Nonlinear Baroclinic Instability on a Beta-Plane

The dynamics of a baroclinic fluid flow consisting of two immiscible liquids in a rotating cylinder, driven by a differentially rotating lid, is investigated experimentally and numerically. This system is a laboratory analogue to large-scale atmospheric and oceanic flows. The topography of the upper and lower bounding surfaces and the rotation rate of the flow are chosen to simulate a polar beta-plane, in which the planetary vorticity varies quadratically with the co-latitude. Results from a 6 wave quasi-geostophic numerical spectral model based on the linear eigenfunctions are compared with the experimental observations. As the forcing is increased, the system bifurcates from axisymmetric flow, to one dominated by a steady amplitude baroclinic wave, to a mixed wave state with multiple steady components, and then to periodic and finally aperiodic amplitude vacillation of the whole fluid system. A new nonlinear interference vacillation (NIV) is observed in the mixed wave state in which two orthogonal waves with different azimuthal wavenumber grow to finite amplitude, propagate with different phase speeds and interact through nonlinearly generated harmonics to cause an oscillation in the zonal background flow whose frequency is a multiple of the fundamental wave phase speed difference. The NIV depends implicitly on the beta-plane geometry (it does not occur on the f-plane), and its parameter space dependence in experiments and model is investigated. The transition to chaos is examined in the experiment and model. Some of the aperiodic flows can be characterized as time evolution on a low-dimensional strange attractor. The region of parameter space exhibiting low-dimensional chaos extends to larger forcing values for a counter-rotating lid (negative Rossby number or easterly basic zonal flows). Qualitative differences between model and experiment behavior and the experiments themselves imply that higher, linearly stable, azimuthal wavenumbers and radial modes are important in the detailed dynamics of many of the periodic and aperiodic flow regimes.