# Your search: "author:"Diamond, Patrick""

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## Scholarly Works (7 results)

An active scalar system refers to a system with a scalar field that is coupled to the fluid dynamics and gives feedback to the velocity field through local forces. Active scalar turbulence systems are ubiquitous, and the study of these systems is a central focus of research in theoretical plasma physics. As examples, the 2D Cahn-Hilliard Navier-Stokes (CHNS) system and 2D Magnetohydrodynamics (MHD) system are studied in this dissertation.

The similarities and differences between 2D CHNS and 2D MHD are discussed. These are both elastic (i.e., self-restoring) systems, and display a memory, governed by freezing-in laws. The CHNS system supports an elastic wave, which is analogous to Alfven wave in MHD. Cascades and spectra in 2D CHNS are investigated, with focus on the interaction between inverse and forward cascades. The inverse cascade of mean square concentration $\langle\psi^2\rangle$, which is closely related to the real space dynamics of blob formation and merger, is found to be the dominant nonlinear transfer process. The spectrum of $\langle\psi^2\rangle_k$ exhibits a scaling law of $\sim k^{-7/3}$, and this exponent is the same as the corresponding one in 2D MHD. On the other hand, the kinetic energy spectrum follows $E_k\sim k^{-3}$. This exponent is closer to that for 2D Navier-Stokes, instead of that for 2D MHD. We suggest this is because the restoring force is significant only in the interfacial regions. The packing fraction of interfacial regions is small because of the formation and merger of blobs.

This suggests that the inverse cascade of $\langle \psi^2 \rangle$ - related to blob coalescence - modifies the forward cascade in 2D CHNS.

The evolution of the concentration field of the Cahn-Hilliard system in the background of a single eddy is studied. This is analogous to the flux expulsion phenomenon in 2D MHD. Though the system is simple, complex evolution is observed. 3 stages are observed: the ``jelly roll'' pattern stage, the stage of topological evolution, and the ``target'' pattern stage. The target pattern is metastable, as the bands gradually merge with time.

We also study turbulent transport in active scalar systems. We intended to first explore the classic problem of the suppression of turbulent transport in 2D MHD as an exercise in code verification, and then move to 2D CHNS. However, novel blob-and-barrier real space structures were observed with higher magnetic Reynolds number $\mathrm{Rm}$ in 2D MHD. We argue that the conventional approach of mean field theory is not applicable for the case without an external large scale magnetic field. The magnetic energy is observed to be concentrated in the intermittent, thin transport barrier regions, which located in the interstices between blobs of magnetic potential. The turbulent transport is quenched primarily because of these barriers. Barrier formation is linked to the inverse cascade of mean square magnetic potential $\langle A^2\rangle$ and negative turbulent resistivity. For small scale forcing, spontaneous formation of layering occurs.

More generally, we demonstrate that synergistic studies of related but different systems -- 2D CHNS and 2D MHD -- can lead to improved understanding. These studies can provide insights for all active scalar turbulence systems, since these systems share important common properties such as memory, elastic waves, and conservation laws.

We develop a simple model for the generation and amplification of intrinsic axial flow in a linear device, Controlled Shear Decorrelation Experiment (CSDX). This model develops a novel dynamical symmetry breaking mechanism in drift wave turbulence, which does not require complex magnetic field structure, such as shear. Thus, the model is applicable to both tokamaks and linear devices. This mechanism is, essentially, a form of negative viscosity phenomenon.

Negative compressibility ITG turbulence can also induce a negative viscosity increment.

However, we show that no intrinsic axial flow can be generated by pure ITG turbulence in a straight magnetic field. When the flow gradient is steepened by any drive mechanism, the flow profile saturates at a level close to the value above which parallel shear flow instability (PSFI) becomes dominant over the ITG instability. This saturated flow gradient exceeds the PSFI linear threshold, and grows with $\nabla T_{i0}$ as $|\nabla V_\parallel| / |k_\parallel c_s| \sim|\nabla T_{i0}|^{2/3} / (k_\parallel T_{i0})^{2/3}$.

The coupling of azimuthal and axial flows in CSDX--in absence of magnetic shear--is investigated.

In particular, we focus on the apportionment of turbulence energy between azimuthal and axial flows, and how the azimuthal flow shear affects axial flow generation and saturation by drift wave turbulence.

Detailed measurements of intrinsic axial flow parallel to the magnetic field are performed on CSDX, with no axial momentum input.

The results present a direct demonstration that the broken spectral symmetry of drift wave turbulence causes the development of axial mean flows in cylindrical magnetized plasmas.

Measurements suggest the axial flow is parasitic to the drift wave--zonal flow system.

Besides, we show that consideration of wave--flow resonance resolves the long-standing problem of how zonal flows (ZFs) saturate in the limit of weak or zero frictional drag and also determines the ZF scale directly from analysis.

We show that resonant vorticity mixing, which conserves potential enstrophy, enables ZF saturation in the absence of drag, and so is effective at regulating the Dimits up-shift regime.

Vorticity mixing is incorporated as a nonlinear, self-regulation effect in an extended 0D predator--prey model of drift--ZF turbulence.

In this dissertation, we present advances in turbulence modeling for magnetically confined plasmas. We investigate the ecology of microscopic drift wave turbulence and the self-generated macroscopic flows in magnetically confined plasmas. We formulate reduced models that self-consistently describe the evolution of turbulence and mean plasma profiles (including flows) and recover trends obtained from the CSDX device and HL-2A tokamak. The dissertation is divided to three parts. The first part presents a reduced model that describes the interplay between drift wave turbulence and zonal and axial flows in the adiabatic plasma of CSDX, where the electron response is Boltzmann. The model explains how free energy released from the density gradient accelerates both axial and azimuthal flows in CSDX. A description of the interactions between the disparate scales of the plasma via the parallel and perpendicular Reynolds stresses $\langle \tilde v_x \tilde v_z \rangle $ and $\langle \tilde v_x \tilde v_y \rangle $ is presented. Expressions for these stresses are decomposed into a diffusive component that relaxes the flow profile, and a residual stress responsible for accelerating the corresponding flow. Moreover, parallel and perpendicular flow dynamics are described using an extended mixing length approach. This accounts for the degree of symmetry breaking in the parallel direction and parametrizes the efficiency of $\nabla n$ in driving the axial flow. In the second part of the dissertation, the relationship between drift waves and zonal flows is examined in depth via a more specific model. Analytical results obtained from this model confirm the published experimental data showing a suppression of turbulence with the increase in magnitude of the magnetic field \textbf{B}. A new criterion for access to enhanced confinement is introduced. This criterion captured by the dimensionless quantity $R_{DT}$, compares the production rate of turbulent enstrophy due to relaxation of the mean profiles, to the corresponding destruction rate via coupling to the mean flow. When $R_{DT} >1$, the profiles steepen and enhanced confinement is accessible. In the third paper, a novel idea for understanding the physics of the density limit problem in low $\beta$ tokamaks is presented. The collapse of the zonal shear flow when the electron response transitions from Boltzmann to hydrodynamic scaling, along with cooling of the edge and the onset of MHD activity is predicted by the observation that the zonal flow drive will drop as the electron parallel diffusion time increases with density. This leads to a simple, verified understanding of the density limit phenomenon in $L$-modes.