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# Diffraction of wavefront around cylinders

Citation Link: https://doi.org/10.15480/882.3344

Publikationstyp

Conference Paper

Publikationsdatum

2019-09

Sprache

English

Author

Herausgeber*innen

TORE-URI

Article Number

43

Citation

11th International Workshop on Ship and Marine Hydrodynamics (IWSH2019), Paper 43

Contribution to Conference

The diffraction of transient waves around an infinite cylinder vertically fixed in deepwater is considered. The velocity potential and corresponding normal derivatives on the cylinder surface are expanded by the Laguerre function in vertical direction and Fourier series along the circumference. Green’s Theorem is applied in the domain external to the cylinder, to obtain the so-called Dirichlet-to-Neumann (DtN) operator, which represents the relationship between series expansion coefficients related to the velocity potential and its normal derivative on the cylinder. Transient waves diffracted from any kind of incoming waves can then be obtained by applying the above DtN operator. The boundary integral equation (BIE) established in the fluid domain is a three-folds integral, two with respect to the cylinder surface and one with respect to time, and the time-domain Green function itself is a single one. In the scheme of Galerkin collocation, to obtain the DtN operator, the boundary integral equation is multiplied by a base function on both sides and integrated over the cylinder surface. A new boundary integral equation connecting the expansion coefficients related with velocity potential and normal derivative is obtained. Although all elements in the coefficients matrix are multi-folds integrals in form, they can be reduced to single ones with respect to wavenumber by using orthogonal properties of Laguerre functions and Fourier series, except for the convolution integral which can be expressed by a summation.

Unlike in classical work where steady-state plane progressive waves are involved, transient waves with wavefronts, which are generated by a wavemaker, are selected as the incoming waves in present study. Wavefront can be observed in real sea, physical wave tank and numerical simulations. A study on transient waves with wavefronts is of importance to understand better the wave diffraction by cylinders. Results from the above method are compared with those from an existing time-domain analyzing method which introduces the frequency domain solution into transient wave elevation on the free surface to express the transient diffracted waves.

Unlike in classical work where steady-state plane progressive waves are involved, transient waves with wavefronts, which are generated by a wavemaker, are selected as the incoming waves in present study. Wavefront can be observed in real sea, physical wave tank and numerical simulations. A study on transient waves with wavefronts is of importance to understand better the wave diffraction by cylinders. Results from the above method are compared with those from an existing time-domain analyzing method which introduces the frequency domain solution into transient wave elevation on the free surface to express the transient diffracted waves.

Schlagworte

Fourier Laguerre series expansion

Time domain Green function

Wave diffraction

Wavefront

DDC Class

600: Technik

620: Ingenieurwissenschaften

Funding Organisations

National Natural Science Foundation of China

More Funding Information

This work has been partially supported by the National Natural Science Foundation of China, project number 51779054.

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