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Shih-Hung Chou and Arthur Z. Loesch

Abstract

Nonlinear evolution of baroclinic waves in the presence of surface topography is investigated in an Eady model modified to include Ekman dissipation and sloping horizontal boundaries. The topographic form drag competes with baroclinicity for the control of amplitude evolution and propagation characteristics of the various disturbance modes. The effectiveness of the topography to phase lock and equilibrate a given mode versus that of baroclinicity to propagate and vacillate that mode depends on the topographic height, its zonal structure, and the level of supercriticality.

When topography is sinusoidal and of the same wavelength as the baroclinically most unstable mode, it induces a short-period amplitude modulation whose envelope represents the baroclinic evolution. The dynamics of this modulation is explored analytically. When the sinusoidal topography is of a longer zonal wavelength, a “mixed” wave state persists with amplitude dominance shifting between the topographic mode and the baroclinic mode, depending on the relative strength of form drag and baroclinicity. When topography is a superposition of the most unstable wavelength and a longer one, amplitude dominance and phase locking tend to shift to the mode associated with the “taller” mountain harmonic. When the harmonic structure of topography corresponds to that observed at 35°N, amplitude dominance is concentrated in the longest seven wavelengths. Model results are also compared, in appropriate parameter limits, with near-resonance asymptotic results and annulus experiments.

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Shih-Hung Chou and Arthur Z. Loesch

Abstract

Finite-amplitude dynamics of baroclinic waves are examined in the presence of asymmetric Ekman pumping at the lower and upper boundaries. Both asymptotic and spectral numerical methods are employed. The resulting amplitude equations yield time evolutions that can lead to an eventual equilibration, a regular perpetual vacillation or a chaotic vacillation depending on the actual values of the supercriticality, the dissipation and the stratification parameters and the fundamental zonal wavenumber. Within the limits of strong bottom dissipation and weak supercriticality, the system always eventually equilibrates and the asymptotic results compare favorably with the numerical results. The vacillation is most likely to occur when the bottom dissipation is weak, supercriticality is strong or the viscous asymmetry is high. Vacillatory final states are possible for up to an order of magnitude larger bottom dissipation than predicted by the symmetric configuration, provided the top dissipation is small in comparison.

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