The effect of sheared diamagnetic flow on turbulent structures generated by the Charney–Hasegawa–Mima equation

Abstract

The generation of electrostatic drift wave turbulence is modeled by the Charney-Hasegawa-Mima equation. The equilibrium density gradient n 0 ϭn 0 (x) is chosen so that dn 0 /dx is nonzero and spatially variable ͑i.e., v * e is sheared͒. It is shown that this sheared diamagnetic flow leads to localized turbulence which is concentrated at max(ٌn 0 ), with a large dv * e /dx inhibiting the spread of the turbulence in the x direction. Coherent structures form which propagate with the local v * e in the y direction. Movement in the x direction is accompanied by a change in their amplitudes. When the numerical code is initialized with a single wave, the plasma behavior is dominated by the initial mode and its harmonics.

Hamiltonian formulation and coherent structures in electrostatic turbulence

“…The calculation and characterization of propagating CS is an important application of the Hamiltonian formalism. Such CS may arise as a result of the saturation of a primary instability [39], they may be driven by small scale fluctuations [22,40], or they may be formed through inverse cascade in two-dimensional turbulence [40]. The standard approach is to look for solutions of the equations of motion of the form ξ j = ξ j (x, y − ut) where u is the propagation velocity of the CS.…”

Statistical properties of Charney-Hasegawa-Mima zonal flows

“…Numerical studies where sheared flow is externally prescribed [18][19][20] lead to energetics that are qualitatively different from those obtained in the drift-wave/zonal-flow feedback mechanism 21 . In the CHM model [22][23][24] sheared flow may be imposed by prescribing the background density gradient 25 . The known solutions of the CHM equation, namely bipolar and monopolar vortices 26 , form in the plasma.…”

“…The periodic y direction is treated spectrally while the x direction as well as the nonlinearity of equation (1) are finite differenced 25 . The CHM equation's nonlinear term is calculated using a conservative scheme for vector nonlinearities 29 .…”

“…In the CHM model [22][23][24] sheared flow may be imposed by prescribing the background density gradient 25 . The known solutions of the CHM equation, namely bipolar and monopolar vortices 26 , form in the plasma.…”

“…The fluid simulations produce quasi-stationary time series (poloidally averaged and sampled at different radial points) of the electrostatic potential and corresponding vorticity that describe the CHM flows [22][23][24][25]27,28 . We apply a standard Box-Jenkins modeling for each time series.…”