3D Modal Solution for Tidally Induced Lagrangian Residual Velocity with Variations in Eddy Viscosity and Bathymetry in a Narrow Model Bay

In this study, we examine the results obtained by the Finite-volume Coastal Ocean Circulation Model(FVCOM) regarding the effects of eddy viscosity and bathymetry on the three-dimensional(3 D) Lagrangian residual velocity(LRV) in a narrow bay. The results are cast in terms of two nondimensional numbers: the ratio of friction to local acceleration(δ) and the ratio of the minimum depth over shoals to the maximum depth in the channel(ε). The ratio δ depends on the eddy viscosity and mean depth. For a given eddy viscosity, when ε > 0.5, the along-estuary LRV tends to be vertically sheared and when ε < 0.5, the exchange is laterally sheared. When ε << 1, the structure of the 3 D, depth-integrated, and breadth-averaged LRV changes only slightly as δ increases. For ε values between 0.33 and 0.5, the structure of the 3 D LRV is mainly laterally sheared. In the same ε range, the 3 D and depth-integrated LRV exhibit reversed structures from high to low δ values. In addition, the breadth-averaged LRV weakens the typical twolayered circulation when δ decreases. When ε is 1, the two-layered vertical structure reverses direction, and a three-layered vertical structure develops in the outer bay as δ decreases.

Analytical Solution for 3D Tidal Flow with Vertically Varying Eddy Viscosity

In this study, a 3D idealized model of tidal flow, in which the tidal elevation and velocities are solved analytically, is developed. The horizontal eddy viscosity is neglected, and the vertical eddy viscosity used in the study is assumed to be independent of time and only varies as a parabolic function in the vertical direction. The analytical solution is obtained in a narrow rectangular bay, with the topography varying only across the bay. The model results are compared with the field observations in the Xiangshan Bay. The results show that the influence of varying vertical eddy viscosity mainly has two aspects. On one hand, it amplifies the magni- tude of the tidal elevation, particularly the amplitude near the head of the bay. On the other hand, it adjusts the axial velocity profile, resulting in an obvious frictional effect. Furthermore, the tidal elevation and velocities are more sensitive to the magnitude of the eddy viscosity near the bottom than the structure in the upper water layer.

Numerical Study on Inter-Tidal Transports in Coastal Seas

Inter-tidal(subtidal) transport processes in coastal sea depend on the residual motion, turbulent dispersion and relevant sources/sinks. In Feng et al.(2008), an updated Lagrangian inter-tidal transport equation, as well as new concept of Lagrangian in- ter-tidal concentration(LIC), has been proposed for a general nonlinear shallow water system. In the present study, the LIC is nu- merically applied for the first time to passive tracers in idealized settings and salinity in the Bohai Sea, China. Circulation and tracer motion in the three idealized model seas with different topography or coastline, termed as ‘flat-bottom', ‘stairs' and ‘cape' case, re- spectively, are simulated. The dependence of the LIC on initial tidal phase suggests that the nonlinearities in the stairs and cape cases are stronger than that in the flat-bottom case. Therefore, the ‘flat-bottom' case still meets the convectively weakly nonlinear condi- tion. For the Bohai Sea, the simulation results show that most parts of it still meet the weakly nonlinear condition. However, the de- pendence of the LIS(Lagrangian inter-tidal salinity) on initial tidal phase is significant around the southern headland of the Liaodong Peninsula and near the mouth of the Yellow River. The nonlinearity in the former region is mainly related to the complicated coast- lines, and that in the latter region is due to the presence of the estuarine salinity front.