C. Cambon et al., STABILITY ANALYSIS AND LARGE-EDDY SIMULATION OF ROTATING TURBULENCE WITH ORGANIZED EDDIES, Journal of Fluid Mechanics, 278, 1994, pp. 175-200
Rotation strongly affects the stability of turbulent flows in the pres
ence of large eddies. In this paper, we examine the applicability of t
he 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 s
treamfunctions that are quadratic. This class includes simple shear an
d 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 vort
ices in a rotating frame. The results of both approaches indicate that
, for a large structure of vorticity W and subject to rotation Omega,
maximum destabilization is obtained for zero tilting vorticity (1/2W 2 Omega = 0) whereas stability occurs for zero absolute vorticity (W
+ 2 Omega = 0). These results are consistent with the Bradshaw-Richard
son criterion; however the numerical results show that in other cases
the Bradshaw-Richardson number B = 2 Omega(W + 2 Omega)/W-2 is not alw
ays a good indicator of the flow stability.