A Numerical Study on Local Depressions on the Lee Side of the Hidaka Mountain Range in Hokkaido

Abstract

It has been well-known that extraordinary deep local depressions are frequently observed at Urakawa on the west side of the Hidaka mountain range in Hokkaido (Arakawa, 1960), when the easterly prevails near the surface. Any easterly near the surface has a critical level, because the westerly prevails over Japan usually. The present numerical investigations show that the local depressions are responsible for a shear flow including a critical level. The results are as follows :1) In the case of a uniform flow, the surface pressure differences between the both feet of the mountain range increase with the wind speed when it is small, and are maintained with small constant values when it is large.2) The local depressions on the lee side are detected on the mid-slope, not on the foot, of the mountain range and the upper atmosphere is affected significantly by the mountain range.3) In the case of a shear flow including a critical level, the surface pressure differences increase with increasing wind speed.4) The local depressions appear on the foot of the mountain range and the atmosphere above the critical level is not affected seriously by the mountain range.

A Supplementary Study of Simulations of Mountain Wave - Critical Level Interactions

“…In case of Klemp and Lilly (1978), it was 0.45 when the large magnitude of momentum flux occurred. This large amplitude mountain wave must be essentially the same as that obtained by Tomine (1984) in which the ratio was smaller than 0.75.…”

“…The overturning instability was clearly seen in the vicinity of the critical level, showing that wave breaking took place there. However, the large amplitude mountain wave in Tomine (1984) could not be explained as any resonant mountain wave shown as by Clark and Peltier (1984), because the ratio of the height of the critical level to the vertical hydrostatic wavelength in his work was 0.31. This is too small to show any resonance.…”

“…But it seems very important for us that their results showed the large amplitude mountain wave owing to nonlinearity. Tomine (1984) simulated a large amplitude mountain wave in a shear flow including a critical level in his nonlinear hydrostatic model. The overturning instability was clearly seen in the vicinity of the critical level, showing that wave breaking took place there.…”

“…Here we are much interested in the large amp-litude mountain wave shown by Klemp and Lilly (1978) and Tomine (1984) which shows the importance of nonlinearity. But before investigating in detail characteristics of the mountain wave, we need make sure nonhydrostatic effects on it.…”

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AbstractAn extraordinarily deep local depression formed on the lee side of a mountain range is investigated under a nonhydrostatic condition and is compared with the results of a hydrostatic model (Tomine, 1984). It is found that nonhydrostatic effects on the large amplitude mountain wave seem insignificant within a framework of the present model.

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