演講訊息 TALKS

摘要： A numerical method for predicting realistically the occurrence of harbor resonance The long wave trains that induce harbor resonance are almost always transient. Therefore, it is unrealistic to predict the occurrence of harbor resonance based on the numerical computations in which the wave field is assumed to be stationary. However if strong resonance can be induced by a stationary wave train due to large incoming and outgoing energy fluxes through the entrance, but not due to energy trapping by the harbor, we may assume that this resonance will also occur when the incident wave train is transient. It is because unlike the accumulation of large energy in the harbor by wave trapping , the large incoming and outgoing energy fluxes through the entrance, which involves no accumulation effects, should occur very soon after the arrival of the incident wave train. As previous numerical techniques cannot be utilized to determine the amount of the incoming and outgoing energy fluxes, and since most harbor resonances are caused by large incoming and outgoing energy fluxes through the entrance, a new numerical technique has been developed by taking into account the energy flux. This technique, though applicable only to the situation when the wave field is stationary so that the variations in the time domain can be neglected to save the computer memories, can, however, be utilized to achieve the same purpose as that when a transient wave field is under consideration. Propagation of deep-water linear gravity waves on three-dimensional, strongly sheared currents Deep-water linear gravity waves propagating obliquely on a steady three-dimensional, strongly sheared current are studied for the case where the current varies slowly in the horizontal directions and deviates slightly from a linear profile in the vertical direction. In this case, a WKBJ description of wave propagation can be developed by solving the boundary-value problem in a local co-ordinate system in which the rotational perturbation velocity can easily be separated from the irrotational one. Without this separation, a perturbation scheme was applied by Voronovich (1976) to successfully derive the action conservation equation in an even more complicated situation. In that case, the variation of the current in the vertical direction can be arbitrary and the variation in the density of the fluid is permitted. This equation, though valid in theory, cannot be implemented in practice. More importantly, this equation, after reduction, cannot be applied to the present case. It is because in this case, the unknown rotational perturbation velocity occurring implicitly in the second-order inhomogeneous boundary-value problem arising from a perturbation scheme can itself be determined independently from another inhomogeneous boundary-value problem in which there is no need to fulfill a secular condition. Therefore this rotational perturbation velocity should be eliminated from the original second-order boundary-value problem before using the secular condition of the latter to derive the modulation equation. This explains why the modulation equation derived here by using a different method is inconsistent with the action conservation equation, implying that the wave action is not conserved in the present case. The numerical computations of the fully nonlinear waves on a strongly sheared current The fast computational method derived by Clamond & Grue (2001) for two-dimensional fully nonlinear non-overturning waves is extended for simulation of these waves propagating on a unidirectional, vertically shear current in the direction parallel to this current. To achieve this purpose, the wave field is decomposed into an irrotational component and a rotational one, and a special relation between these two components is subsequently derived. This relation can serve as a closure equation so that the irrotational component can be solved independently by using the Clamond-Grue method, after which the rotational component can also be estimated at the free surface. This approach involves fewer assumptions than that developed by Nwogu (2009), so that only the assumption that the current profile in the vertical direction is nearly linear has been made here. By using this numerical scheme, we clearly demonstrate that even nonlinear waves can be blocked and reflected by a vertically shear current. Since this phenomenon is stable, it is not unusual to be seen in the ocean and may therefore be related to freak waves. The above-mentioned relation between the irrotational and rotational components of the wave field can result in a solution of the wave field which is accurate at least to the third order in the wave slope, ensuring that the above conclusions are quite reliable. Whether this relation is also valid for fully nonlinear waves will be verified in the near future. 敬請公告，歡迎參加