Elasticity in drift-wave-zonal-flow turbulence

International audienceWe present a theory of turbulent elasticity, a property of drift-wave-zonal-flow (DW-ZF) turbulence, which follows from the time delay in the response of DWs to ZF shears. An emergent dimensionless parameter vertical bar 'vertical bar/Delta omega(k) is found to be a measure of the degree of Fickian flux-gradient relation breaking, where vertical bar 'vertical bar is the ZF shearing rate and Delta omega(k) is the turbulence decorrelation rate. For vertical bar 'vertical bar/Delta omega(k) > 1, we show that the ZF evolution equation is converted from a diffusion equation, usually assumed, to a telegraph equation, i.e., the turbulent momentum transport changes from a diffusive process to wavelike propagation. This scenario corresponds to a state very close to the marginal instability of the DW-ZF system, e.g., the Dimits shift regime. The frequency of the ZF wave is Omega(ZF) = /-gamma(1/2)(d)gamma(1/2)(modu), where gamma(d) is the ZF friction coefficient and gamma(modu) is the net ZF growth rate for the case of the Fickian flux-gradient relation. This insight provides a natural framework for understanding temporally periodic ZF structures in the Dimits shift regime and in the transition from low confined mode to high confined mode in confined plasmas