Theory and simulation of rotational shear stabilization of turbulence

Numerical simulations of ion temperature gradient (ITG) mode transport with gyrofluid flux tube codes first lead to the rule that the turbulence is quenched when the critical E×B rotational shear rate γE−crit exceeds the maximum of ballooning mode growth rates γ0 without E×B shear [Waltz, Kerbel, and Milovich, Phys. Plasmas 1, 2229 (1994)]. The present work revisits the flux tube simulations reformulated in terms of Floquet ballooning modes which convect in the ballooning mode angle. This new formulation avoids linearly unstable “box modes” from discretizing in the ballooning angle and illustrates the true nonlinear nature of the stabilization in toroidal geometry. The linear eigenmodes can be linearly stable at small E×B shear rates, yet Floquet mode convective amplification allows turbulence to persist unless the critical shear rate is exceeded. The flux tube simulations and the γE−crit≈γ0 quench rule are valid only at vanishing relative gyroradius. Modifications and limits of validity on the quench rule are suggested from analyzing the finite relative gyroradius “ballooning-Schrödinger equation” [R. L. Dewar, Plasma Phys. Controlled Fusion 39, 437 (1997)], which treats general “profile shear” (x variation in γ0) and “profile curvature” (x2 profile variation).