Abstract
Rotation is present in many physical and geophysical systems and its role in determining flow properties and modifying turbulent fluctuations is of crucial importance. Here we focus on the role of rotation on temperature fluctuations in turbulent thermal convection. The system used consists of a rotating half soap bubble heated from below. This system has features, curvature and a quasi two dimensional character, which are reminiscent of atmospheric and planetary systems. Our experiments and numerical simulations show that rotation changes the nature of turbulent fluctuations and a new scaling regime is obtained for the temperature field. This change in the scaling behavior of temperature fluctuations, due to rotation, is put forth by studying the so called second moment of temperature differences across different scales. For high enough rotation rates, these temperature differences display a transition from Bolgiano Obukhov scaling to a new scaling regime. This scaling is at odds with expectations from theory, numerics, and experiments in three dimensions, suggesting that the effects of rotation on turbulent flows depend strongly on geometry and spatial dimension.
Highlights
Turbulent thermal convection is important for numerous processes of meteorological, geophysical, and industrial interest
The examination of the role of rotation on the velocity fluctuations in three dimensional (3D) hydrodynamic turbulence has been shown to introduce novel features and changes in scaling behavior in experiments and simulations[21,22,23,24]. This change in scaling for the velocity field has direct consequences on the scaling of scalar fields in rotating turbulent flows according to numerical simulations[24] but no experiments exist so far
Our diagnostics of the effects of rotation on the turbulent thermal convection is based on the so called temperature structure functions extracted from temperature fields on the surface of the bubble
Summary
A hemisphere of radius 1, subjected to thermal convection is described by the coupled Navier -Stokes and the heat equation in the Boussinesq approximation which are simulated using a stereographic projection A steepening of the second order structure function, at scales comparable to the range where experiments show a higher exponent, is observed This steepening is consistent with the increase of the exponent observed experimentally as an exponent near 1 is observed for two different Ra numbers and for Ro values smaller than 1 increase again and and comparable to those of the experiments. Further and as Ro decreases to small values of order 0.1 where rotation effects are supposed to dominate the flow, the scaling exponent becomes even steeper
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