双三次数值模式与理想Lamb波、龙卷扰动对比模拟分析  

Bicubic Numerical Model:Ideal Parallel Simulations of Lamb Wave and Tornado Disturbance in the Atmosphere

作　　者：辜旭赞[1] 张兵[1] 

机构地区：[1]中国气象局武汉暴雨研究所,武汉430074

出　　处：《气象科技》2007年第5期613-620,共8页Meteorological Science and Technology

基　　金：国家自然科学基金项目"双三次数值模式研究"(40575053)资助

摘　　要：通过"双三次曲面拟合—时间步长积分—双三次曲面拟合……",实现成为一种双三次曲面拟合新算法数值模式。它对模式大气作非线性(空间二阶可导)描述,是用数值分析(三次样条/双三次曲面)与计算方法近似求解大气运动非线性偏微分方程组。用Z坐标系高分辨率双三次数值模式,采用原始大气运动方程组和采用欧拉时间积分方案,设置理想扰动,对大气声波Lamb波做数值模拟;采用大气不可压假定,除去声波,对大气重力波龙卷扰动做数值模拟。对比模拟发现:理想Lamb波以声速在水平方向传播,扰动能量频散快,仅能在原地持续数秒钟;理想龙卷扰动则在原地可持续约1 min,且波动内圈(外圈)自下至上始终处于风场辐合(辐散)状态,具冷心结构和气压驻波特征,可因水汽进入扰动与借助凝结潜热释放而得到发展。A new numerical model with a new algorithm of the Coons bicubic curved-surface fitting by means of ＂bicubic curved surface fittingtime step integration- bicubic curved- surface fitting...＂ is presented. Obviously, this model can give a non-linear description to atmospheric motion and can get the solution （approximate numerical solution） of a non-linear partial differential equation system by the numerical analysis method. Actually, with the cubic spline function, BiNM is a Coons bicubic curved-surface fitting model for many physical fields of the atmospheric motion in the x, y, or z directions （but the time-dimension is not considered here）. It can make the fitting of the synoptic system by a continuous regular polyhedrons composed with N pieces of Hermite bicubic patches in mathematical RN space. By this kind of fitting, the atmospheric physical field P, as well as its differential px and pXX, and P＇s integral in the X （X = x, y, z） space can be all obtained at any time. It is indicated that, by the differential quotient instead of linear difference, BiNM can describe multi-scale and non- linear atmospheric motions and forecast （simulate） them by time integration for their governing equations. A Bicubic Numerical Model （BiNM） with the Z coordinate system and high resolution （22 m grid spacing in hori- zontal and 52 layers in vertical） is used. An ideal predefined disturbance of atmospheric acoustic waves （Lamb waves） is simulated by using the primary atmospheric equations of motion and the Eulerian time integration scheme; meanwhile, the same gravity wave as an ideal tornado disturbance is also simulated by assuming that the free atmosphere be incompressible, such that the acoustic wave is eliminated in the simulation, showing that tornados are not acoustic waves but gravity waves in the atmosphere. It is also found that： （ 1 ） the simulated Lamb wave would propagate in horizontal direction at a speed similar to the speed of acoustic waves in the atmosphere and last for on

关 键 词：双三次数值模式 原始大气运动方程组 欧拉时间积分方案 LAMB波 龙卷扰动 数值模拟 

分 类 号：P456.7[天文地球—大气科学及气象学]