Interpretation of the Effect of Mountains on Synoptic-Scale Baroclinic Waves

Abstract

Linear and nonlinear simulations of idealized baroclinic waves interacting with topography are examined in the context of quasigeostrophy. The purpose is to provide a simple conceptual interpretation of the transients resulting from this interaction. A perturbation expansion is employed, with the small parameter being proportional to topographic slope, to isolate fundamentally different topographic effects, and show how they enter systematically at each order. First- and second-order corrections appear to capture the essence of the topographic effect for all cases considered, even for values of the ?small? parameter as large as 0.5, and are qualitatively useful for a parameter value of unity. Results indicate the importance of surface Rossby wave dynamics at first order near the mountain and downshear from the mountain a distance inversely proportional to the growth rate of the most unstable mode of the system. The second-order correction projects onto the initial baroclinic wave. Being primarily out of phase with the initial wave, it contributes systematically to weakening the initial disturbance. This behavior changes notably for meridionally localized topography offset from the symmetry axis of the initial zonally invariant jet flow. The first-order correction affects the translational speed of the initial wave and, downshear from the mountain, grows as an unstable mode projecting strongly onto the scale of the initial wave. For a mountain to the south of the jet, the incident baroclinic wave is accelerated; for a mountain to the north, it is slowed. The dominant effect at second order is still a weakening of the initial wave. In the nonlinear regime, with a meridionally invariant mountain, the total topographic perturbation can be decomposed into a part excited by the wave-induced zonal-mean flow, and a part excited by the remaining transients whose interaction with topography qualitatively resembles that of the linear solution.