Turbulence elasticity: a key concept to a unified paradigm of L → I → H transition

We present a theory of turbulence elasticity, which follows from delayed response of drift waves (DWs) to zonal flow (ZF) shears. It is shown that when |〈V〉'ZF|/Δωk ⩾ 1, with |〈V〉'ZF| the ZF shearing rate and Δωk the local turbulence decorrelation rate, the ZF evolution equation is converted from a diffusion equation to a telegraph equation. This insight provides a natural framework for understanding temporally periodic ZF structures, e.g., propagation of the ZF/turbulence intensity fronts. Furthermore, by incorporating the elastic property of the DW–ZF turbulence, we propose a unified paradigm of low-confinement-mode to intermediate-confinement-mode to high-confinement-mode (L → I → H) transitions. In particular, we predict the onset and termination conditions of the limit cycle oscillations, i.e. the I-mode. The transition from an unstable L-mode to I-mode is predicted to occur when Δωk < |〈V〉'ZF|<〈V〉'cr, where 〈V〉'cr is a critical flow shearing rate and is derived explicitly. If |〈V〉'E×B| > 〈V〉'cr(〈V〉E×B is mean E × B shear flow driven by edge radial electrostatic field), the I-mode will terminate and spiral into the H-mode.