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

  • Yanxing Cui
  • Wensheng JiangEmail author
  • Fangjing Deng
Article

Abstract

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.

Keywords

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

Notes

Acknowledgements

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).

References

  1. Abbott MR (1960) Boundary layer effects in estuaries. J Mar Res 18:83–100Google Scholar
  2. Backhaus JO (1985) A three-dimensional model for the simulation of shelf sea dynamics. Deutsche Hydrografische Zeitschrift 38:165–187CrossRefGoogle Scholar
  3. Basdurak NB, Valle-Levinson A (2012) Influence of advective accelerations on estuarine exchange at a Chesapeake Bay tributary. J Phys Oceanogr 42:1617–1634CrossRefGoogle Scholar
  4. Burchard H, Schuttelaars HM (2012) Analysis of tidal straining as driver for estuarine circulation in well-mixed estuaries. J Phys Oceanogr 42:261–271CrossRefGoogle Scholar
  5. Carballo R, Iglesias G, Castro A (2009) Residual circulation in the Ría de Muros (NW Spain): a 3D numerical model study. J Mar Systs 75:116–130CrossRefGoogle Scholar
  6. Cheng RT, Casulli V (1982) On Lagrangian residual currents with applications in South San Francisco Bay. Water Resour Res 18:1652–1662CrossRefGoogle Scholar
  7. Cheng P, Valle-Levinson A, De Swart HE (2010) Residual currents induced by asymmetric tidal mixing in weakly stratified narrow estuaries. J Phys Oceanogr 40:2135–2147CrossRefGoogle Scholar
  8. Deng FJ, Jiang WS, Feng SZ (2017) The nonlinear effects of the eddy viscosity and the bottom friction on the Lagrangian residual velocity in a narrow model bay. Ocean Dyn 67:1105–1118CrossRefGoogle Scholar
  9. 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
  10. Feng SZ, Cheng RT, Xi PG (1986a) On tide-induced Lagrangian residual current and residual transport, 1. Lagrangian residual current. Water Resour Res 22:1623–1634CrossRefGoogle Scholar
  11. Feng SZ, Cheng RT, Xi PG (1986b) On tide-induced Lagrangian residual current and residual transport, 2. Residual transport with application in South San Francisco Bay. Water Resour Res 22:1635–1646CrossRefGoogle Scholar
  12. Feng SZ, Xi PG, Zhang SZ (1984) The baroclinic residual circulation in shallow seas. Chin J Oceanol Limnol 2:49–60CrossRefGoogle Scholar
  13. Fischer HB, List EJ, Koh R, Imberger J, Brooks NH (1979) Mixing in inland and coastal waters. Academic, New YorkGoogle Scholar
  14. Huijts KMH, Schuttelaars HM, de Swart HE, Friedrichs CT (2009) Analytical study of the transverse distribution of along-channel and transverse residual flows in tidal estuaries. Cont Shelf Res 29:89–100CrossRefGoogle Scholar
  15. Jiang WS, Feng SZ (2011) Analytical solution for the tidally induced Lagrangian residual current in a narrow bay. Ocean Dyn 61:543–558CrossRefGoogle Scholar
  16. Jiang WS, Feng SZ (2014) 3D analytical solution to the tidally induced Lagrangian residual current equations in a narrow bay. Ocean Dyn 64(8):1073–1091CrossRefGoogle Scholar
  17. 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
  18. Leveque R (2007) Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems. Society for Industrial and Applied Mathematics, PhiladelphiaCrossRefGoogle Scholar
  19. Li CY, Chen CS, Guadagnoli D, Georgiou IY (2008) Geometry-induced residual eddies with curved channels: observations and modeling studies. J Geophys Res 113:C01005.  https://doi.org/10.1029/2006JC004031 Google Scholar
  20. Li CY, O’Donnell J (1997) Tidally driven residual circulation in shallow estuaries with lateral depth variation. J Geophys Res 102(C13):27915–27929CrossRefGoogle Scholar
  21. Li CY, O’Donnell J (2005) The effect of channel length on the residual circulation in tidally dominated channels. J Phys Oceanogr 35:1826–1840CrossRefGoogle Scholar
  22. Liu GL, Liu Z, Gao HW, Gao ZX, Feng SZ (2012) Simulation of the Lagrangian tide-induced residual velocity in a tide-dominated coastal system: a case study of Jiaozhou Bay. China Ocean Dyn 62:1443–1456CrossRefGoogle Scholar
  23. 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
  24. Longuet-Higgins MS (1969) On the transport of mass by time-varying ocean currents. Deep-Sea Res 16:431–447Google Scholar
  25. Lopes JF, Dias JM (2007) Residual circulation and sediment distribution in the Ria de Aveiro lagoon, Portugal. J Mar Syst 68:507–528CrossRefGoogle Scholar
  26. Moore D (1970) The mass transport velocity induced by free oscillations at a single frequency. Geophysical Fluid Dynamics 1:237–247CrossRefGoogle Scholar
  27. Muller H, Blanke B, Dumas F, Lekien F, Mariette V (2009) Estimating the Lagrangian residual circulation in the Iroise Sea. J Mar Syst 78:S17–S36CrossRefGoogle Scholar
  28. Nihoul ICJ, Ronday FC (1975) The influence of the tidal stress on the residual circulation. Tellus A 27:484–489CrossRefGoogle Scholar
  29. Pohlmann T (1996) Predicting the thermocline in a circulation model of the North Sea part I: model description, calibration and verification. Cont Shelf Res 16(2):131–146CrossRefGoogle Scholar
  30. Pohlmann T (2006) A meso-scale model of the central and southern North Sea: consequences of an improved resolution. Cont Shelf Res 26(19):2367–2385CrossRefGoogle Scholar
  31. Quan Q, Mao XY, Jiang WS (2014) Numerical computation of the tidally induced Lagrangian residual current in a model bay. Ocean Dyn 64:471–486CrossRefGoogle Scholar
  32. Roache PJ (1976) Computational fluid dynamics. Hermosa Publishers, New MexicoGoogle Scholar
  33. Robinson IS (1983) Tidally induced residual flows. In: Johns B (ed) Physical oceanography of coastal and shelf seas. Elsevier, Amsterdam, pp 321–356CrossRefGoogle Scholar
  34. Salas-de-León DA, Carbajal-Pérez N, Monreal-Gómez MA, Barrientos- MacGregor G (2003) Residual circulation and tidal stress in the Gulf of California. J Geophys Res 108(C10):3317.  https://doi.org/10.1029/2002JC001621 CrossRefGoogle Scholar
  35. Sun WX (1987) A further study of ultra-shallow water storm surge model. J Shandong College of Oceanology 17(1):34–45Google Scholar
  36. 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
  37. 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
  38. 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
  39. 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
  40. Winant CD (2008) Three-dimensional residual tidal circulation in an elongated, rotating basin. J Phys Oceanogr 38:1278–1295CrossRefGoogle Scholar
  41. Zimmerman JTF (1979) On the Euler-Lagrange transformation and the Stokes’ drift in the presence of oscillatory and residual currents. Deep-Sea Res 26A:505–520CrossRefGoogle Scholar

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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