The FDR Prize

Abstract

From the 38 papers published in 2011 in Fluid Dynamics Research the following paper has been selected for the fifth FDR prize:'Interaction between thermal convection and mean flow in a rotating system with a tilted axis' by N Saito and K Ishioka, published in volume 43 (December 2011) 065503.In this paper, the interaction between a horizontal shear flow and thermal convection in a rotating system is examined. The convecting fluid lies between two horizontal boundaries at different temperatures and develops on a basic state of a sine-type horizontal east–west shear flow in a rotating system with the rotation axis tilted from the vertical direction. The system is investigated for various values of three parameters: the tilt angle of rotation axis, the Taylor number Ta, and the Rayleigh number Ra.The critical Rayleigh number Rac for the onset of thermal convection is first obtained for several values of Ta and tilt angles using the Fourier–Legendre spectral method. Nonlinear long-time evolution of thermal convection for Ra larger than Rac is also examined with this method. It is found that there is a parameter region in which the emergence of roll convection possessing a herringbone pattern with non-zero east–west wavenumber accelerates the mean east–west zonal shear flow. In another parameter regime the emergence of large-scale two-dimensional (2D) roll convection that is uniform in the east–west direction accelerates the mean zonal flow strongly, while there are further regions where turbulent or laminar thermal convection without this acceleration is observed. The parameter region in which steady solutions corresponding to the large-scale 2D roll convection are stable is also determined by a linear stability analysis. Moreover, it is found that when the steady solutions are unstable, quasi-periodic solutions oscillating around them can be observed in long-time nonlinear simulations. Finally, a physical explanation of the mechanism for the acceleration of a mean zonal flow by the large-scale 2D roll convection is given, in which both the tilt of rotation axis and the existence of horizontal shear flow are important.The detailed examination of thermal convection in a rotating system with a horizontal zonal shear flow for a wide range of parameters, and the discovery of the parameter region in which a large-scale 2D roll convection accelerates the mean zonal flow strongly, are important contributions of this paper to fluid dynamics. The indication of a clear positive feedback mechanism on the acceleration of a horizontal shear flow and the reinforcement of thermal convection is also an interesting result. By suggesting a new fundamental mechanism acting on thermal convection in a rotating system with a horizontal shear flow, this paper also contributes to the study of atmospheric motion in giant planets such as Jupiter with a strong zonal flow. Therefore, this paper will undoubtedly have a large impact on the fluid dynamics community.