Numerical modelling of Lagrangian residual current in the Bohai Strait

The Bohai Strait is the only passage-way of the semienclosed Bohai Sea into the outer ocean. The various dynamical processes have great effects on both sides of the strait, especially on the Bohai Sea. Tidal current dominates in the strait, and among the tida! components the M, component tide is prevailing.The seawater in the strait is homogeneous vertically almost the whole year because of strong tidal mixing. The M, component tide was simulated numerically using two dimensional barotropical model, and the Eulerian tide-induced residual currents were also deduced. The results showed that the tidal currents were dominated by the coastal line and topography. There exist many eddies in the tide-induced residual current fields, particularly near the northern coast.On the basis of the simulation of the tidal currents, the movements of the water particles in the strait were tracked by means of Lagrangian techniques. Consequently the Lagrangian residual currents were obtained. Somewhat similar to the Eulerian     

A Eulerian–Lagrangian method for the simulation of wave propagation

A Eulerian–Lagrangian method (ELM) is employed for the simulation of wave propagation in the present research. The wave action conservation equation, instead of the wave energy balance equation, is used. The wave action is conservative and the action flux remains constant along the wave rays. The ELM correctly accounts for this physical characteristic of wave propagation and integrates the wave action spectrum along the wave rays. Thus, the total derivative for wave action spectrum may be introduced into the numerical scheme and the complicated partial differential wave action balance equation is simplified into an ordinary differential equation. A number of test cases on wave propagation are carried out and show that the present method is stable, accurate and efficient. The results are compared with analytical solutions and/or other computed results. It is shown that the ELM is superior to the first-order upwind method in accuracy, stability and efficiency and may better reflect the complicated dynamics due to the complicated bathymetry features in shallow water areas.     

Interactions of nonlinear gravity waves and uniform current in Lagrangian system

The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an EulerLagrange transformation. The thirdorder asymptotic solution is a periodic bounded function of Lagrangian labels and time, which imply that the entire solution is uniformlyvalid. The explicit parametric solution highlights the trajectory of a water particle and mass transport associated with a particle displacement can now be obtained directly in Lagrangian form. The angular frequency and Lagrangian mean level of the particle motion in Lagrangian form differ from those of the Eulerian. The variations in the water particle orbits resulting from the oblique interaction with a steady uniform current of different magnitudes are also investigated.     

Nonlinear Lagrangian Breaker Characteristics for Waves Propagating Normally Toward A Mild Slope

Because of shoaling, refraction, friction, and other effects, a surface-wave propagating on a gently sloping bottom of slope will eventually break. In this paper, by nonlinearizing the problem and using a perturbation method, an analytical solution for the velocity potential is derived to the second order for the bottom slope a and the wave steepness e in a Eulerian system. Then, the wave profile and the breaking wave characteristics are found by transforming the flow field into a Lagrangian system. By use of the kinematic stability parameter （K. S. P. ）, new theoretical breaker characteristics are derived. Thus, the linear theories of other scholars are extended to breaking waves. A Comparison of the present analytical solution with experimental studies of other scholars shows reasonable agreement except that the breaking depth is underestimated.     

A Lagrangian mean theory on coastal sea circulation with inter-tidal transports I. Fundamentals

A brief review is made on the theory of the Lagrangian residual circulation and inter-tidal transports in a convectively weakly nonlinear system. In the review the emphasis is put on the systematical development of the theory and its weakness of convectively weakly nonlinear approximation. The fundamentals of a Lagrangian tidally-averaged theory on circulation with inter-tidal transport processes have been proposed for a general nonlinear coastal/estuarine system. The Lagrangian residual velocity is strictly de- fined, and it has been verified to be able to embody the velocity field of circulation. A new concept of the concentration for inter- tidal transport processes is presented. The concentration describing the inter-tidal transport processes should be a ＂Lagrangian inter-tidal concentration＂ defined and named, but not the Eulcrian tidally-averaged concentration used traditionally. The circulation described here contains a set of infinite temporal-spatial fields of velocity/concentration, each of which corresponds to a specific value of tidal phases varying continuously over one tidal cycle. When the convectively weakly nonlinear condition（ with a smaller order of eddy diffusion and sources） is approximately satisfied, a set of infinite temporal-spatial fields of velocity/concentration can be reduced to a single one.. the mass transport velocity/the Eulerian tidally averaged concentration as exhibited traditionally.     

A Lagrangian mean theory on coastal sea circulation with inter-tidal transports Ⅱ. Numerical Experiments

The results of the new concept of coastal sea circulation are demonstrated by numerical simulations for the first time. The numerical experiments in three types of rectangular model seas illustrate the dependence of circulation on tidal phases due to the convectively nonlinear effect which is estimated by a newly defined drift dispersion in-dex. Then, the present theory is applied in the Bohai Sea of China. At the Bohai Straits and the Huanghe River mouth area the circulation direction even reverses owing to different initial tidal phases which shows that the the-ory copes with nonlinearity well. The calculated M2 tide-induced residual circulation shows that a clockwise gyre exists in the center of an anticlockwise gyre in the central Bohai Sea due to the topographic features. In the Bo-hai Gulf the tide induced circulation shows a 3D structure with outflow at the surface and the inflow at the bottom which can partly explains the spread of the Huanghe River fresh water out of the Bohai Gulf and the inflow of the sediment from the Huanghe River.     

