Unsteady and quasi-steady state solutions of shallow water flow having a lee hydraulic jump over a mountain range in a channel of variable width are calculated by expanding Houghton and Kasahara's (1968) theoretical model.
In an unsteady flow regime in which a lee jump moves downstream, both the decrease of the channel width and the increase of the mountain height contribute to the increase in the moving speed of the lee jump. This result confirms Arakawa's (1969) suggestion which indicated that a steady state flow is deformed by the channel width in the same way as by the mountain height. On the other hand, in the quasi-steady flow regime in which a lee jump stays in the lee of the mountain, the jump develops at the more leeward side when the channel width decreases, while it tends to develop at the more windward side when the mountain height increases. Namely, Arakawa's (1969) suggestion does not hold for the location of the stationary jump. This response of the lee jump in a quasi-steady regime to the magnitude of the channel width is analogous to the behavior of an internal hydraulic jump in a non-linear flow over a mountain range with a col.
The velocity of the fluid just before the hydraulic jump increased with the decrease of the channel width. This result corresponds to the fact that strong downslope winds tend to occur in the lee of a col of a mountain range.