Locality and Universality in Gyrokinetic Turbulence

The nature of nonlinear interactions in gyrokinetic turbulence, driven by the ion-temperature gradient instability, is investigated using direct numerical simulations in toroidal flux tube geometry. To account for the level of separation existing between scales involved in an energetic interaction, the degree of locality of the free energy scale flux is analyzed employing Kraichnan’s infrared (IR) and ultraviolet locality functions. Because of the nontrivial dissipative nature of gyrokinetic turbulence, an asymptotic level for the locality exponents, indicative of a universal dynamical regime for gyrokinetics, is not recovered and an accentuated nonlocal behavior of the IR interactions is found instead, in spite of the local energy cascade observed.

Figure 1

The free energy rhs terms [of Eq. (3)] spectra (a) and the free energy flux across the shell boundaries (b) normalized by the total dissipation rate $\mathcal{D}$. The vertical dashed lines represent the shell boundaries. The insert picture (c) depicts the shell-to-shell transfer for this run (negative values for $P>K$); for details see Ref. 8.

Figure 2

The IR and UV locality functions, displayed for selected cutoff wave numbers identified by the shell index $c$. Dashed lines equal or proportional to different power laws of the abscissae are displayed for reference.

Figure 3

The IR and UV locality functions (“half-box” run), displayed for selected cutoff wave numbers identified by the shell index $c$.