Wavenumber Selection in Nonlinear Baroclinic Instability

Abstract

Laboratory experiments with finite-amplitude baroclinic waves arising from instability of a two-layer f-plane shear flow are reported. They show that as the system becomes more and more supercritical, as measured by decreasing E½/Ro, where E is the Ekman number and Ro the Rossby number associated with the driving, there are a succession of wavenumber transitions to lower and lower wavenumbers. At finite amplitude, the dominant wavenumber is considerably smaller than that predicted by linear stability theory. A simple weakly nonlinear model is constructed to interpret the laboratory results. It shows that because the longer growing waves do not extract energy as rapidly from the mean flow as the shorter ones, at finite amplitude, the preferred equilibrium states are dominated by the former. The theoretical calculation also indicates that at least near the neutral curve sideband harmonics do not substantially affect the equilibration process. In addition, a mechanism that may explain the observation of extremely long equilibration times is offered.