3D numerical computation of the tidally induced Lagrangian residual current in an idealized bay

  • Yanxing Cui
  • Wensheng JiangEmail author
  • Fangjing Deng


A numerical model that solves 3D first-order Lagrangian residual velocity (uL) equations is established by modifying the HAMSOM model. With this model, uL is studied in a wide, idealized bay. The results show that the vertical eddy viscosity term of Stokes’ drift (π1) in the tidal body force determines the overall flow state of uL, and the contribution of the advection term (π2) is responsible for the small correction. In addition, two types of Coriolis effects introduced into the residual current system not only enhance the lateral flow and break the symmetry of the flow regime in the bay but also slightly correct the flow state driven by the entire tidal body force. It is also found by numerical sensitivity experiments that the increase in the aspect ratio δ, implying a decrease in the topographic gradient, can simplify the residual flow state. The increase in tidal amplitude at the open boundary significantly enhances the intensity of uL and causes the residual flow regime to be more complicated in the bay. This can be ascribed to the disproportionate increase in the tidal body force. The proportion of the vertical eddy viscosity term of Stokes’ drift in the tidal body force also varies with the vertical eddy viscosity coefficient, which leads to different residual current states. Compared with the influence of incoming tidal strength on the residual current, the effect of the bottom friction coefficient on the residual current is relatively mild. An increase in the quadratic bottom friction coefficient induces an unbalanced decrease in the tidal body force. Therefore, uL decreases, but the flow regime is more complex. The influence of the nonlinear effect of the bottom friction decreases from the bay head towards the bay mouth. The residual current only changes in magnitude near the bay mouth but changes in pattern near the bay head for different bottom friction coefficients. By keeping the bottom friction coefficient in the zeroth-order tidal equations constant, the sensitivity experiment shows that uL is insensitive to the change in bottom friction coefficient in the governing equations of uL.


Lagrangian residual current Residual water elevation Tidal body force Tide amplitude Bottom friction coefficient Vertical eddy viscosity coefficient Wide bay 



The authors would like to express sincerest thanks to the anonymous reviewers for their comments.

Funding information

This study was supported by the National Natural Science Foundation of China (41676003) and the NSFC Shandong Joint Fund for Marine Science Research Centers (Grant U1606402).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratory of Marine Environment and EcologyOcean University of ChinaQingdaoPeople’s Republic of China
  2. 2.Changzhi UniversityChangzhiPeople’s Republic of China
  3. 3.Physical Oceanography Laboratory/CIMSTOcean University of China and Qingdao National Laboratory for Marine Science and TechnologyQingdaoPeople’s Republic of China

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