On the Numerical Experiments by the Method of Characteristics of One-Dimensional Unsteady Airflow over the Mountain Ridge

In order to investigate the characteristics of the lee waves, numerical experiments are performed by integrating the equations of the so-called Boussinesq system as an initial value problem for a given topography with rigid upper boundary. Some considerations on the linear theory are presented for a better understanding of the results. For almost all internal Froude number Fi, a quasi-steady pattern is obtained. Calculated patterns are discussed in connection with the linear theory, and good agreements are obtained. For relatively large values of the Fi, a laminar sinusoidal flow is obtained. On the other hand for small values of the Fi, a S-shaped or Rotor-like flow pattern is obtained, in which a statically unstable region is found to survive. Such a flow may be considered as a result of a nonlinear interference of the waves. Occurrence of such an overturning flow also depends on the height of the mountain. The criterion for the overturning flow seems to be linear dependency in terms of the nondimensional mountain height D and Fi, which appears to be consistent with Long's analytical study (1955). Strong lee-side surface winds are discussed in relation to the simulated lee waves. The possibility of a strong downslope wind or horizontal wind at the lee side of the mountain is stressed.

Section: Introductionmentioning

confidence: 99%

Numerical Experiments of the Airflow over Mountains 1. Uniform current with constant static stability

Furukawa¹

1973

“…6. Afterwards the modified jump is supposed to propagate downstream (Houghton and Kasahara, 1968;Arakawa and Oobayashi, 1968). In order to simulate more accurately the jump phenomenon, the governing equations should include the internal and surface fractions, because according to the turbulent theory there is much kinetic energy dissipation at the area of the jump region.…”

Section: Basic Equationsmentioning

confidence: 99%

“…Fuji (Magata, 1968). In many cases when a strong wind blows over the lee side of mountain, the inversion layer appears over the slope (Arakawa, 1968). The flow under the inversion layer is similar in its character to the shallow fluid flow.…”

Section: Introductionmentioning

confidence: 98%

“…The flow under the inversion layer is similar in its character to the shallow fluid flow. The one-dimensional airflow over an isolated mountain at the bottom of the atmosphere has therefore been investigated as the shallow fluid flow by Jih-Ping, Kung-Kuan and Ming (1964), Larsen (1966), Houghton and Kasahara (1968), Arakawa (1968) and Arakawa and Oobayashi (1968). Furthermore the three-dimensional airflow passing over an isolated mountain was first studied by Magata (1968), using a two-layer model for a nonhydrostatic atmosphere.…”

Section: Introductionmentioning

confidence: 99%

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A Numerical Study of Two-Dimensional Airflow over an Isolated Mountain

Oobayashi¹

1970

Self Cite

In order to simulate numerically one of the most remarkable phenomena of airflow over a mountain, i. e., the hydraulic jump on the lee side of the mountain, several numerical experiments are conducted with the shallow fluid flow system. Since the jump is a kind of shock phenomenon in the fluid, we need to use a highly accurate finite difference scheme. In the present study the one-step Lax-wendroff method is adopted. The following four cases of uniform flows are given as the initial conditions over the whole domain, i. e., two cases of subcritical flows and remaining two cases of supercritical flows. The results are in good agreement with those of the one-dimensional flow obtained by Houghton and Kasahara (1968). In the present experiment the jump is set up on the lee side of an isolated bell-shaped obstacle in one out of two subcritical flows and in one out of two supercritical flows. In another case of the subcritical flow the wave of wave length which is close to the width of the obstacle predominates. The flow pattern similar to that of the one-dimensional flow is observed in the remaining case of the supercritical flow. The zonal flow crossing over the obstacle is more predominant than that passing around the obstacle.

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

Tomine¹

1984

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.