【正文】 evolume approach is better suited to guarantee mass conservation in both the individual control element and the entire putational domain. From a technical point of view, FVCOM bines the best attributes of finitedifference methods for simple discrete coding and putational efficiency and finiteelement methods for geometric flexibility. This model has been successfully applied to study several estuarine and shelf regions that feature plex irregular coastline and topographic geometry, including intertidal flooding and drying (see or for descriptions of these initial applications).我們開發(fā)了三維自由網(wǎng)格、自由表面、原始方程、有限體積海岸大洋環(huán)流模型（FVCOM）(Chen et al. 2003a。The remaining chapters are organized as follows. Chapter 2: the model formulation。 Chapter 10: the 3D Lagrangian particle tracking。本手冊(cè)可能不包括一些近期的修正。 P is the pressure。 z: upward. 直角坐標(biāo)系圖解：x：東；y：北；z：豎直向上。The surface and bottom boundary conditions for salinity are： 鹽度的表面和底邊界條件如下：where and are precipitation and evaporation rates, respectively. .Note that a groundwater flux can be easily added into the model by modifying the bottom boundary conditions for vertical velocity and salinity.其中和分別為降水率和蒸發(fā)率；；可以通過(guò)改變底邊界條件的垂直速度和鹽度將地下水流量加入模型。Chen et al. (2006a) 給出了一個(gè)式（）和（）中底部沒(méi)有法向通量條件的精確表達(dá)式的例子。從物理上說(shuō)，這種簡(jiǎn)化等同于假定水平擴(kuò)散僅出現(xiàn)在平行層。這種近似已成功應(yīng)用于普林斯頓大洋模型（POM）和羅格斯大洋模型系統(tǒng)（ROMs）。例如，水溫（T）由下式給出where is the area of the individual tracer control element (see Chapter 3 for definition and is the Prandtl number.其中為單獨(dú)示蹤控制元的面積（定義見(jiàn)第三章）；為普朗特?cái)?shù)。 ( q ql )和(k ) 湍流閉合模型（其中為湍流動(dòng)能；為湍流耗散）。 Kq is the vertical eddy diffusion coefficient of the turbulent kinetic energy。 The turbulent kinetic energy and macroscale equations are closed by defining 湍流動(dòng)能和尺度方程定義如下：Sm and Sh are defined as the stability functions和定義為如下穩(wěn)定函數(shù)：where . In the original MY level turbulent closure model (Mellor and Yamada, 1974, 1982), Sm and Sh are functions of the gradient Richardson number. By removing a slight inconsistency in the scaling analysis, Galperin et al. (1988) simplified the MY turbulent closure model so that Sm and Sh depend only on Gh . Gh has an upper bound of for the case of unstable () stratification and a lower bound of for the case of stable () stratification. Parameters A1, A2, B1, B2, and C1 are given as , , , , and , respectively.其中。 Mellor and Blumberg (2004) introduced a new turbulent kinetic energy flux surface boundary condition into the MY level model, in which Mellor and Blumberg (2004)where is a parameter related to the wave age。 Mellor and Blumberg, 2004) 的改進(jìn)，可有下式給出where H s is the significant wave height defined as 4H rms (H rms is the rms wave height). As suggested by Donelan (1990) and Smith et al. (1992), H s can be estimated based on the wave age and airside roughness parameter (z o ) in a form of其中為主波的高度，定義為4（為rms波高）。在此模型中，旋轉(zhuǎn)粘性（）仍由式（）給出，但由水平速度和垂直成層結(jié)構(gòu)的垂直剪切函數(shù)給出。 In the standard k model, 在標(biāo)準(zhǔn)k 模型中where其中and R i is the gradient Richardson number defined as為理查森數(shù)梯度，定義如下The eddy viscositycan be estimated by旋轉(zhuǎn)粘度可由下式估計(jì)給出where is a constant. In this standard k model, the empirical constants are specified as其中為常數(shù)。也是復(fù)雜波動(dòng)力學(xué)的一個(gè)經(jīng)驗(yàn)參數(shù)。因此，和在表面和底部總為0。 H is the mean water depth。. The Model. In the boundary layer approximation where the shear production of turbulent kinetic energy is produced by the vertical she ar of the horizontal flow near the boundary, the equations for and can be simplified as 在邊界層近似中，湍流動(dòng)能的剪切分量由近邊界水平流動(dòng)的垂直剪切產(chǎn)生，和的方程可簡(jiǎn)化為：where is the turbulent kinetic energy。Recently, the General Ocean Turbulent Model (GOTM) has bee a very popular opensource munity model (Burchard, 2002). The GOTM implements a number of turbulence modules which range from a simple Richardson parameterization to plex Reynoldsstress turbulence closure models. These modules include the ( q ql ) and (k ) turbulent closure models (where is the turbulent kinetic energy and is the turbulent dissipation). The k model is an alternative turbulent closure model that is very similar in dynamics to the q ql turbulent closure model. The most recent version of the k model also includes a more plete form of the pressurestrain covariance term with buoyancy, anisotropic production and vorticity contributions such that the cutoff of mixing is shifted from (original model) to (Canuto et al., 2001). The GOTM library has been interfaced with FVCOM and the full functionality of GOTM is available to FVCOM users. Brief descriptions of the original (q ql ) and the general form of the k model now featured in FVCOM are given below. Detailed descriptions of these models can be found in the GOTM manual and references listed in this paragraph. 近期，大洋湍流模型（GOTM）成為了普遍使用的開放源碼模型。顯然，的值隨模型分辨率和水平速度梯度變化：隨網(wǎng)格尺度水平速度梯度的減小而減小。在給出海表面上升的條件下也可解決三維方程。在此坐標(biāo)系下，方程（）（）化為：In the s coordinate system, the horizontal diffusion terms are defined as:在坐標(biāo)系下，水平擴(kuò)散項(xiàng)為：where and are the horizontal eddy and thermal diffusion coefficients, respectively. According to the argument made by Mellor and Blumberg (1985), the simplification made in ()(227) helps to ensure the validity of the locally 1D bottom boundary layer simulation in the scoordinate transformation system. Physically speaking, these simplifications are equivalent to the assumption that horizontal diffusion occurs only parallel to the slayers. It is clear that this simplification can lead to additional vertical mixing in the slope region due to the s transformation, thus making the modelpredicted thermoclines too diffusive in the vertical. Questions related to the horizontal diffusion terms and the stability of FVCOM without these terms are being addressed in the FVCOM development and will be improved in a later version.其中和分別為水平旋轉(zhuǎn)和熱擴(kuò)散系數(shù)。在有限差分近似中由這兩項(xiàng)的不精確計(jì)算引起的錯(cuò)誤可能使實(shí)際值偏大。這種吸收面首先由Kraus（1972）提出，Simpson和 Dickey (1981a, b)以及其他學(xué)者將其用于上部海洋日熱量的數(shù)學(xué)研究。Fig. : Illustration of the orthogonal coordinate system: x: eastward。 S is the salinity。第二章：模型公式；第三章：有限體積離散方法；第四章：外強(qiáng)迫；第五章：開邊界處理；第六章：四維數(shù)