Baroclinic Waves in a Rotating Fluid Subject to Internal Heating

• Published in: Philosophical Transactions of the Royal Society of London, Series A: Mathematical and Physical Sciences Series A: Mathematical and Physical Sciences, 1970-11, Vol.268 (1186), p.201-232
• Main Authors: Hide, R., Mason, Paul James
• Format: Article
• Language: English
• Subjects: Axial flow; Baroclinic waves; Convection; Cylinders; Flow distribution; Heat transfer; Liquids; Rotating fluids; Streak photography; Waves
• ISSN: 1364-503X; 0080-4614; 0962-8428; 1471-2962; 2054-0272
• DOI: 10.1098/rsta.1970.0073

Free thermal convection in a vertical rotating fluid annulus subject to axisymmetric heating and cooling applied at the side-walls has been the subject of extensive previous studies, one of the principal findings of which is that four distinct types of flow are possible, each characteristic of definite ranges of impressed experimental conditions. Three of these flow types are characterized by departures from axial symmetry and arise when the basic axisymmetric flow is ‘ baroclinically unstable ’; they comprise ‘ baroclinic waves ’ of varying degrees of complexity (steady waves, waves subject to periodic fluctuations in form, amplitude and/or wavenumber (‘vacillation’) and waves subject to irregular non-periodic fluctuations). The present paper reports an experimental and theoretical study of effects associated with the introduction of heat throughout the body of the fluid (rather than via one of the side-walls) and removal via the inner side-wall, the outer side-wall, or both side-walls simultaneously. The experiments show that the principal characteristics of the flow are fairly insensitive to the radial dependence of heating and cooling (upon which, for example, the horizontal shear of the basic axisymmetric flow depends), thereby strengthening the basis of the application to large-scale geophysical and astrophysical systems of theoretical ideas stemming from the laboratory work. Just as previous experiments have shown that the presence of an inner wall does not preclude the occurrence of irregular baroclinic waves, one of the present experiments shows that the absence of an inner wall does not preclude the occurrence of steady baroclinic waves (thus refuting a certain conjecture which seems to have gained widespread acceptance among meteorologists). Determinations have been made of the general form of the flow pattern, top-surface flow velocities, total heat transfer and the transition between axisymmetric flow and baroclinic waves, and the results interpreted, where possible, in terms of theoretical ideas. The experiments provide striking support for a simple theoretical model that treats the jet stream associated with the baroclinic waves as a quasigeostrophic detached thermal boundary layer.