CHAPTER 53 THE " SWAN " WAVE MODEL FOR SHALLOW WATER
CHAPTER 53 THE " SWAN " WAVE MODEL FOR SHALLOW WATER
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发表时间：
2010
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通讯作者：
N. Booij;L. Holthuijsen;R. Ris
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作者：
N. Booij;L. Holthuijsen;R. Ris
简要描述了用于计算环境水流浅水中波浪条件的数值模型 SWAN（近岸模拟波浪）。该模型基于动作平衡方程的全谱表示，并明确建模了所有物理过程。对光谱演化没有任何先验的限制。这使得该模型成为第三代模型。在 Holthuijsen 等人中。 (1993) 和 Ris 等人。 (1994) 的传播、产生和耗散测试用例已在没有电流的情况下进行了展示。现在已添加当前效果，并在此处显示学术案例。该模型还应用于相当学术性的浅湖案例（澳大利亚乔治湖）和复杂而现实的潮间带水流案例（荷兰弗里斯切泽加特）。将结果与观察结果进行比较。提出了在曲线网格上制定模型以适应与水动力循环模型的联系的新发展，并展示了第一次测试。简介 在过去的十年中，海岸工程中用于计算近岸条件下波浪的传统波浪线模型正在被根据规则网格上的光谱能量平衡（或存在环境电流时的作用平衡）来制定波浪演化的模型所取代。在此类模型的第三代版本中，波谱可以不受任何先验限制地演化，并且所有相关的物理过程都以离散谱公式明确表示。这里描述了包含环境电流的这种波模型（SWAN 模型）。从概念上讲，它是深水第三代波浪模型的延伸，但所涉及的物理过程和数值技术更加复杂。 SWAN波浪模型被认为是计算上可行的第三代谱波模型，适用于咨询环境中具有环境电流的浅水（包括冲浪区）中的波浪，在台式计算机上返回时间小于30分钟。代尔夫特理工大学土木工程系，P.O. Box 5048, 2600 GA 代尔夫特, 荷兰。 “SWAN”波模型 669 SWAN 波模型 SWAN 波模型（Ris 等人，1994）是基于作用平衡方程的完全离散谱模型，该方程隐含地考虑了波与电流之间通过辐射应力的相互作用（例如，Phillips，1977）： |NW)+VIy.[ciyNW)]4KNW)]4[c,NM]=M ot do do o 左侧第一项是动作密度随时间的变化率，第二项是动作在地理 x、y 空间中的直线传播。第三项描述了由于电流和随时间变化的深度而在 cr 空间中随传播速度 c„ 产生的相对频率的变化。第四项表示在 0 空间（深度和电流引起的折射）中随传播速度 ce 的传播。作用平衡方程右侧的项 S(<x,6) 是表示风增长、波浪与波浪相互作用以及底部摩擦、白顶和深度引起的波浪破碎引起的衰减的源项。为了减少计算机时间，我们删除作用平衡方程中的时间（即 d/dt = 0）是可以接受的，因为波浪的停留时间通常远小于波浪边界条件、周围海流、风或潮汐变化的时间尺度。对于这些变化的时间尺度变得重要的情况，即边界处的变化的传入波浪或变化的风或海流，可以通过在预定义的时间间隔内重复计算来采取准稳态方法。生成、耗散和四重波相互作用的公式取自 WAM 模型（WAM 循环 3，WAMDI 组，1988 年，以及可选的 WAM 循环 4，Komen 等人，1994 年，目前在欧洲中期天气预报中心运行），本研究使用了 WAM 循环 3 的公式，并补充了用于深度引起的 Battjes 和 Janssen 破坏的耗散模型的频谱版本。 (1978) (使用 Nelson, 1987 的最大波高与深度比) 和最近制定的三重波-波相互作用的离散相互作用近似 (Eldeberky 和 Battjes, 1995) 在 SWAN 模型中使用完全隐式数值方案来在地理空间和光谱空间中传播（迭代、前向、四扫技术，Ris 等人，1994）。与传统谱波模型的显式方案相比，传统谱波模型仅是条件稳定的，因此在浅水中需要非常小的时间步长（在 10 m 的水深中，100 m 分辨率通常为 10 s，其中在 SWAN 模型中，时间增量可能高达 15 分钟），这在潮汐入口、潮滩和 670 等尺度变化很大的区域中是不方便的。 COASTAL ENGINEERING 1996 河口。在这种情况下，采用递减分辨率的网格嵌套是一种传统方法，但它需要额外的计算，特别是如果网格符合该区域的地形，那么它还可以适应通常在此类网格上制定的水动力环流模型的联系。对于 x 方向，这是针对网格点 i 、j 的非等距有限迎风差（网格点在 x 、y 空间中排序）：
The numerical model SWAN (Simulating WAves Nearshore) for the computation of wave conditions in shallow water with ambient currents is briefly described. The model is based on a fully spectral representation of the action balance equation with all physical processes modelled explicitly. No a priori limitations are imposed on the spectral evolution. This makes the model a third-generation model. In Holthuijsen et al. (1993) and Ris et al. (1994) test cases for propagation, generation and dissipation have been shown without currents. Current effects have now been added and academic cases are shown here. The model is also applied in a fairly academic case of a shallow lake (Lake George, Australia) and in a complex, realistic case of an inter-tidal area with currents (Friesche Zeegat, the Netherlands). The results are compared with observations. A new development to formulate the model on a curvi-linear grid to accommodate linkage to hydro-dynamic circulation models is presented and a first test is shown. INTRODUCTION Over the last decade, the traditional wave ray models in coastal engineering to compute waves in nearshore conditions are being replaced by models that formulate the wave evolution in terms of a spectral energy balance on a regular grid (or the action balance in the presence of ambient currents). In third-generation versions of such models the wave spectrum is allowed to evolve free of any a priori limitations and all relevant physical processes are represented explicitly in a discrete spectral formulation. Such a wave model (the SWAN model), with the inclusion of ambient currents is described here. Conceptually it is an extension of deep water thirdgeneration wave models but the physical processes and the numerical techniques involved are more complicated. The SWAN wave model has been conceived to be a computationally feasible third-generation spectral wave model for waves in shallow water (including the surf zone) with ambient currents in a consulting environment with return times of less than 30 min on a desk top computer. Delft University of Technology, Department of Civil Engineering, P.O. Box 5048, 2600 GA Delft, Netherlands. "SWAN" WAVE MODEL 669 THE SWAN WAVE MODEL The SWAN wave model (Ris et al., 1994) is a fully discrete spectral model based on the action balance equation which implicitly takes into account the interaction between waves and currents through radiation stresses (e.g., Phillips, 1977): |NW)+VIy.