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 fin...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 fiat 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 pattems 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.展开更多
A general stochastic model of the atmospheric pressure at the ocean surface was proposed, in which the pressure variation was represented by a spectral decomposition through a random process of orthogonal increments. ...A general stochastic model of the atmospheric pressure at the ocean surface was proposed, in which the pressure variation was represented by a spectral decomposition through a random process of orthogonal increments. From the basic equations of ideal and incompressible fluid a set of perturbation equations up to second order had been derived and solved. The pressure variation in the flow field had been calculated using the explicit solutions obtained, and which demonstrated a clear relation between the atmospheric pressure and the one at the bottom of deep ocean. It can be seen that there is a part of the pressure variation which is not attenuating with the depth. The result had been compared with those of Longuet-Higgins and Kadota et al. and all previous results are contained in the solution given in this artice. The restriction on the previous works with regard to the probability law has been removed, and all conclusions are deduced without specific assumptions. The flexibility of the proposed model allows for further generalization and extension in the physical aspects and statistical treatment.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.10602032)the Shanghai Rising-Star Program (Grant No. 07QA14022)the Shanghai Leading Academic Discipline Project (Grant No. Y0103)
文摘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 fiat 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 pattems 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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10372056)the Shanghai Leading Academic Discipline Project (Grant No. Y0103).
文摘A general stochastic model of the atmospheric pressure at the ocean surface was proposed, in which the pressure variation was represented by a spectral decomposition through a random process of orthogonal increments. From the basic equations of ideal and incompressible fluid a set of perturbation equations up to second order had been derived and solved. The pressure variation in the flow field had been calculated using the explicit solutions obtained, and which demonstrated a clear relation between the atmospheric pressure and the one at the bottom of deep ocean. It can be seen that there is a part of the pressure variation which is not attenuating with the depth. The result had been compared with those of Longuet-Higgins and Kadota et al. and all previous results are contained in the solution given in this artice. The restriction on the previous works with regard to the probability law has been removed, and all conclusions are deduced without specific assumptions. The flexibility of the proposed model allows for further generalization and extension in the physical aspects and statistical treatment.
