The Island Rule With Consideration Of Frictional Effect And Its Application

The Island Rule,derived from the Sverdrup theory,is widely used to estimate and analyze water transport through a channel between the islands or between the island and basin boundary.In this paper,a brief review of the source on the circulation theory is given,and the development and research process of the Island Rule are introduced.And then started with the momentum equation,the Island Rule is systematically deduced by integrating the depth integration of the momentum equation.The applicable range on the theory is dicussed.The advantages and disadvantages of the theory are analyzed.For the Island Rule on which one island is only considered,the conclusion is generalized.Firstly,the situation of the two islands is considered.Three cases on the islands which consisted of overlapped,the latitude of left island including right island and the latitude of right island including left island are analyzed.The Island rule with two islands is obtained,and the conclusion is extended to multiple islands.The Island Rule requires the island to stay away from the western boundary flow and left friction to be ignored.The condition is analyzed in the paper.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 thickness,the role of the bottom friction is greater than that of the lateral friction.The multi-islands theory with consideration of lateral friction and bottom friction are obtained in this paper by considering the friction effect.After a brief summary and review of the situation on the studied sea area is given,based on the CCMP data,the wind fields of 27 years from 1988 to 2014 are used.The wind stress is converted in the paper.The volume transport on the Indonesian Flows is calculated by annual mean wind stress.By comparing the values which the frictions are considered,the model yielded a reduction of approximately 20% in the transport.Seung considered a analytical model for the dynamics of volume transport of the Tsushima Current.This model is basically baroclinic on both ends of the basin but allows bottom friction over the shallow barotropic channel.The model is different from previous models which are either purely barotropic with bottom friction,or purely baroclinic with bottom friction completely ignored.This model is extended.By using the idea of Godfrey' Island Rule,the Two-islands theory with consideration of baroclinic and barotropic effect are derived and is applied to the Tsushima Current.