper, a wave scattering of a solitary wave traveling over a submerged horizontal plate was studied, and the flow underneath the plate was found to behave almost like a plug flow, driven by the time-dependent, spatially uniform pressure gradient between the two openings.

Abstract: Wave scattering of a solitary wave traveling over a submerged horizontal plate was studied. Experiments for normal incidence were conducted in a wave flume, with a horizontal plate suspended at two different depths in the middle of the flume. Gauge pressures above and underneath the plate, surface elevations on and near the plate, and flow velocities at three representative fields of view were measured. The flow underneath the plate was found to behave almost like a plug flow, driven by the time-dependent, spatially uniform pressure gradient between the two openings. Complex vortices formed near the two edges of the plate as the plate acted like a flow divider. A numerical model based on two-dimensional Navier-Stokes equations was used to confirm the main features captured by the experimental measurements. Analytical solutions based on the linear long wave theory, which admits a soliton-like impulse wave solution, were also derived. The linear theory was applicable for obliquely incident impulse w...

45 citations

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TL;DR: In this article, the authors considered the three-dimensional interaction between water waves and a submerged disc, in deep water, and reduced the problem to a hypersingular integral equation over the surface of the disc.

38 citations

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TL;DR: In this paper, an analytic solution for the total velocity potential for an arbitrary body of the array and accordingly, to express the hydrodynamic pressure, the exciting forces and the wave elevation in compact analytic closed-form.

29 citations