[ciyNW)]4KNW)]4[c,NM]=M ot do do o The first term in the left-hand side is the rate of change of action density in time, the second term is the rectilinear propagation of action in geographical x-,yspace. The third term describes the shifting of the relative frequency due to currents and time-varying depths with propagation velocity c„ in cr-space. The fourth term represents the propagation in 0-space (depthand current-induced refraction) with propagation velocity ce. The term S(<x,6) at the right hand side of the action balance equation is the source term representing the growth by wind, the wave-wave interactions and the decay by bottom friction, whitecapping and depth-induced wave breaking. To reduce computer time, we remove time from the action balance equation (i.e., d/dt = 0). This is acceptable for most coastal conditions since the residence time of the waves is usually far less than the time scale of variations of the wave boundary conditions, the ambient current, wind or the tide. For cases in which the time scale of these variations becomes important, i.e., variable incoming waves at the boundary, or variable winds or currents, a quasi-stationary approach can be taken by repeating the computations for predefined time intervals. The formulations for the generation, the dissipation and the quadruplet wavewave interactions are taken from the WAM model (WAM Cycle 3, WAMDI group, 1988 and optionally WAM Cycle 4, Komen et al., 1994 as presently operational at the European Centre for Medium Range Weather Forecasting). For the present study the formulations from WAM Cycle 3 are used. These are supplemented with a spectral version of the dissipation model for depth-induced breaking of Battjes and Janssen (1978) (with the maximum wave height to depth ratio from Nelson, 1987) and a recently formulated discrete interaction approximation for the triad wave-wave interactions (Eldeberky and Battjes, 1995). Fully implicit numerical schemes are used in the SWAN model for propagation in both geographic space and spectral space (an iterative, forward-marching, foursweep technique, Ris et al., 1994). This scheme is unconditionally stable in contrast with the explicit schemes of conventional spectral wave models which are only conditionally stable and which require therefore very small time steps in shallow water (typically 10 s for 100 m resolution in water depth of 10 m where in the SWAN model the time increment may be as large as 15 min). The formulation is basically in terms of finite differences on a regular, rectangular grid. This is inconvenient in regions with highly variable scales such as tidal inlets, tidal flats and 670 COASTAL ENGINEERING 1996 estuaries. Nesting of grids with decreasing resolution is the conventional approach in such cases but it requires extra computations. A variable resolution grid would avoid such extra computations, in particular if the grid would conform to the topography of the region. It would also accommodate the linkage with hydrodynamic circulation models which are often formulated on such grids. Such a curvilinear approach is implemented in the SWAN model by considering in the numerical scheme of each spatial grid point, two separate, non-equidistant finite up-wind differences in each of two orthogonal directions. For the x -direction this is for grid point i ,j (the grid points are ordered in x , y-space):