Title: Nonlinear diffraction and refraction of regular an random sea waves – with application to low-frequency spectra in a harbor

Speaker: Chiang C. Mei (Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA / Marine Renewable Energy Research Team, University of Ulsan )

Date: 2009년 7월 31일 금요일 오후 4:00-5:30

Venue: 창의학습관 101호

Abstract

For monochromatic incident waves of infinitesimal amplitues, the

mild-slope equation is an effective approximation for treating the combined

effects of refraction and diffraction, for it reduces the spatial dimension

of the linear boundary value problem from three to two. We

first extend this approximation to nonlinear waves up to the second

order in wave steepness, in order to simplify the inherently threedimensional

task.

We next present a spectral theory of the low-frequency response of

a harbor to short and random incident waves. Assuming the incident

sea to be stationary and Gaussian, nonlinear extensions are made for

the response spectrum. Advantage is taken of the typical wind-wave

spectrum which is dominated by high-frequency components. After

showing that nonlinearity is needed only up to the second order in wave

steepness, the mild-slope approximations for constructing the first and

second-order transfer functions. Numerical examples are presented for

a square harbor and constant depth. Discounting friction losses, the

effects of different entrances are compared.

Needs for further development of computational algorithm will be

discussed. The theory can be modified to predict the slow-drift motion

of floating vessels such as semi-submercibles.