The Lagrangian Residual Circulation And Inter-tidal Salinity Transport In A General Nonlinear Tidal System, Jiaozhou Bay

The distribution and regime shift of coastal environmental quality andecosystem health is much related to coastal circulation and subtidal transport. In thesubtidal timescales, two methods of averaging the primitive conservation areestablished: the Eulerian mean and general nonlinear Lagrangian mean. The lattercan be simplified as the weakly nonlinear Lagrangian mean under weakly nonlinearconditions.In theory, the distinction between the Eulerian and Lagrangian residualvelocities has been recognized for decades, but the definition of appropriate residualvelocities and mean concentrations is still an open question. In this paper, the generalnonlinear Lagrangian mean theory was applied to a potential general nonlinearsea-Jiaozhou Bay to study the residual circulation and subtidal salinity transport. Thetrajectories of drifter, simulated Lagrangian residual velocity and subtidal salinitytransport were used to clarity the residual velocities and mean concentrations.The Lagrangian residual velocity and subtidal concentration depend on theinitial tidal phases. That is much different from steady Eulerian mean velocity andEulerian mean concentration, weakly nonlinear Lagrangian mean velocity andconcentration. The drifters were released in the middle south and southwest of InnerBay inside Jiaozhou bay. It is found that even at the same initial position, thetrajectories and net displacements of drifter over25h show much difference atdifferent tidal phases. Following the fluid particle path, the inter-tidal salinity andtemperature also vary much. That is in accordance with the general nonlinearLagrangian mean theory, but can not be explained with the Eulerian mean theory andweakly nonlinear Lagrangian mean theory.The drifter observations are sparse and disturbed. Thus, the Lagrangian residualvelocity, which is applicable to general nonlinear systems, the first-order Lagrangianresidual velocity and the Eulerian residual transport velocity were simulated andcompared. The Lagrangian residual circulation in Jiaozhou Bay highly depends on the initial tidal phases in the M2barotrophic tidal system. The strong intra-tidalvariation of Lagrangian residual velocity indicate that the M2tidal system of JZB isgeneral nonlinear rather than weakly nonlinear. The strong dependence of waterflushing time on the initial tidal phase can be explained by the significant intra-tidalvariation of the Lagrangian residual velocity. Several vortexes in the Eulerianresidual circulation near the capes disappear in the Lagrangian residual circulation. Alarge counterclockwise eddy embedding two small counterclockwise vortexdominates the Inner Bay of JZB. The composition of the Lagrangian residualvelocity at different tidal phases coincides well with the observed net surfacesediment transport pattern. But the first-order Lagrangian residual velocity andEulerian residual transport velocity can not describe the intra-tidal variation offlushing time and net surface sediment transport pattern. Thus, the Lagrangianresidual velocity should depict the coastal circulation more properly than theEulerian residual transport velocity and the first-order Lagrangian residual velocityin general nonlinear tidal systems. In the surface layer, horizontal advection is themain contributor to the strong nonlinearity near the bay mouth, while in the bottomlayer, the strong nonlinearity near the bay mouth may result from the verticalviscosity and horizontal advection. The tidal flat, wind and density inducedLagrangian residual velocities have obvious intra-tidal variation and threedimensional structures. In general, the Lagrangian residual velocity is stronger in thesurface layer than that in the bottom layer, and the Lagrangian residual velocity athigh tide is larger than that at the low tide. The effect of tidal flat slightly enhancesthe counterclockwise eddy inside the Inner Bay but does not change the pattern. Thewind-induced Lagrangian residual current flows with the wind in the surface layerbut against the wind in the bottom layer. The depth averaged wind-inducedLagrangian residual current roughly flows with the wind in the coastal shallowregion. In the baroclinic-M2tidal system, the density induced Lagrangian residualvelocity with magnitude above4cm/s flows toward the bay mouth in the surfacelayer, greatly enhance the M2semidiurnal tide induced Lagrangian residual velocity.While in the bottom layer, the density induced Lagrangian residual velocity flowstowards the top of JZB, which make the density-M2tide induced Lagrangian residualvelocity towards the top of JZB.In contrast with the Eulerian mean salinity, the intra-tidal variation ofLagrangian inter-tidal salinity is comparable with the intra-tidal variation of salinity.The subtidal salinity transport is mainly advected by Lagrangian residual velocity. Thus, the subtidal salinity transport also highly depends on the initial tidal phase.The bay mouth is an important transport pathway. The exchange with Yellow sea isweaker at low tide than that at high tide. The difference between Lagrangianinter-tidal salinity SLand initial salinity S could be used to measure the integral effectof diffusion on the labeled water parcel over one or several tidal periods. Theeffective Lagrangian subtidal diffusion of salinity (SL-S) was strongly influenced byLagrangian residual velocity. The effect of tidal flat, wind and density do not changethe distribution pattern of Lagrangian inter-tidal salinity. The variation of subtidalsalinity transport and diffusion due to tidal flat, wind and density is higher in thesurface layer than that in the bottom layer, higher at high tide than that at low tide.The subtidal transport is related to both Lagrangian residual current and Lagrangianinter-tidal concentration. The subtidal salinity transport can change a lot even due tominor variation of Lagrangian inter-tidal salinity but obvious variation of Lagrangianresidual velocity. For example, under the effect of northwest wind, thecounterclockwise transport of salinity in the Inner bay becomes counterclockwisetransport in the southwest Inner Bay and clockwise transport in the rest part of InnerBay.