Theory of turbulence regulation by oscillatory zonal flows

The theory of turbulence regulation by oscillatory zonal flows is presented for passive scalar field models. Zonal flows are assumed to have linear spatial variation of the form U=-xΩ(t)y, where Ω(t) has amplitude Ωm and frequency ωz. The flux and fluctuation levels are found to scale as 1/|kyUm| and τ*/|kyUm|, respectively, for Ωm>ωz. Here, τ*=τη(ωz/Ωm)2 is the effective decorrelation time, τη=τ*(Ω=0), Um=xΩm, and ky is the typical poloidal wave number of the turbulence. The effect of stochasticity of oscillatory zonal flows on shear decorrelation is discussed. The results complement the theory of turbulence regulation by low-frequency random zonal flows [E. Kim and P. H. Diamond, Phys. Rev. Lett 91, 075001 (2003)]