山の風下における運動量の鉛直フラックスの発散により発生するカルマン渦の数値的研究

Abstract

We investigated formation mechanism of vortex streets in the lee of mountains by using a three-dimensional numerical model. The model is based upon the hydrostatic Boussinesq equations in which the vertical turbulent mixing is parameterized using the level 2.5 model of Mellor and Yamada (1982), but the horizontal viscosity is assumed constant.Kármán vortex streets can form even without surface friction in a constant ambient flow with uniform stratification. The flow in the lee of the mountain is decelerated due to divergence of the total vertical momentum flux associated with mountain drag. The divergence of momentum flux can be explained by the wave saturation theory given by Lindzen (1981) with some modification. Simulations in this study show that the momentum flux in the lower levels is much larger than the saturated momentum flux, whereas it is almost equal to the saturation value at the upper levels as expected from the saturation theory. This means that large flux divergence is produced between surface layer and upper levels (about 2.5km). As a result, the mean flow is decelerated behind the mountain and the horizontal wind shear forms. When the decelerated flow has a strong enough horizontal shear, the Kármán vortex will form due to an absolute instability as mentioned by Schär and Durran (1997).In case of a three-dimensional, bell-shaped mountain, the wave breaking occurs if the Froude number (Fr=U/Nh) is less than about 0.8, while a Kármán vortex forms if Fr is less than about 0.22. The results of the momentum budget calculated by the hydrostatic model are almost the same as nonhydrostatic results as long as the horizontal scale of the mountain is larger than 10km. A well developed Kármán vortex similar to the hydrostatic one was simulated in the nonhydrostatic case. Therefore, we conclude that the hydrostatic assumption is adequate to investigate the origin of the Kármán vortex from the viewpoint of momentum budget.