3D numerical computation of the tidally induced Lagrangian residual current in an idealized bay
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.
KeywordsLagrangian 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.
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).
- Abbott MR (1960) Boundary layer effects in estuaries. J Mar Res 18:83–100Google Scholar
- Feng SZ (1987) A three-dimensional weakly nonlinear model of tide-induced Lagrangian residual current and mass-transport, with an application to the Bohai Sea. In: Nihoul JCJ, Jamart BM (eds) Three-dimensional models of marine and estuarine dynamics, Elsevier oceanography series 45. Elsevier, Amsterdam, pp 471–488CrossRefGoogle Scholar
- Fischer HB, List EJ, Koh R, Imberger J, Brooks NH (1979) Mixing in inland and coastal waters. Academic, New YorkGoogle Scholar
- Lei K, Sun WX, Liu GM (2004) Numerical study of the circulation in the Yellow Sea and East China Sea IV: diagnostic calculation of the baroclinic circulation. J Ocean University of China 34(6):937–941Google Scholar
- Liu GM, Sun WX, Lei K, Jiang WS (2002) A numerical study of circulation in the Huanghai Sea and East China Sea Ш: numerical simulation of barotropic circulation. J Ocean University of Qingdao 32(1):1–8Google Scholar
- Longuet-Higgins MS (1969) On the transport of mass by time-varying ocean currents. Deep-Sea Res 16:431–447Google Scholar
- Roache PJ (1976) Computational fluid dynamics. Hermosa Publishers, New MexicoGoogle Scholar
- Sun WX (1987) A further study of ultra-shallow water storm surge model. J Shandong College of Oceanology 17(1):34–45Google Scholar
- Sun WX, Liu GM, Jiang WS, Wang H, Zhang P (2000) The numerical study of circulation in the Yellow Sea and East China Sea I. The numerical circulation model in the Yellow Sea and East China Sea. J Ocean University of Qingdao 30(3):369–375Google Scholar
- Sun WX, Liu GM, Lei K, Jiang WS, Zhang P (2001) A numerical study on circulation in the Yellow and East China Sea II numerical simulation of tide and tide-induced circulation. J Ocean University of Qingdao 31(3):297–304Google Scholar
- Wang JX, Gao HW, Lei K, Sun WX (2006) Numerical study of the circulations in the Yellow Sea and East China Sea V: dynamic adjustment of the baroclinic circulation. J Ocean University of China 36(Sup.II):001–006Google Scholar
- Wang H, Shu ZQ, Feng SZ, Sun WX (1993) A three-dimensional numerical calculation of the wind-driven thermohaline and tide-induced Lagrangian residual current in the Bohai Sea. Acta Oceanol Sin 12(2):169–182Google Scholar