A zero-flux principle for extracting secondary flows in arbitrary vertical planes of naturalrivers

The cross-sectional transverse flow field(represented by u_(con),)of rivers comprises a convective part(represented by ucon)and a circulatory part(represented by ueire),and a zero-flux principle of the ucire has been known for a long time.However,it is still difficult to separate the circulatory part from the convective part quantitatively in a 3-D velocity field,for an arbitrarily vertical plane in natura ivers of iregular shape this study,a ero-flux prineiple of the uis derived,o replace th old zero-fux principle of the ueire:.Based on the new principle,an all-purpose new method is proposed for extracting the circulations in arbitrary vertical planes of natural rivers of irregular shape.The calculation with the new method requires only the distribution of the horizontal velocities of a single vertical line(VL),and is simple.The calculation can be made based on either the velocity field simulated by a 3-D hydrodynamic model or the field measurements obtained by the acacoustic Doppler velocimetry(ADV).The new method is validated by using the field data of the lower Yangtze River.The extracted circulations are reasonable,while the results of the circulation extraction,respectively,based on the velocity field of a 3-D model and the field measurements of the ADV,are shown to be consistent.The capability of the method is also demonstrated,using the typical riverbends of the Yangtze River as examples.