Stability analysis and large-eddy simulation of rotating turbulence with organized eddies

Rotation strongly affects the stability of turbulent flows in the presence of large eddies. In this paper, we examine the applicability of the classic Bradshaw-Richardson criterion to flows more general than a simple combination of rotation and pure shear. Two approaches are used. Firstly the linearized theory is applied to a class of rotating two-dimensional flows having arbitrary rates of strain and vorticity and streamfunctions that are quadratic. This class includes simple shear and elliptic flows as special cases. Secondly, we describe a large-eddy simulation of initially quasi-homogeneous three-dimensional turbulence superimposed on a periodic array of two-dimensional Taylor-Green vortices in a rotating frame. The results of both approaches indicate that, for a large structure of vorticity W and subject to rotation Ω, maximum destabilization is obtained for zero tilting vorticity (½ W + 2 Ω = 0) whereas stability occurs for zero absolute vorticity (2Ω = 0) These results are consistent with the Bradshaw-Richardson criterion; however the numerical results show that in other cases the Bradshaw-Richardson number B=2Ω(W+2Ω)/W² is not always a good indicator of the flow stability.