Figure Captions Grid-generated Turbulence with and without Rotation

Fig. 1. Omnidirectional energy spectrum E(k) versus wavenumber k, computed from Eqs. (9)-(11), for the case A = 0:7, = 1, varying the rotation rate = 0; 10; 100. There is a smooth transition from the Komogorov`? 5=3' case = 0 to a spectrum = 100 that approaches a ` ? 2' form. Spontaneous breaking of reeexional symmetry in real quasi-two-dimensional turbulence: stochastic traveling waves and helical solitons in atmosphere and laboratory, Proc. R. References 1. A. N. Kolmogorov, \The local structure of turbulence in incompressible viscous uid for very large Reynolds number". 8 is directly proportional to the short time scale = 1=. Therefore, it appears that Zeman's basic assumption that leads to his energy spectrum is not supported by LES computation. Indeed, Zeman 16 noted that a further assumption 1 + C 4 y ?1 = y ?1=2 (21) is needed to obtain the \-2" spectrum (Eq. 4) from Eqs. (17)-(19) (C 4 is another constant introduced by Zeman). Bershadskii et al. 27 have proposed a E(k) / 2=3 jkj ?7=3 spectral form for rotating turbulence with some observational supports from stratospheric turbulence. Here is the rate of spontaneous helicity generation. This spectral form was originally obtained by Brissand et al. 28 for the case of three dimensional turbulence, Bershadskii et al. 27 argued that the quasi-two-dimensional turbulence regime arises as a result of a spontaneous breaking of reeexional symmetry, which in turn is a consequence of the instability of two dimensional turbulence to three dimensional helical traveling waves and solitons. 5 Conclusions The strong similarity between the MHD turbulence and isotropic turbulence subject to rotation has been noted. The MHD phenomenologies of Kraichnan 4 and Matthaeus and Zhou 15 were applied to rotating turbulence. When the turbulence is subject to strong rotation, an energy spectrum, E(k) = C (() 1=2 k ?2 ; where the constant C = 1:22?1:87 is found. A hypothesis on the triple correlation decay rate, Eq. (7), leads to the spectral law given in Eqs. (9)-(11), which varies between thè?5=3' (without rotation) and`?2' laws (with strong rotation). We deduced a `rule' (Eq. 8) that relates spectral transfer times to the eddy turnover time and the time scale for decay of the triple correlations. For intermediate rotation rate, the spectrum varies according to the value of a dimensionless parameter that measures the strength of the rotation wavenumber k = ((3 ==) 1=2 relative to …