A NUMERICAL STUDY OF WAVE-NUMBER SELECTION IN THE BAROCLINIC ANNULUS FLOW SYSTEM

An investigation is made of the wavenumber selection of baroclinic disturbances in the rotating, differentially heated annulus flow system with a three-dimensional fully nonlinear high resolution model. Along the constant thermal contrast of 10-degrees-C that traverses the nondimensional parameter space defined by the laboratory experiments of Pfeffer et al. (1980b), a series of numerical experiments with a quiescent-start initial condition is conducted to explore the equilibrated flow regimes as a function of the rotation rate of the annulus. The wavenumber selections in the regular wave regime are robust in the sense that the time required for the dominant wavenumber to emerge is short, and the wavenumber selected tends to persist over a relatively wide region of parameter space. In contrast, the wavenumber selections in wavenumber transition regions are characterized by one or more of the following behaviors: two-stage equilibration, side-banded wave dispersion, and irregular wavenumber selection as a function of the external parameter (here, rotation rate). Wavenumber selection in the wavenumber transition regions is highly sensitive to physical and numerical parameters and is only statistically predictable. In a set of incremental-start experiments, it is shown that hysteresis effects prevail inside and near the wavenumber transition regions.