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

The cross-sectional transverse flow field (represented by u(tau)) of rivers comprises a convective part (represented by u(con)) and a circulatory part (represented by u(circ)), and a zero-flux principle of the u(circ) 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 natural rivers of irregular shape. In this study, a zero-flux principle of the u(tau) is derived, to replace the old zero-flux principle of the u(circ). 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.

Automated summary

A new method is proposed in this study to extract circulations in arbitrary vertical planes of natural rivers with irregular shape. The method is simple and only requires the distribution of horizontal velocities, which can be calculated based on a 3-D model or field measurements. The validity of the method is confirmed using field data from the lower Yangtze River, and its capability is demonstrated through examples of typical riverbends.