Thermal Convection in a Rotating Fluid Subject to a Horizontal Temperature Gradient: Spatial and Temporal Characteristics of Fully Developed Baroclinic Waves
Detailed studies of the azimuthal structure of fully developed waves in a differentially heated rotating fluid annulus have been carried out with the aid of instrumentation capable of providing frequent determinations of the temperature variation around a circle concentric with the walls of the annulus. Owing to the cyclic nature of the data they are conveniently analyzed in terms of azimuthal Fourier modes. The time-averaged azimuthal spectra thus obtained show that in the regular regime, where the flow is dominated by a single mode of wavenumber M, say, significant “energy” is found not only in the harmonics required to describe the jet stream structure of the flow but also in the sideband modes of wavenumber M=1 which describe the observed azimuthal modulations in the amplitude and/or phase of the wave. At the high-wavenumber end of those spectra for which an inertial subrange can be resolved the “spectral energy” follows a (wavenumber)−3 law. The time-dependent behavior of the phases of the sidebands and the main baroclinic mode, &phisM−1, ϕM+1 and ϕM respectively, is such that the value of φ≡2ϕM−ϕM−1−ϕM+1, remains nearly constant (and close to π), implying that a frame of reference can be found in which the average intrinsic frequencies of the main mode and its side bands are equal. This special frame is fixed relative to the rotating apparatus when the waves are only weakly dispersive, but it can be altered by sloping the endwalls of the apparatus so as to introduce dispersion and returned to the apparatus frame by introducing irregular topography. The theoretical implications of these results are explored with simple wave-interaction theory, which suggests that the sidebands interact strongly with baroclinically stable long waves, but in such a way that in equilibrium the net energy transfer into the long waves is small.