Time variability and Simmons-Wallace-Branstator instability in a simple nonlinear one-layer model

Using a global, one-layer shallow water model, the response of a westerly f low to a localized mountain is investigated. A steady, linear response at s mall mountain heights successively gives way first to a steady flow in whic h nonlinearities are important and then to unsteady, but periodic, how at l arger mountain heights. At first the unsteady behavior consists of a low-fr equency oscillation of the entire Northern Hemisphere zonal how. As the mou ntain height is increased further, however, the oscillatory behavior become s localized in the diffluent jet exit region downstream of the mountain. Th e oscillation then takes the form of a relatively rapid vortex shedding eve nt, followed by a gradual readjustment of the split jet structure in the di ffluent region. Although relatively simple, the model exhibits a surprising ly high sensitivity to slight parameter changes. A linear stability analysi s of the time-averaged flow is able to capture the transition from steady t o time-dependent behavior, but fails to capture the transition between the two distinct regimes of time-dependent response. Moreover, the most unstabl e modes of the time-averaged flow are found to be stationary and fail to ca pture the salient features of the EOFs of the full time-dependent flow. The se results therefore suggest that, even in the simplest cases, such as the one studied here, a linear analysis of the time-averaged flow can be highly inadequate in describing the full nonlinear behavior.