A Lagrangian mean theory on coastal sea circulation with inter-tidal transports Ⅱ. Numerical Experiments

The results of the new concept of coastal sea circulation are demonstrated by numerical simulations for the first time. The numerical experiments in three types of rectangular model seas illustrate the dependence of circulation on tidal phases due to the convectively nonlinear effect which is estimated by a newly defined drift dispersion index. Then, the present theory is applied in the Bohai Sea of China. At the Bohai Straits and the Huanghe River mouth area the circulation direction even reverses owing to different initial tidal phases which shows that the theory copes with nonlinearity well. The calculated M2 tideinduced residual circulation shows that a clockwise gyre exists in the center of an anticlockwise gyre in the central Bohai Sea due to the topographic features. In the Bohai Gulf the tide induced circulation shows a 3D structure with outflow at the surface and the inflow at the bottom which can partly explains the spread of the Huanghe River fresh water out of the Bohai Gulf and the inflow of the sediment from the Huanghe River.     

Drift of Surface Lagrangian Buoys in the Central Sea of Japan in October–November 2011

Izvestiya, Atmospheric and Oceanic Physics - In early October 2011, two surface buoys were deployed off Peter the Great Bay in the Sea of Japan. They drifted in that area first, then crossed the...     

Numerical investigation on the penetration of gravity installed anchors by a coupled Eulerian–Lagrangian approach

Gravity installed anchors (GIAs) are released from a height of 30–150 m above the seabed, achieving velocities up to 19–35 m/s at the seabed, and embed to depths of 1.0–2.4 times the anchor length. Challenges associated with GIAs include the prediction of anchor initial embedment depth, which determines the holding capacity of the anchor. Based on the coupled Eulerian–Lagrangian approach, a numerical framework is proposed in this paper to predict the embedment depth of GIAs, considering the effects of soil strain rate, soil strain-softening and hydrodynamic drag (modeled using a concentrated force), with the anchor-soil friction described appropriately. GIAs are influenced by the hydrodynamic drag before penetrating into the soil completely, hence the anchor accelerates less than the previous investigations in shallow penetration, even decelerates directly at the terminal impact velocity. The hydrodynamic drag has more influence on OMNI-Max anchors (with an error of ∼4.5%) than torpedo anchors, and the effect becomes more significant with increasing impact velocity. An extensive parametric study is carried out by varying the impact velocity, strain rate and strain-softening parameters, frictional coefficient, and soil undrained shear strength. It is concluded that the dominant factor affecting the penetration is the soil undrained shear strength, then are the impact velocity, strain rate dependency and frictional coefficient, and the minimal is the strain-softening of soil. In addition, although the strain rate dependency is partly compensated by the softening, the anchor embedment depth accounting for the effects of strain rate and strain-softening is lower than that for ideal Tresca soil. Strain rate dependency dominates the combined effects of strain rate and strain-softening in the dynamic installation of GIAs, on which should pay more attention, especially for the calibration of the related parameters and the measured solutions. In the end, the theoretical model based on the bearing resistance method is extended by accounting for the hydrodynamic drag effect.     

A three-dimensional numerical calculation of the wind-driven thermohaline and tide-induced Lagrangian residual current in the Bohai Sea

On the basis of a three-dimensional weakly nonliear theory of Lagrangian residual current in the Baroclinic shallow seas, a diagnostic numerical calculation of wind-driven, thermohaline and tide-induced Lagrangian residual current in the Bohai Sea is made. The model involves the Richardson number in the eddy viscosity coefficient, wind, thcrmolialine and tidal effects in the focing terms. The runoff of the Huanghe River and a part of the Huanghai Warm Water coming from the Huanghai Sea through the Bohai Sea Strait is also considered. The velocity-splitting method is adopted. The wind-driven circu lation, thermohaline circulation and the tide-induced Lagrangian residual circulation are also obtained individually and analysed. The dynamics of the three main eddies in the Lagrangian mean circulation is discussed. Finally, the numerical result is partly verified with the observed data.     

An efficient approach to incorporate anchor line effects into the coupled Eulerian–Lagrangian analysis of comprehensive anchor behaviors

With the application of innovative anchor concepts and advanced technologies in deepwater moorings, anchor behaviors in the seabed are becoming more complicated and significantly affected by the anchor line. Based on the coupled Eulerian–Lagrangian (CEL) method, a numerical approach incorporating anchor line effects is developed to investigate comprehensive anchor behaviors in the soil, including penetration of drag anchors, keying of suction embedded plate anchors and diving of gravity installed anchors. Compared to the method directly incorporating the anchor line into the CEL analysis, the proposed method is computationally efficient. To examine the robustness and accuracy of the proposed method, numerical probe tests and then comparative studies are carried out. It is found that the penetration (or diving) and keying behaviors of anchors can be well simulated. A parametric study is also undertaken to quantify the effects of various factors on the behavior of OMNI-Max anchors, whose mechanisms are not yet fully understood. The maximum embedment loss of OMNI-Max anchors during keying is not influenced by the initial anchor embedment depth, whereas significantly increases with increasing drag angle at the embedment point. With decreasing initial anchor embedment depth or increasing soil strength gradient, drag angle at the embedment point and diameter of the anchor line, the behavior of OMNI-Max anchors could change from diving to pullout, which is undesirable in offshore engineering practice. If the drag angle increases over a certain limit, the anchor will fail similar to a suction anchor.     

Drift currents in the southern New Zealand region as derived from Lagrangian measurements and the remote sensing of sea‐surface temperature distributions

Four drift bottles, cast adrift south of the Subtropical Convergence at 48°S, 156°E in November 1980, landed within 123 days of release at a short stretch of coast north of Banks Peninsula. A high degree of coherence in the responsible drift pattern is indicated. The contemporary surface circulation inferred from satellite‐derived sea‐surface temperature distributions indicates that the bottles were entrained in a meridionally‐converging flow after drifting across the southern Tasman Sea without crossing the Convergence. They were prevented from further eastward drifting because of a marked southward flexing of the Convergence east of the Southland Current during February 1981. Because of local weather and tide effects, the bottles finally beached in Pegasus Bay.