Tracing the Pathway from Drift-Wave Turbulence with Broken Symmetry to the Production of Sheared Axial Mean Flow

Abstract

This study traces the emergence of sheared axial flow from collisional drift-wave turbulence with broken symmetry in a linear plasma device-the controlled shear decorrelation experiment. As the density profile steepens, the axial Reynolds stress develops and drives a radially sheared axial flow that is parallel to the magnetic field. Results show that the nondiffusive piece of the Reynolds stress is driven by the density gradient, results from spectral asymmetry of the turbulence, and, thus, is dynamical in origin. Taken together, these findings constitute the first simultaneous demonstration of the causal link between the density gradient, turbulence, and stress with broken spectral symmetry and the mean axial flow.

The ecology of flows and drift wave turbulence in CSDX: A model

“…Measurements also indicate a weak coupling between v y and v z . 32,33 This is consistent with the observation that r v y ( jxj (i.e., moderate azimuthal flow) and the absence of transport barriers, because of a decoupled v z from v y . Analytically, in order to simplify the model, a slaved expression for e is replaced in the equations for density and azimuthal flow.…”

“…Energy released from r n also accelerates v z via the parallel Reynolds stress hṽ xṽz i. This trend is in agreement with the experimental results, 32,33 and supports the analogy between the plasma and an engine. 39 The model thus unfolds a coupling relation between v z and v y , as both flows are accelerated by the same free energy source.…”

“…q 2 s , as indicated by measurements of modest axial flow velocities. 32,33 The hk m k z i correlator can thus be neglected in f. However, in the parallel Reynolds stress, hk m k z i appears as the zeroth order and so cannot be dropped. Here, it will be expressed in terms of an empirical constant r VT that will be introduced in a Sec.…”

“…22,25,30,38 Theoretical studies also show that both axial and zonal flows are driven by turbulence, particularly by the non-diffusive residual stress in both expressions for hṽ xṽy i and hṽ xṽz i. 21,23,32,39,40 Reference 26 investigates the relation between the axial and azimuthal flows and turbulence, and formulates a new zonal momentum balance theorem for the coupled drift-ion acoustic waves. Due to acoustic coupling, a dynamical mechanism for ZF generation is established.…”

“…Experimental results from CSDX show that the energy transfer to the axial flow via the parallel Reynolds power density: Ð À@ x hṽ xṽz i v z dx, i.e., the power exerted by turbulence on the axial flow, is less than that exerted on the azimuthal profile via: Ð À@ x hṽ xṽy i v y dx, by a factor of five. 32,33 The axial flow then can be considered as parasitic to the system of r v y and r n. The model can be reduced even further, to 2 fields, by neglecting the axial flow equation v z , and solving the density and azimuthal flow equations using the stationary slaved expression for e obtained from the equation for the mean fluctuating energy.…”