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Dynamic stability of a jet near a transition in static stability

The vertical profile of the Earth's atmosphere in middle latitudes contains a sharp transition region between two roughly constant stability layers, termed the tropopause and also exhibits jet streams at nearly the same altitude, with the jet stream core possibly above or below the tropopause, depending on time and location. This proximity of the jet to the tropopause would be expected to greatly affect the dynamic stability of the jet, treated here with the jet modelled with the Bickley profile and the tropopause modelled as a smooth transition region with a tanh profile. Stability results are obtained numerically using a Chebyshev collocation spectral method. The results show that the jet becomes more unstable as it is moved further beneath the tropopause. Corresponding two- and three-dimensional nonlinear simulations of the flow confirm the initial growth, and indicate that when a jet is above the tropopause, the configuration is more stable and more likely to produce a strong single unstable mode. The simulations indicate that this instability will grow to form a solitary wave envelope pattern. Conversely, when a jet is below the tropopause, the jet is more likely to form a broad spectrum of motion.