By vertical boundary conditions, a spectral expansion of horizontal tide wave velocity is done in vertical direction in terms of a complete basis functions selected properly, hence a relation between tide levels and...By vertical boundary conditions, a spectral expansion of horizontal tide wave velocity is done in vertical direction in terms of a complete basis functions selected properly, hence a relation between tide levels and spectral components is found theoretically under condition of ignoring the horizontal friction stress and nonlinear effect. And a relation between bottom friction of tide current, which satisfies the viscous condition on sea bottom, and tide levels is determined. The relation is different from the relation of the traditional parameterizing of bottom friction. Moreover integration of the continuity equation and momentum equations is carried out in the vertical direction using zero flux condition on solid boundaries and inputting condition on open boundaries, and then a boundary value problem of elliptic form on the tide levels is constructed.展开更多
The Island Rule, derived from the Sverdrup theory, is widely used to estimate and analyze water transport through a strait. Previous studies presented single-or multi-island rules with either lateral or bottom frictio...The Island Rule, derived from the Sverdrup theory, is widely used to estimate and analyze water transport through a strait. Previous studies presented single-or multi-island rules with either lateral or bottom friction. In this paper,an analytical model of wind-driven circulation is assumed based on linear dynamics. Considering both lateral and bottom friction, the analytic solutions of the transport streamfunction around the islands are derived and the volume transport through the channel is presented. The results are similar to those of Wajsowicz, but the frictional constants represent different values. The analytic solution shows that the relationship between the lateral frictional and bottom frictional dissipation is complex in terms of the frictional constants. To understand the interaction between the two friction types, lateral and bottom friction values were randomly chosen on a barotropic beta plane. The result shows an approximately linear relationship between the lateral and bottom friction in consisting of the combined frictional constants. We studied the effect of the channel width on the transport through the channel. The results show that the friction enhances the flow under some widths, which is similar to the flow behavior when only the lateral friction is considered. We also compared the transport through the channel at different depths and founded that the deeper the water, the smaller the transport reduction ratio when the horizontal eddy viscosity coefficient and the bottom drag coefficient remained constants. To further present the combined role of lateral frictional and bottom frictional dissipation, we compared our model with the model of Wajsowicz for two islands, where only the lateral or bottom friction were considered, with different channel widths. The results showed that the effect of the lateral friction is greater than the bottom friction when the channel is narrow, especially in the Munk boundary layer thickness. When the channel is much wider than the Munk boundary layer thicknes展开更多
This paper is a sequel to Tian’s (1994) preceding paper in which the blow-up theory was sug gested for finding an analytical (as opposed to a numerical) description of long-wave breaking. The pre sent long-wave break...This paper is a sequel to Tian’s (1994) preceding paper in which the blow-up theory was sug gested for finding an analytical (as opposed to a numerical) description of long-wave breaking. The pre sent long-wave breaking numerical results agree quite well with the author’s previous analytical and theo retical results.展开更多
The propagation of long-waves, such as tidal waves from the coastal oceam into shallow estuarine waters,often produces asymmetries of veolcity and water level in time series resulting in long-wave breaking.Tian (1994)...The propagation of long-waves, such as tidal waves from the coastal oceam into shallow estuarine waters,often produces asymmetries of veolcity and water level in time series resulting in long-wave breaking.Tian (1994) studied the mechanism of long-wave breaking in an infinite channel with constant depth,considering nth power bottom friction. This study is for the case of a half infinite channel with bottomslope, taking linear bottom friction into account. The wave breaking time and wave breaking location areestimated and the criteria for long-wave breaking in this particular case are obtained. The results obtainedcan also be e asily applied to the case considering wind stress.展开更多
文摘By vertical boundary conditions, a spectral expansion of horizontal tide wave velocity is done in vertical direction in terms of a complete basis functions selected properly, hence a relation between tide levels and spectral components is found theoretically under condition of ignoring the horizontal friction stress and nonlinear effect. And a relation between bottom friction of tide current, which satisfies the viscous condition on sea bottom, and tide levels is determined. The relation is different from the relation of the traditional parameterizing of bottom friction. Moreover integration of the continuity equation and momentum equations is carried out in the vertical direction using zero flux condition on solid boundaries and inputting condition on open boundaries, and then a boundary value problem of elliptic form on the tide levels is constructed.
基金The National Key Research and Development Program of China under contract No.2016YFC0301103the Scientific and Technological Innovation Project financially supported by Qingdao National Laboratory for Marine Science and Technology under contract No.2015ASKJ01+2 种基金the SOA Program on Global Change and Air-Sea Interactions under contract Nos GASI-IPOVAI-03,GASI-IPOVAI-02 and GASI-IPOVAI-01-02the National Natural Science Foundation of China under contract Nos 40476025,41876027and 41506036the Office of Naval Research of United States under contract No.N00014-08-01-0618
文摘The Island Rule, derived from the Sverdrup theory, is widely used to estimate and analyze water transport through a strait. Previous studies presented single-or multi-island rules with either lateral or bottom friction. In this paper,an analytical model of wind-driven circulation is assumed based on linear dynamics. Considering both lateral and bottom friction, the analytic solutions of the transport streamfunction around the islands are derived and the volume transport through the channel is presented. The results are similar to those of Wajsowicz, but the frictional constants represent different values. The analytic solution shows that the relationship between the lateral frictional and bottom frictional dissipation is complex in terms of the frictional constants. To understand the interaction between the two friction types, lateral and bottom friction values were randomly chosen on a barotropic beta plane. The result shows an approximately linear relationship between the lateral and bottom friction in consisting of the combined frictional constants. We studied the effect of the channel width on the transport through the channel. The results show that the friction enhances the flow under some widths, which is similar to the flow behavior when only the lateral friction is considered. We also compared the transport through the channel at different depths and founded that the deeper the water, the smaller the transport reduction ratio when the horizontal eddy viscosity coefficient and the bottom drag coefficient remained constants. To further present the combined role of lateral frictional and bottom frictional dissipation, we compared our model with the model of Wajsowicz for two islands, where only the lateral or bottom friction were considered, with different channel widths. The results showed that the effect of the lateral friction is greater than the bottom friction when the channel is narrow, especially in the Munk boundary layer thickness. When the channel is much wider than the Munk boundary layer thicknes
文摘This paper is a sequel to Tian’s (1994) preceding paper in which the blow-up theory was sug gested for finding an analytical (as opposed to a numerical) description of long-wave breaking. The pre sent long-wave breaking numerical results agree quite well with the author’s previous analytical and theo retical results.
文摘The propagation of long-waves, such as tidal waves from the coastal oceam into shallow estuarine waters,often produces asymmetries of veolcity and water level in time series resulting in long-wave breaking.Tian (1994) studied the mechanism of long-wave breaking in an infinite channel with constant depth,considering nth power bottom friction. This study is for the case of a half infinite channel with bottomslope, taking linear bottom friction into account. The wave breaking time and wave breaking location areestimated and the criteria for long-wave breaking in this particular case are obtained. The results obtainedcan also be e asily applied to the case considering wind stress.
