Effects of Critical Levels on Two-Dimensional Back-Sheared Flow over an Isolated Mountain Ridge on an f Plane

Abstract

It is well known that there exist three singular points, U ? c = ±f/k and U = c, where the corresponding levels will be called inertia critical levels (ICLs) and the classic critical level (CCL), in the equation governing a two-dimensional, rotating, continuously stratified, hydrostatic, back-sheared Boussinesq flow. Here U and c are basic wind and phase speed, respectively; f is the Coriolis force; and k is the wavenumber. The effects of these critical levels on flows over an isolated mountain ridge are investigated both analytically and numerically, based on a broad range of Rossby numbers (Ro) and Richardson numbers (Ri). Each wave mode generated from the isolated mountain with a continuous spectrum has its own ICL. To indicate the net effects of all ICLs, the authors define the effective ICL as the height above which the amplitude of the inertia-gravity wave mode is very small. The findings for linear flows are summarized as follows. Regime I is inertia-gravity waves. The flow behaves like unsheared inertia-gravity waves and the effective lower ICL plays a similar role as the CCL does in a nonrotating flow. Regime II is combined inertia-gravity waves and baroclinic lee waves. These waves behave like those in regime I below the lower effective ICL, and like baroclinic lee waves near the CCL. In this regime, the horizontal warm advection by the baroclinic lee wave plays an important role in the formation of the lee pressure trough. On the other hand, near the downslope of the mountain, both the warm advection by the inertia gravity and the adiabatic warming also contribute significantly to the lee trough. Therefore, Smith?s quasigeostrophic theory of lee cyclogenesis is extended to a nongeostrophic regime. Regime III is combined evanescent and baroclinic lee waves. These waves still behave like baroclinic lee waves near the CCL, but they are trapped near the surface. Regime IV is transient waves. Nongeostrophic baroclinic instability exists, as evidenced by the positive domain-averaged north?south heat flux. There exists no steady state. At earlier times, the flow behaves like trapped baroclinic lee waves. For a relatively large Ri (e.g., Ri > 25), the flow falls into regime I when Ro is relatively large (e.g., Ro ≥ 2). It then shifts to regime II, and finally to regime III as Ro decreases. For a relatively small Ri (e.g., Ri < 25), the flow shifts from regime I to II, and then finally to regime IV when both Ro and Ri decrease.