降低水平压力梯度误差的方法比较

由于坐标变换的关系,σ坐标海洋模式在处理陡峭地形时会产生较大的水平压力梯度误差.为减少水平压力梯度误差,前人提出了一系列改进的方法,这些方法可分为减去平均密度法、平滑地形法、网格变换法和水平压力梯度计算方程变换法4类.水平压力梯度计算方程变换法又可分为密度雅克比法、高阶精度法、有限体积法和转换到z坐标下计算水平压力梯度法.利用POM模式模拟理想海山来比较标准密度雅克比法、线性插值到z坐标法、四阶精度插值法、三次方多项式拟合法和权重密度雅克比法在计算水平压力梯度中出现的误差.模式初始时垂向分成,水平均匀,外模时间步长为12 s,内模时间步长为360 s,计算时间为360 d.从最大流速误差的结果可以看出,标准密度雅克比法得到的最大流速误差为0.45 m/s左右;线性插值到z坐标法得到的最大流速误差达到0.7 m/s;四阶精度方法计算得到的最大流速误差为0.3 m/s;权重密度雅克比方法和三次方多项式拟合法计算得到的最大流速误差相差不大,都只有0.2 m/s左右.标准密度雅克比法计算得到的单位质量平均动能最大,为9×10-4 m2/s2;四阶精度方法和线性插值到z坐标方法计算得到的单位质量平均动能差不多,为3×10-4 m2/s2;三次方多项式拟合法计算得到的单位质量平均动能为1.9×10-4 m2/s2;权重密度雅克比方法计算得到的单位质量平均动能最小,仅为1×10-4 m2/s2.标准密度雅克比法的计算耗时最短,为294 min;与其相比,三次方多项式拟合法的计算耗时增加了5.9%;权重密度雅克比法的计算耗时增加了8.8%;四阶精度插值法的计算耗时增加了23.6%.线性插值到z坐标法的计算耗时最长,需要384.5 min,相对于标准密度雅克比法的计算耗时增加了30.6%.因此,综合最大流速误差、平均动能和计算耗时的结果可知,线性插值到z坐标法的计算结果相对较差,采用权重密度雅克比法能较好地降低水平压力梯度误差.     

Application of a two-way nested model to the seamount problem

A two-way nested model has been constructed and applied to the idealized ocean where a uniform mean flow impinges on the isolated Gaussian-shaped seamount and produces two eddies (cold and warm) in the depths. The performance of the nested model has been evaluated subjectively and objectively. Both subjective and objective analyses confirm the traditional view that the nested model can well capture the performance of isolated eddies. Objective analysis, however, reveals some quantitatively important features of a two-way nested model. One is penetration of improved features into the coarse domain and another is the deterioration of mean flow field inside the nested area, neither of which is clear from subjective analysis. With successful application of two-way nested model to the seamount problem, we expect that such a nested model will also be applicable to other oceanic phenomena, particularly to some coastal problems whose time scale is short and where the topographic effects are dominant.     

河口海岸三维双σ坐标斜压水流数值模型研究

在海底地形陡变、垂向密度分层明显的水域,三维σ坐标模式中会出现一种"伪"水平斜压梯度力,并会引起"伪"密度流,以至于影响模拟的精度。垂向上引入双σ坐标变换,建立河口海岸水域三维斜压水流数值模型。数值试验结果表明,在海底地形陡变水域,双σ坐标模式可以减小水平斜压梯度力处理引起的误差。