In a vertically 2-dimensional steady adiabatic fluid system, there exists a vorticity-like conserved quantity, which is a function of the stream function. In Smith (1985)'s original model of downslope windstorm, this function is assumed to be linear, and the proportionality constant to be negative. However, the possibility of its positiveness can not be excluded. In this note, the case for the constant to be positive is examined, and the followings are shown. Also in this case, there exist solutions representing downslope windstorms. The unnatural upper bound for the atmospheric height in Smith (1985)'s solution does not emerge, and the solution may exist for any large value of the atmospheric height. The ratio of the mountain height to the atmospheric height is somewhat greater than that of Smith (1985)'s solution.
A brief comparison between the Deutscher Wetterdienst's next generation nonhydrostatic regional forecast model (the Local-Modell of DWD) and the Meteorological Research Institute mesoscale nonhydrostatic model (MRI-NHM) is performed by computing the numerical solutions of the 3-dimensional mountain waves over an isolated circular mountain. For linear cases with a free-slip lower boundary condition, both models well reproduce the characteristics of the Smith's (1980) analytic solutions for the 3-dimensional nonhydrostatic mountain waves. Analysis of the CPU time of the two models with the CRAY C-98 of DWD shows the tendency that the Local-Modell (time-splitting, horizontally explicit model) is relatively efficient in lower horizontal resolution while MRI-NHM (3D-implicit model) becomes more efficient at higher horizontal resolution. This is because the number of small time step integrations of the horizontally explicit model increases when the horizontal resolution becomes higher. The CPU time for one iterative procedure in the direct method for the three dimensional elliptic pressure equation in MRI-NHM is 2.1∼2.6 times of that for one small time step integration in the Lokal-Modell. A rough yardstick which determines the comparative efficiency of the two models is given by the relative magnitude between the Courant-number for sound wave speed and the number of iterative procedures in the elliptic pressure equation solver in the 3D implicit model.