建立η坐标系下的假不压模式及其数值试验

A Pseudo-incompressible Model in the η Coordinate and Its Numerical Experiments

滤除声波的大气运动方程中不包含声波,基于滤除声波方程建立的数值模式可以用较大的时间步长进行数值积分。Durran在1989年提出了一种新的滤除声波的方法,命名为"假不可压"方程,该方程考虑了温度扰动引起的密度变化,忽略了气压扰动引起的密度变化。本文根据Durran提出的假不可压理论,推导出了一组地形追随坐标下的通量形式的假不可压方程。该方程在形式上与WRF(Weather Research and Forecasting)模式中ARW(Advanced Research WRF)动力框架的控制方程非常接近。我们进一步将推导出的假不可压控制方程改写到了WRF模式中,建立了基于WRF模式框架的假不可压模式。用构建的假不可压模式和WRF模式做了两组对比试验:湿热泡对流试验和重力流试验。比较两种模式的模拟结果,可以看出假不可压模式的模拟结果与WRF模式的模拟结果非常接近,说明在WRF模式框架下建立的假不可压模式是合理可信的。

Soundproof equations do not contain acoustic waves, which is why numerical models based on soundproof equations can use relatively lager timesteps for numerical integration. Durran proposed a new method to eliminate acoustic waves in 1989 and named it ＂pseudo-incompressible＂ equations, which retain the air density variations caused by temperature perturbations but ignore the density variations caused by pressure perturbations. In this paper, the authors followed the pseudo-incompressible theory and derived a set of flux-form pseudo-incompressible equations in the terrain-following coordinate. The form of the set of equations the authors derived is quite similar to that of the equations in the ARW （Advanced Research WRF） dynamic solver of the WRF （Weather Research and Forecasting） model. The authors further modified the codes of WRF model according to the flux-form pseudo-incompressible equations, and thus established the ＂pseudo-incompressible model＂ based on the frame of WRF model. The authors then conducted two sets of numerical experiments, i.e. a heat-bubble convection experiment and a gravity current experiment, using the pseudo-incompressible model and WRF model, respectively. Comparing the results of these simulations, the authors found that the meteorological fields simulated by the pseudo-incompressible model are quite close to those by the WRF model, which indicates that the pseudo-incompressible model we built within the frame of WRF model is reliable.