Abstract
Novel mechanisms for zonal flow (ZF) generation for both large relative density fluctuations and background density gradients are presented. In this non-Oberbeck–Boussinesq (NOB) regime ZFs are driven by the Favre stress, the large fluctuation extension of the Reynolds stress, and by background density gradient and radial particle flux dominated terms. Simulations of a nonlinear full-F gyro-fluid model confirm the predicted mechanism for radial ZF propagation and show the significance of the NOB ZF terms for either large relative density fluctuation levels or steep background density gradients.
Highlights
Self-organization from turbulent to coherent states is a ubiquitous process in fluids
We show that the relative contribution Mi of the NOB zonal flow (ZF) terms (T2, . . . , T5) decreases with the reference background density gradient length Ln in the high col lisionality regime (α = 0.0005)
We have generalized the ZF equation (3) to account for NOB effects in equation (9). The former Reynolds stress R is replaced by the Favre stress F, which adds to its predecessor in case of high relative density fluctuations
Summary
Self-organization from turbulent to coherent states is a ubiquitous process in fluids. All of the work on ZF theory so far rely on δf models [1, 13, 22], which invoke the so called Oberbeck–Boussinesq (or thin layer) approx imation [23, 24] The latter breaks down, if the background density varies over more than one order of magnitude or if the relative density fluctuations exceed roughly 10%. In the following we generalize the theory of ZFs to NOB effects To this end, we decompose the density and electric potential of a full-F gyro-fluid model of a magnetized plasma [43] with the help of a density weighted Favre average [44]. We show how the ZF dynamics is distributed among the proposed NOB actors and provide scalings with collisionality, reference background density gradient length and the maximum of the relative density fluctuation amplitude
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