Abstract
For a two-layered fluid with l2/l1=0.4 (l1=N1/U;l2=N2/U; N1 and N2 are Brunt-Vaisala frequencies of the lower and upper layers, respectively; U, horizontal wind speed), the dependence of non-linear aspects of the flow past a two-dimensional bell-shaped mountain on (l1 h, l1 D) (h: the height of a mountain; D: the depth of the lower layer) is numerically examined, with special emphasis on high-drag states and foehns, using a 2-dimensional non-hydrostatic model.
The flow in a high-drag state is generally characterized by the large downward displacement of the air and strong downslope wind with hydraulic jump on the lee side. For π/2<l1D<2π, the transition to a high-drag state occurs when l1h is larger than the critical value (l1h)c. For π/2<l1D<3π/2, the critical value of l1 h for the transition to a high-drag state increases as l1D increases. This is qualitatively similar to the case of l2/l1=0 predicted exactly by Smith's theory (1985). For π/2<l1D<π, transition to a high-drag state is not necessarily accompanied by a wave-induced critical layer. On the other hand, for 3π/2<l1D<2π, transition to a high-drag state is accompanied by a wave-induced critical layer formed in the lower layer.
A significant foehn occurs when the flow evolves into a high-drag state with hydraulic jump. For π/2<l1D<3π/2, both the critical value of l1h for the occurrence of a foehn and the coefficient of the linear dependence of a foehn index (a non-dimensionalized potential temperature rise on the lee slope) on the inverse Froude number l1h increase as l1D increases. The critical lh for the occurrence of a foehn predicted by a steady linear theory in θ-coordinates (Smith, 1988) is found to be much larger than that obtained by non-linear numerical solutions.
