Krommes' theory on dynamics of zonal flow in strong collisionless drift wave turbulence was analyzed. In the cold ion limit, the nonlinear growth rate generalized Kelvin-Helmholtz (GKH) mode and the equivalent expression, became identical, modulo notation for response function in the case when the background turbulence is isotropic. It was found that all of the substantive claims therein are incorrect. The results show that except for a factor of 1/2 in front of the diagonal Reynolds stress term in Kim and Diamond (KD) which should be corrected to unity, all other criticisms raised by Krommes are unfounded.

We elucidate the role of zonal flows in transient phenomena observed during L-H transition by studying a simple L-H transition model which contains the evolution of zonal flows, mean ExB flows, and the ion pressure gradient. Zonal flows are shown to trigger the L-H transition and cause time-transient behavior through the self-regulation of turbulence before a mean shearing, due to a steep pressure profile, secures a quiescent H mode. Surprisingly, this self-regulation lowers the power threshold for the ultimate transition to a quiescent H-mode state.

A study was performed on mean shear flows, zonal flows and generalized Kelvin-Helmholtz modes in drift wave turbulence. A minimal model for the L→H (low- to high-confinement) transition was proposed, which involved the amplitude of drift waves, zonal flows and the density gradient. The effect of poloidally nonaxisymmetric structures on anomalous transport was investigated.

An analytical theory of the tails of the probability distribution function (PDF) for the local Reynolds stress (R) is given for forced Hasegawa–Mima turbulence. The PDF tail is treated as a transition amplitude from an initial state, with no fluid motion, to final states with different values of R due to nonlinear coherent structures in the long time limit. With the modeling assumption that the nonlinear structure is a modon (an exact solution of a nonlinear Hasegawa–Mima equation) in space, this transition amplitude is determined by an instanton. An instanton is localized in time and can be associated with bursty and intermittent events which are thought to be responsible for PDF tails. The instanton is found via a saddle-point method applied to the PDF, represented by a path integral. It implies the PDF tail for R with the specific form exp[−cR3/2], which is a stretched, non-Gaussian exponential.

We examine the dynamics of turbulent reconnection in 2D and 3D reduced MHD by calculating the effective dissipation due to coupling between small-scale fluctuations and large-scale magnetic fields. Sweet-Parker type balance relations are then used to calculate the global reconnection rate. Two approaches are employed -- quasi-linear closure and an eddy-damped fluid model. Results indicate that despite the presence of turbulence, the reconnection rate remains inversely proportional to $\sqrt{R_m}$, as in the Sweet-Parker analysis. In 2D, the global reconnection rate is shown to be enhanced over the Sweet-Parker result by a factor of magnetic Mach number. These results are the consequences of the constraint imposed on the global reconnection rate by the requirement of mean square magnetic potential balance. The incompatibility of turbulent fluid-magnetic energy equipartition and stationarity of mean square magnetic potential is demonstrated.

We analytically compute the probability distribution function (PDF) of the local Reynolds stress ( R) for forced Hasegawa-Mima turbulence. With the assumption that the PDF tail is due to an instanton with the spatial form given by the modon solution, the tail of the PDF of R is found to be a stretched, non-Gaussian exponential, with the specific form exp[-cR(3/2)] ( c is a constant). We relate the temporal localization of the instanton to the degree of "burstiness" of the momentum transport event.

We reconsider the important question of the effect of a strong mean shear flow on the transport of a passive scalar field. By incorporating the effect of resonance, we show that the flux scales with the mean shear Omega as Omega(-1). The results also indicate that the scaling of the flux and cross phase with shear is rather weak and that the cross phase is not always more heavily suppressed than the amplitude of the turbulence. Furthermore, we show that the scalings of flux and cross phase with Omega depend on the statistics of the turbulent flow.

The diffusion of uni-directional magnetic fields by two dimensional turbulent flows in a weakly ionized gas is studied. The fields here are orthogonal to the plane of fluid motion. This simple model arises in the context of the decay of the mean magnetic flux to mass ratio in the interstellar medium. When ions are strongly coupled to neutrals, the transport of a large--scale magnetic field is driven by both turbulent mixing and nonlinear, ambipolar drift. Using a standard homogeneous and Gaussian statistical model for turbulence, we show rigorously that a large-scale magnetic field can decay on at most turbulent mixing time scales when the field and neutral flow are strongly coupled. There is no enhancement of the decay rate by ambipolar diffusion. These results extend the Zeldovich theorem to encompass the regime of two dimensional flows and orthogonal magnetic fields, recently considered by Zweibel (2002). The limitation of the strong coupling approximation and its implications are discussed.

Generalized Kelvin–Helmholtz (GKH) instability is examined as a mechanism for the saturation of zonal flows in the collisionless regime. By focusing on strong turbulence regimes, GKH instability is analyzed in the presence of a background of finite-amplitude drift waves. A detailed study of a simple model with cold ions shows that nonlinear excitation of GKH modes via modulational instability can be comparable to their linear generation. Furthermore, it is demonstrated that zonal flows are likely to grow faster than GKH mode near marginality, with insignificant turbulent viscous damping by linear GKH. The effect of finite ion temperature fluctuations is incorporated in a simple toroidal ion temperature gradient model, within which both zonal flow and temperature are generated by modulational instability. The phase between the two is calculated self-consistently and shown to be positive. Furthermore, the correction to nonlinear generation of GKH modes appears to be small, being of order O(ρi2k2). Thus, the role of linear GKH instability in the saturation of collisionless zonal flows, in general, seems dubious.