Feng Shizuo

A three-dimensional weakly nonlinear dynamics on tide-induced Lagrangian residual current and mass-transport

In recent years, studies of the environmental hydrodynamics in coastal seas and tidal estuaries have placed focus on the processes which determine the “fate” of longer-term transport. The lagrangian residual current has been recognized as an important factor which affects the longer term transport processes since it is more relevant to use a Lagrangian mean velocity rather than an Eulerian mean velocity to determine the origin of Water masses. In the present paper, an attempt is made to formulate a three-dimensional dynamics on the tideinduced Lagrangian residual current and mass-transport based upon a three-dimensional weakly-nonlinear model of tides. The Lagrangian residual velocity is shown to be the sum of the mass-transport velocity, which is the sum of the Eulerian residual velocity and the Stokes’ drift velocity, and the Lagrangian residual drift velocity which is dependent on the tidal current phase. This reveals that it is the mass-transport velocity which is the tidal cycle Eulerian mean of the Lagrangian residual velocity and that the mass-transport velocity is correct to the second order of approximation rather than to the first order. And then, a new longer-term transport equation which correctly describes the Lagrangian nature of transport processes without introducing the Fickian hypothesis for tidal dispersion is derived. In fact, the convection can be correctly represented by the Eulerian mean of the Lagrangian residual velocity, as the convective velocity in the longer-term transport equation is nothing but the mass-transport velocity.

Annual cycle and budgets of nutrients in the Bohai Sea

The environmental problems in the Bohai Sea have become more serious in the last decade. High nutrient concentration contributes much to it. A Sino-German cooperation program has been carried out to improve the understanding of the ecosystem by observations and modelling. A three-dimensional ecosystem model, coupled with a physical transport model, is adopted in this study. The simulation for the year 1982 is validated by the data collected in 1982/1983. The simulated annual mean nutrient concentrations are in good agreement with observations. The nutrient concentrations in the bohai Sea, which are crucial to the algal growth, are high in winter and low in summer. There are depletion from spring to summer and elevation from autumn to winter for nutrients. The nutrients’ depletion is a response to the consumption of the phytoplankton bloom in spring. Internal recycle and external compensation affect the nutrient cycle. Their contributions to the nutrient budgets are discussed based on the simulated results. Production and respiration are the most important sink and source of nutrients. The process of photosynthesis consumes 152 kilotons-P and 831.1 kilotons-N while respiration releases 94.5 kilotons-P and 516.6 kilotons-N in the same period. The remineralization of the detritus pool is an important source of nutrient regeneration, It can compensate 23 percent of the nutrient consumed by the production process. The inputs of phosphates and nitrogen from rivers are 0.55 and 52.7 kilotons respectively. The net nutrient budget is −3.05 kilotons-P and 31.6 kilotons-N.

Pelagic nitrogen cycling in Jiaozhou Bay, a model study I: The conceptual model

A zero-dimensional box model (PNCMjzb) with six state variables (ammonium, nitrate, dissolved organic nitrogen, phytoplankton, zooplankton and detritus) was developed to study nitrogen cycling in the Jiaozhou Bay pelagic ecosystem. The dominant processes within these compartments are considered with nitrogen as flow currency. Phytoplankton and zooplankton are treated as separate state variables, assuming that the species composition was dominated by two or three species the dynamic constants of which are similar and that they represent the entire plankton community. The microbial loop has not been integrated explicitly in the model. The turnover of bacteria is included implicitly in processes such as detritus decomposition, DON remineralization, pelagic nitrification and denitrification. The model is driven by two forcing variables, viz. water temperature and light intensity. Historical data from the 1980s and 1990s were compiled and used for model calibration. In this paper (part I), the consideration of every main compartment in the model is interpreted in detail. And the applied equations and parameters are presented. The main results from the simulations together with discussion about phytoplankton dynamics and primary production in Jiaozhou Bay are presented in the next paper (part II).

A Lagrangian model of Circulation in Bohai Sea

The Bohai Sea is a typical shallow sea. The modeling of the time mean circulation in the Bohai Sea and a more thorough understanding of its dynamics are of interest. The problem of winter circulation in the Bohai Sea is referable to the physics of sea-ice and will be not discussed in this chapter. Preliminary researches suggested that the summer circulation pattern in the Bohai Sea can be grossly characterized by a big counterclockwise gyre (Guan et al, 1977). And then the big counterclockwise gyre in the summer circulation pattern was numerically simulated based on a depth-averaged wind-driven and thermohaline circulation model (Zhang et al., 1984). However, such a simple pattern of the summer circulation cannot be used to explain, directiy or indirectiy, some field data and long-term transport processes in the Bohai Sea. Recently the tide-induced Lagrangian residual current field in the Bohai Sea has been obtained by a numerical model for a typical summer condition of flow through the Bohai Strait (Zheng, 1992). The contribution of this numerical simulation was an inspiration that the tide-induced residual circution should be an important component of the mean circulation in the Bohai Sea (Feng, 1990).

