Turbulence Elasticity: A Key Concept to A Unified Paradigm of L-I-H Transition

Abstract 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 |hV iZF |/ !k > 1, with |hV iZF | the ZF shearing rate and !k the local turbulence decorrelation rate, the ZF evolution equation is converted from a di↵usion 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 front. 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 highconfinement-mode (L-I-H) transitions. Especially, we derive the onset and termination conditions of the limit cycle oscillations(LCOs), i.e., the I-mode. The transition from an unstable L-mode to I-mode is predicted to occur when !k < |hV iZF | < hV icr, where hV icr is a critical flow shearing rate induced by the turbulence elasticity and is derived explicitly. If |hV iE⇥B| > hV icr(hV iE⇥B is mean E ⇥ B shear flow driven by edge radial electrostatic field), the I-mode will terminate and spiral into the H-mode.