Abstract
The dynamic response of an ice-covered fluid to transient disturbances was analytically investigated by means of integral transforms and the generalized method of stationary phase. The initially quiescent fluid of finite depth was assumed to be inviscid, incompressible, and homogenous. The thin ice-cover was modeled as a homogeneous elastic plate. The disturbances were idealized as the fundamental singularities. A linearized initial-boundary-value problem was formulated within the framework of potential flow. The perturbed flow was decomposed into the regular and the singular components. An image system was introduced for the singular part to meet the boundary condition at the flat bottom. The solutions in integral form for the vertical deflexion at the ice-water interface were obtained by means of a joint Laplace-Fourier transform. The asymptotic representations of the wave motion were explicitly derived for large time with a fixed distance-to-time ratio. The effects of the finite depth of fluid on the resultant wave patterns were discussed in detail. As the depth increases from zero, the critical wave number and the minimal group velocity first increase to their peak values and then decrease to constants.
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Project supported by the National Natural Science Foundation of China (Grant No.10602032), the Shanghai Rising-Star Program (Grant No. 07QA14022), and the Shanghai Leading Academic Discipline Project (Grant No. Y0103).
Biography: LU Dong-qiang (1972- ), Male, Ph. D., Associate Professor
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Lu, Dq., Le, Jc. & Dai, Sq. Flexural-Gravity Waves Due to Transient Disturbances in an Inviscid Fluid of Finite Depth. J Hydrodyn 20, 131–136 (2008). https://doi.org/10.1016/S1001-6058(08)60038-4
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DOI: https://doi.org/10.1016/S1001-6058(08)60038-4