A new efficient 3D non-hydrostatic free-surface flow model for simulating water wave motions

A new three-dimensional, non-hydrostatic free surface flow model is presented. For simulating water wave motions over uneven bottoms, the model employs an explicit project method on a Cartesian the staggered gird system to solve the complete three-dimensional Navier–Stokes equations. A bi-conjugated gradient method with a pre-conditioning procedure is used to solve the resulting matrix system. The model is capable of resolving non-hydrostatic pressure by incorporating the integral method of the top-layer pressure treatment, and predicting wave propagation and interaction over irregular bottom by including a partial bottom-cell treatment. Four examples of surface wave propagation are used to demonstrate the capability of the model. Using a small of vertical layers (e.g. 2–3 layers), it is shown that the model could effectively and accurately resolve wave shoaling, non-linearity, dispersion, fission, refraction, and diffraction phenomena.     

A higher-order σ-coordinate non-hydrostatic model for nonlinear surface waves

A higher-order non-hydrostatic model in a σ-coordinate system is developed. The model uses an implicit finite difference scheme on a staggered grid to simultaneously solve the unsteady Navier-Stokes equations (NSE) with the free-surface boundary conditions. An integral method is applied to resolve the top-layer non-hydrostatic pressure, allowing for accurately resolving free-surface wave propagation. In contrast to the previous work, a higher-order spatial discretization is utilized to approximate the large horizontal pressure gradient due to steep surface waves or rapidly varying topographies. An efficient direct solver is developed to solve the resulting block hepta-diagonal matrix system. Accuracy of the new model is validated by linear and nonlinear standing waves and progressive waves. The model is then used to examine freak (extreme) waves. Features of downshifting focusing location and wave asymmetry characteristics are predicted on the temporal and spatial domains of a freak wave.     

High-order compact MacCormack scheme for two-dimensional compressible and non-hydrostatic equations of the atmosphere

This study is devoted to application of the fourth-order compact MacCormack scheme to spatial differencing of the conservative form of two-dimensional and non-hydrostatic equation of a dry atmosphere. To advance the solution in time a four-stage Runge–Kutta method is used. To perform the simulations, two test cases including evolution of a warm bubble and a cold bubble in a neutral atmosphere with open and rigid boundaries are employed. In addition, the second-order MacCormack and the standard fourth-order compact MacCormack schemes are used to perform the simulations. Qualitative and quantitative assessment of the numerical results for different test cases exhibit the superiority of the fourth-order compact MacCormack scheme on the second-order method.     

两方程湍流模型对内背风波数值模拟的影响

为了深入理解非静力近似下的波-湍相互作用问题,本研究在σ坐标的海洋环境研究和预报模型(MERF)中引入常用的Mellor-Yamada两方程湍混合参数化方案(MY2.5),评估垂向湍混合对小尺度背风波传播过程的影响.瞬时状态场的模拟结果表明,无论是否为非静力近似条件,上述湍参数化方案的引入都会减弱背风波传播的模拟效果.从时间平均场的试验结果来看,垂向湍混合过程会显著减小非静力近似和静力近似之间的差异.此外,能量收支分析的诊断结果表明,MY2.5方案会显著抑制陆坡地形下的背风波传播过程,进而将更多的潮能转化到不可逆的湍混合过程中.     

On the importance of non-hydrostatic processes in determining tidally induced mixing in sill regions

The importance of using a non-hydrostatic model to compute tidally induced mixing and flow in the region of a sill is examined using idealized topography representing the sill at the entrance to Loch Etive. This site is chosen since detailed measurements were recently made there. Calculations are performed with and without the inclusion of non-hydrostatic dynamics using a vertical slice model for a range of sill widths corresponding to typical sill regions. Initial non-hydrostatic calculations showed that the model could reproduce the observed flow characteristics in the region. However, when calculations were performed using the model in hydrostatic form, the significant artificial convective mixing that occurred in order to remove density inversions led to excessively high vertical mixing. This influenced the computed temperature field and the intensity of the current jet that separated from the sill on its lee side. In addition it affected the magnitude and spatial characteristics of the lee waves generated on the lee side of the sill. Calculations with a range of sill widths, showed that as the sill width decreased the difference between the solution computed with the non-hydrostatic and hydrostatic model increased.     

多尺度非静力通用模式框架的设计策略

针对目前国际上数值预报模式的最新发展趋势,综述了新形势下多尺度非静力通用数值预报模式框架的设计策略。目前世界上开发通用模式主要有两个途经,一是建立一个离散化方案和源程序代码共享的、全球和有限区通用的模式,二是建立一个单一的全球可变分辨率的模式。还从通用模式方程组的选取策略、模式网格属性的构造,时间积分方案、空间离散方案,垂直坐标的选取等方面进行了分析。     

On the influence of stratification and tidal forcing upon mixing in sill regions

A cross-sectional non-hydrostatic model with idealized topography was used to examine the processes influencing tidal mixing in the region of sills. Initial calculations with appropriate parameters for the sill at the entrance to Loch Etive showed that the model could reproduce the main features of the observed mixing in the region. In particular, the hydraulic jump in the sill region was reproduced, as was an intense mid-water jet that was observed to separate from the lee side of the sill. Shear instabilities associated with the jet appeared to be a source of mixing within the thermocline. In addition, internal lee waves were generated on the lee side of the sill, with the observed amplification because of trapping during the flood stage. Their magnitude and hence the mixing increased with increasing Froude number (F _r). In the case of vertically varying buoyancy frequency, its value near the sill top determined the F _r number, with its value below influencing internal waves magnitude at depth. At high F _r values particularly with strong currents, short waves and overturning occurred.     

A wetting and drying algorithm with a combined pressure/free-surface formulation for non-hydrostatic models

A wetting and drying method for free-surface problems for the three-dimensional, non-hydrostatic Navier–Stokes equations is proposed. The key idea is to use a horizontally fixed mesh and to apply different boundary conditions on the free-surface in wet and dry zones. In wet areas a combined pressure/free-surface kinematic boundary condition is applied, while in dry areas a positive water level and a no-normal flow boundary condition are enforced. In addition, vertical mesh movement is performed to accurately represent the free-surface motion. Non-physical flow in the remaining thin layer in dry areas is naturally prevented if a Manning–Strickler bottom drag is used. The treatment of the wetting and drying processes applied through the boundary condition yields great flexibility to the discretisation used. Specifically, a fully unstructured mesh with any finite element choice and implicit time discretisation method can be applied. The resulting method is mass conservative, stable and accurate. It is implemented within Fluidity-ICOM [1] and verified against several idealized test cases and a laboratory experiment of the Okushiri tsunami.     

包含正定水汽高精度算法的MM5模式的暴雨实例试验

本文首先对非静力中尺度模式ＭＭ５的水汽输送方案作了半理想试验。结果显示,ＭＭ５原有的水汽平 流输送算法在水汽梯度较大的地方产生水汽负值,影响模式的模拟结果和模式的稳定性,对此,本文把一个正定的水汽输送算法Ｐｒａｔｈｅｒ算法引入ＭＭ５,并用实例作了数值试验,检验了模式的模拟能力,结果表明,对ＭＭ５的改进是敏感的有效的,Ｐｒａｔｈｅｒ格式增强了模式暴雨落区,暴雨中心的模拟能力。