Scalings of forced Hasegawa–Mima equation by power-law noise

Abstract

For the plasma modeled by the Hasegawa–Mima equation forced by a noise, Kolmogorov-type phenomenology (KP) predicts the power-law scaling in two inertial regimes. In the spatial scale, which is larger than the ion gyroradius, the energy spectrum scales as k−11/3 where the energy cascades to larger scales and k−5 where the enstrophy is transferred to smaller scales down to the dissipation range. The renormalization-group (RG) approach, however, provides different scaling k−1−4δ/3 that strongly depends on the power exponent δ of the noise spectrum. Through numerical simulations it is found that, for δ ⩽ 2 or δ ⩾ 3, the energy spectrum follows KP while, for 2 ⩽ δ ⩽ 3, RG scaling prevails.