Abstract
We conduct experiments on the convective dynamics of a rotating fluid in a novel configuration, which comprises of a cylindrical annulus with peripheral spot heating at the bottom on the outer edge and uniform cooling on the inner edge. This system naturally provides an additional vertical gradient on the outer edge of the annulus, along with a radial gradient, thereby mimicking the thermal gradient patterns encountered in a real atmosphere. Localized heating is carried out at the bottom using a thin annular metal strip of thickness, h=5 mm. Water is used as the working fluid. Once the system reaches a statistically steady state, localized temperature measurements are carried out at various radial locations along the vertical fluid height. We measure time series of the temperature at several locations and visualize the flow structures over a range of Taylor number Ta (spanning 6.5 × 108- 2.7 × 109) and Rayleigh number Ra (spanning 2.2 × 108- 6.2 × 108). Temperature time series data at different heights, z, near the outer edge, along with two point correlations of temperature data indicate that, in the presence of rotation, columnar convective plumes (CCP) exist above the heating zone that aid in the vertical transport of heat. Qualitative flow field and temperature measurements in the bulk fluid also indicate the existence of baroclinic waves, which aid in the horizontal transport of cold and hot fluids between the annuli. The two point temperature correlations show that these waves break into eddies as the value of Ta increases. Overall, it is speculated that heat transport in this new configuration is governed by the co-existence and interplay of convective plumes and baroclinic waves/eddies, which closely simulates the dynamics of geophysical motions. It is found that the heat transport near the outer edge and in the fluid bulk is a strong function of Ra and Ta. For the highest value of Ra=6.2 × 108, the radial heat transport was most effective at Ta=0. However, at lower values of Ra, the radial heat transport in the outer and bulk regions was highest at Ta=1.5 × 109. These results indicate that an optimum value of Ra and Ta exists at which the convection driven radial heat transport is most energetic through the interaction of CCP and baroclinic waves/eddies.
Highlights
INTRODUCTION2014; Hussam et al, 2014 among many others). The many variants of the problem include, (i) rotating convection between vertically spaced isothermal hot and cold horizontal plates, commonly referred to as the rotating Rayleigh-Benard convection (RBC) which aims to address the oceanic deep convection and convection in stars and giant planets (Chandrasekhar, 1953; Sakai, 1996; Vorobieff and Ecke, 2002; Liu and Ecke, 2009; King and Aurnou, 2012), (ii) rotating convection in a annulus confined by hot and cold cylindrical surfaces, known as Hide-Mason experiment, which addresses the baroclinic instability in atmosphere, responsible for heat and momentum transport (Fowlis and Hide, 1965; Hide and Mason, 1975; Davies and Walin, 1975; Wordsworth et al, 2008; Harlander et al, 2011; Vincze et al, 2014), and (iii) rotating horizontal convection (HC), wherein a radially varying temperature is provided on the base
Convection in a rotating fluid is a classical fluid mechanics problem encountered in many geophysical (Gerkema et al, 2008), astrophysical (Aurnou et al, 2008; Gerkema et al, 2008), and engineering systems (Lopez et al, 2015), where differential heating and background rotation co-exist
R1 is at 118 mm from outer edge, R2 is at 50 mm from outer edge and R3 is at 2 mm from outer edge
Summary
2014; Hussam et al, 2014 among many others). The many variants of the problem include, (i) rotating convection between vertically spaced isothermal hot and cold horizontal plates, commonly referred to as the rotating Rayleigh-Benard convection (RBC) which aims to address the oceanic deep convection and convection in stars and giant planets (Chandrasekhar, 1953; Sakai, 1996; Vorobieff and Ecke, 2002; Liu and Ecke, 2009; King and Aurnou, 2012), (ii) rotating convection in a annulus confined by hot and cold cylindrical surfaces, known as Hide-Mason experiment, which addresses the baroclinic instability in atmosphere, responsible for heat and momentum transport (Fowlis and Hide, 1965; Hide and Mason, 1975; Davies and Walin, 1975; Wordsworth et al, 2008; Harlander et al, 2011; Vincze et al, 2014), and (iii) rotating horizontal convection (HC), wherein a radially varying temperature is provided on the base. Dominant mechanisms for non-linear equilibration of baroclinic and convective instabilities in the atmosphere are not clear either (Schneider and Walker, 2006; Stone, 2008) This is partly due to the nature of Hide-Mason configuration, where the fluid in the rotating annulus is subjected to a uniform constant temperature on both the inner and outer walls. The fluid is subjected to a radial temperature gradient in the bulk region and a vertical temperature gradient along the periphery, thereby loosely combining classical Hide-Mason system and rotating horizontal convection system We believe this system will provide a better understanding of the heat transport due to the strong convection near the tropics to the stably-stratified sub-tropics and mid-latitude. The underlying scope of the present paper is to interpret the flow physics from thermal measurements and two-point correlation analysis
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