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| Baroclinic flows can be studied in laboratory environments and in direct numerical simulations within a differentially heated rotating annulus, the so-called baroclinic cavity. In the present study a high resolution technique based on spectral collocation methods is used for the investigation of the complex flow regimes arising in a baroclinic cavity. The coupled Navier-Stokes and temperature equations are solved for a Boussinesq fluid. With a fluid with a high Prandtl number, Pr = 16, it is found that the stable stratified flow exhibits inertia-gravity waves. These waves have very small wavelength and period in comparison with the characteristic parameters of the baroclinic instability wave. In the atmosphere and in the oceans the thermal stratification is more important than the rotation rate, the representative Brunt Vais\"al\"a frequency being typically about hundred times the Coriolis parameter $f$ . In the present baroclinic cavity the local values of the Brunt Vais\"al\"a frequency $N$ are smaller than the rotation rate (of the order of one tenth). The inertia-gravity waves are first observed near the inner cold cylindrical wall, in the concave part of the baroclinic wave. In order to study the characteristic parameters of the inertia-gravity wave the numerical flow results have been filtered, the time dependent variables are decomposed into three parts: the time-averaged flow, the flow corresponding to the large-scale baroclinic wave and the flow representing the inertia-gravity wave. The baroclinic instability wave makes the effect of a background wind and the value of the intrinsic frequency for the small-scale wave is close to the Brunt Vais\"al\"a frequency, thus in the low-frequency waves limit $f >> \omega\approx N$. In the results of the study, the phase velocity, the group velocity and the polarization of the inertia-gravity wave are discussed. An attempt to determine the generation mechanism of the spontaneous occurrence of these inertia-gravity waves simultaneously with the baroclinic instability is proposed. |
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