Comparison of the Eulerian and Lagrangian tidal residuals in the Bohai Sea

Tidal residual is very important to the transport of water particles, nutrients, plankton, etc. in the coastal sea. Eulerian scheme and Lagrangian scheme are two different ways to get the time averaged residual. Solution of the Bohai Sea’s hydrodynamic system using a semi-implicit layer averaged numerical model yielded different direction Eulerian and Lagrangian tidal residuals. The latter were stronger than the former in most sea areas. Their different directions produced different circulation pattern in some areas. Compared with the Eulerian residual, the Lagrangian residual seemed to be more in accord with the observation.

ON THE BEHAVIORS OF OCEAN BOTTOM EDDY

On the basis of scaling analysis, this paper presents a frontal geostrophic dynamic system which can be used to describe the dynamics of an isolated bottom eddy and shows that five possible dynamic subregimes are included in the system. A particle-in-cell method is used to investigate the behavior of the eddy in the two dynamic subregimes, with 1) nonlinear effect (ε) relevant to the sloping bottom-induced beta effect (β1) and 2) seamount-induced beta effect (β2) dominant. In the dynamic subregime ofβ1∼ε∼10-2 andβ2=0, the eddy can keep as a whole for a long time and migrates for a long distance. In the dynamic subregime where the seamount-induced beta effect (β1∼10-1) is dominant, the seamount traps the water particles, causing the eddy to break up into a discrete set of eddies moving around the seamount.

Simple simulation of the annual variation of the specific photosynthesis rate in Jiaozhou Bay

A simple diagnostic simulation of the annual cycling of the surface specific photosynthesis rate (SPR) in Jiaozhou Bay is described in this paper. Light intensity, temperature and nutrients (nitrate+ammonia, phosphate) were considered as main factors controlling photosynthesis of phytoplankton and were introduced into the model by different function equations. The simulated variation of specific photosynthesis rate coincided with the measured data. Analysis of the effect of every factor on photosynthesis indicated that the variation of photosynthesis rate was controlled by all these three factors, while temperature showed good correlation with SPR as measurement showed. This diagnostic simulation yielded the values of some parameter relating with the photosynthesis in Jiaozhou Bay.

NUMERICAL EXPERIMENTS ON THE WIND-DRIVEN CIRCULATION IN THE BOHAI, HUANGHAI AND EAST CHINA SEAS IN WINTER

A new semi-implicit numerical model developed to investigaté the wind-driven circulation (with inflow and outflow) in the Bohai, Huanghai and East China Sea in winter showed that the open boundary conditions and wind forcing are important in controlling general circulation in wintertime; that open boundary conditions (such as Kuroshio, Changjiang River runoff) are primary factors controlling the East China Sea circulation; and that wind driven current is more important in the upper layer in shallow sea area (such as Bohai Sea, North Huanghai Sea, as well as coastal area) in winter. Two numerical experiments are discussed to demonstrate the circulation responding to the changes of the open boundary conditions.

The dynamic effects of a finite depth ambient fluid on bottom eddy

Scaling analysis shows that ifo(ε2,β1ε,γ)∼o(δ), frontal geostrophic dynamics governs the behavior of an isolated bottom eddy in a finite depth ambient fluid; and that the ambient flow induced by bottom eddy migration satisfies quasi-geostrophic dynamics. This two layer model includes the important processes of advection of bottom eddy due to ambient flow, baroclinic instability, and form drag introduced by Rossby waves. The numerical results show that the three processes enhance the instability and alter the migration speed of the bottom eddy, and that the form drag induces a significant meridional drift of the eddy.

A three-dimensional nonlinear hydrodynamic model with variable eddy viscosity in shallow seas

Considerable scientific and practical interest exists in ascertaining the dynamic processes in shallow seas. This is especially true for China having a vast area of shallow seas. To simulate the observed data and study the dynamical mechanism of waves and currents in shallow seas a numerical model is developed in this paper. In view of the notable nonlinearity of shallow sea waves and currents, and in order to solve the current distribution in the vertical direction, and to examine the effect of variable eddy viscosity, the model proposed is a three-dimensional nonlinear one with variable eddy viscosity. The eddy viscosity can be considered as a physically acceptable arbitrary function of depth, which is realized in terms of a Sturm-Liouville System. The currents are expressed by using the eigenfunctions satisfying the Sturm-Liouville System just mentioned. A boundary-value problem (or an initio-boundary-value problem) of free surface elevation is derived. And then, the application of the proposed shallow sea model to nonlinear tides, ultra-shallow water storm surges and steady circulation is given, respectively. Finally, a generalized linear law between the bottom friction and the transport is derived.