Approaches to decomposing turbulence during an L-to-H mode transition in DIII-D tokamak

Previous works analyzing the Low-to-High confinement-mode transition in tokamaks depict a transient event involving nonlinear interactions between flows, turbulence, and inhomogeneous velocity shear [Phys.Fluids B2, 1 (1990)]. The modal ansatz adopted in neoclassical theory describes only the time-asymptotic behavior of instabilities, neglecting local finite-time effects and other transient growth mechanisms. Simulations are consistent with important experimental observations, but fall short in explaining the finite-time behavior of the transition dynamics [Phys. Plasmas 4, 1736 (1997)], pointing to the necessity to refine the theory to incorporate the interactions of evolving non-orthogonal (non-normal) modes. We treat the transient growth of the perturbation as being physically equivalent to the development of an instability. We have identified transients in the DIII-D shot data, explained transients using non-modal decomposition of turbulence [Annu. Rev. Fluid Mech. 39:129–62 (2007)] in the presence of velocity shear [Phys. Rev. E 66, 066409 (2002)], and distinguished stationary from nonstationary dynamics. Examples of the above, in theory, in experiment, and in conceptual illustrations, will be presented.