和陆架区域的特征复杂的不规则海岸线和地形几何学，包括内潮涨落（对这些早期应用的描述见http://codfish.smast.umassd.edu 或 http://fvcom.smast.umassd.edu）。
This manual is provided to help users to 1) understand the basic discrete structure and numerical methods used in FVCOM and 2) learn how to use the model for their own applications. Detailed instructions are given for all steps (e.g., grid generation, model input and output, compilation, parallel computation, etc.). Several experiments are included to provide new users with simple examples of model setup and execution
本手册将为用户提供以下帮助：（1）理解FVCOM使用的基本离散结构和数学方法；（2）学习怎样应用本模式。给出了所有步骤的详细说明（如网格生成、模式输入和输出、汇编、平行计算等）。包括几个实验结果为新用户提供模式建立和运行的几个简单例子。
The remaining chapters are organized as follows. Chapter 2: the model
formulation; Chapter 3: the finite-volume discrete method; Chapter 4: the external forcings; Chapter 5: the open boundary treatments; Chapter 6: the 4-D data
assimilation methods; Chapter 7: the sediment module; Chapter 8: the biological modules; Chapter 9: the tracer-tracking model; Chapter 10: the 3-D Lagrangian
particle tracking; Chapter 11: the sea ice module, Chapter 12: the code parallelization; Chapter 13: the model coding description and general information; Chapter 14: the model installation; Chapter 15: the model setup; Chapter 16: examples of model applications, and Chapter 17: an example of the unstructured grid generation.
剩余章节结构如下。第二章：模型公式；第三章：有限体积离散方法；第四章：外强迫；第五章：开边界处理；第六章：四维数据同化方法；第七章：沉积模块；第八章：生物模块；第九章：示踪物追踪模型；第十章：三维拉格朗日粒子追踪模型；第十一章：海冰模块；第十二章：代码平行计算；第十三章：模式编码和总说明；第十四章：模型安装；第十五章：
模型设置；第十六章： 模型应用的举例；第十七章：自由网格产生的一个例子。
Users should be aware that this manual is only useful for the current version of FVCOM. FVCOM is in continually testing and improvement by a
SMAST/UMASSDWHOI effort led by Changsheng Chen and Robert C. Beardsley. Some very recent modifications may not have been included in this manual. If users find any inconsistency between this manual and the FVCOM code, it is likely to be due to a typo in the manual. Please report any problems with this manual as well as suggestions for improvement, so that future versions can be enhanced.
用户应该知道本手册仅适用于FVCOM的当前版本。FVCOM由陈常胜博士和罗伯特C.比尔兹利博士领导的SMAST/UMASSDWHOI不断地测试和改进。本手册可能不包括一些近期的修正。如果用户发现任何这本手册和FVCOM代码之间的矛盾，可能是手册中的印刷问题。为了提高下一版本的质量，请提出本手册存在的问题以及改进建议。
Chapter 2: The Model Formulation
第二章：模型公式
2.1. The Primitive Equations in Cartesian Coordinates
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2.1 直角坐标系下的原始方程
The governing equations consist of the following momentum, continuity, temperature, salinity, and density equations:
控制方程包括下列动量方程、连续方程、温度方程、盐度方程和密度方程：
where x, y, and z are the east, north, and vertical axes in the Cartesian coordinate system; u, v, and w are the x, y, z velocity components; T is the temperature; S is the salinity; ? is the density; P is the pressure; f is the Coriolis parameter; g is the gravitational acceleration; Km is the vertical eddy viscosity coefficient; and Kh is the thermal vertical eddy diffusion coefficient. Fu,Fv,FT,andFS represent the horizontal momentum, thermal, and salt diffusion terms. The total water column depth is D ??H ??z , where H is the bottom depth (relative to z = 0) and z is the height of the free surface (relative to z = 0).
其中在直角坐标系中x，y，z分别表示东，北和竖直坐标轴；u，v，w是x，y，z方向的速度分量；T为温度；S为盐度；?为密度；P为压强；f为科氏参量； g为重力加速度；Km为垂直旋转粘性系数；Kh为热量垂直旋转扩散系数；Fu,Fv,FT,和FS代表水平动量，热量和盐度的扩散项。整体水柱深度为
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其中H为底部深度（z=0）；?为自由面高度（z=0）。
Fig. 2.1: Illustration of the orthogonal coordinate system: x: eastward; y: northward; z: upward.
图2.1 直角坐标系图解：x：东；y：北；z：竖直向上。
The surface and bottom boundary conditions for temperature are:
温度的表面和底边界条件为：
where Qn(x,y,t) is the surface net heat flux, which consists of four components: downward shortwave, longwave radiation, sensible, and latent fluxes, SW( x, y,0,t ) is the shortwave flux incident at the sea surface, and cp is the specific heat of seawater.
AH is the horizontal thermal diffusion coefficient, ?is the slope of the bottom bathymetry, and n is the horizontal coordinate shown in Figure 2.2 (Pedlosky, 1974; Chen et al., 2004b).
其中Qn(x,y,t)为表面净热量通量，包括四部分：向下的短波，长波辐射，显通量和潜通量；
SW(x,y,0,t)为海表面的短波通量；cp为海水比热；AH水平热量扩散系数;?为底面地形；
n为图2.2所示的水平坐标(Pedlosky, 1974; Chen et al.2004b)。
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Fig. 2.2: Schematic of the no-flux boundary condition on the bottom slope.
图2.2 底面倾斜无通量边界条件示意图
The longwave, sensible and latent heat fluxes are assumed here to occur at the ocean surface, while the downward shortwave flux SW( x, y, z, t ) is approximated by:
假设长波通量、显热通量和潜热通量发生在海表面，向下的短波通量SW(x,y,z,t)近似由下式给出：
where a and b are attenuation lengths for longer and shorter (blue-green) wavelength components of the shortwave irradiance, and R is the percent of the total flux associated with the longer wavelength irradiance. This absorption profile, first
suggested by Kraus (1972), has been used in numerical studies of upper ocean diurnal heating by Simpson and Dickey (1981a, b) and others. The absorption of downward irradiance is included in the temperature (heat) equation in the form of
其中a和b为组成短波辐照度的长波长和短波长（蓝-绿）的衰减长度；R为长波长辐照度占总通量的百分比。这种吸收面首先由Kraus（1972）提出，Simpson和 Dickey (1981a, b)以及其他学者将其用于上部海洋日热量的数学研究。向下辐照度的吸收包含于下式的温度（热量）方程：
This approach leads to a more accurate prediction of near-surface temperature than the flux formulation based on a single wavelength approximation (Chen et al., 2003b).
与基于一种单一波长近似的通量公式相比，这种近似可以得到近表面温度更精确的预报
(Chen et al., 2003b)。
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The surface and bottom boundary conditions for salinity are： 盐度的表面和底边界条件如下：
whereP andE 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
^^P和E分别为降水率和蒸发率；
^^；可以通过改变底边界条件的垂
直速度和盐度将地下水流量加入模型。
The surface and bottom boundary conditions for u, v, and w are: u，v，w的表面和底边界条件如下：
where and are the x and y components of
surface wind and bottom stresses, Qbis the groundwater volume flux at the bottom and ??is the area of the groundwater source. The drag coefficient Cd is determined by matching a logarithmic bottom layer to the model at a heightzab above the bottom, i.e.,
其中
和
为表面风和底压力的x，y方向的成
分；Qb为底部地下水流量；?为地下水源的面积。牵引系数Cd为在底面高度zab出将对数底层引入模型，例如
where k = 0.4 is the von Karman constant and zo is the bottom roughness parameter.
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