title: Wave-number spectrum of dissipative drift waves and a transition scale.
abstract: We study the steady state spectrum of the Hasegawa-Wakatani (HW) equations that describe drift wave turbulence. Beyond a critical scale k_{c}, which appears as a balance between the nonlinear time and the parallel conduction time, the adiabatic electron response breaks down nonlinearly and an internal energy density spectrum of the form F(k_{⊥})∝k_{⊥}^{-3}, associated with the background gradient, is established. More generally a dual power law spectrum, approximately of the form F(k_{⊥})∝k_{⊥}^{-3}(k_{c}^{-2}+k_{⊥}^{-2}) is obtained, which captures this transition. Using dimensional analysis, an expression of the form k_{c}∝C/κ is derived for the transition scale, where C and κ are normalized parameters of the HW equations signifying the electron adiabaticity and the density gradient, respectively. The results are numerically confirmed using a shell model developed and used for the Hasegawa-Wakatani system.
authors.affiliation: Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France; Sorbonne Universités, UPMC Univ Paris 06, UMR7648, Laboratoire de Physique des Plasmas, F-91128 Palaiseau, France; CNRS, UMR7648, Laboratoire de Physique des Plasmas, F-91128 Palaiseau, France; and Univ Paris-Sud, UMR7648, Laboratoire de Physique des Plasmas, F-91128 Palaiseau, France.
authors.forename: K
authors.initials: K
authors.lastname: Ghantous
authors.affiliation: Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France; Sorbonne Universités, UPMC Univ Paris 06, UMR7648, Laboratoire de Physique des Plasmas, F-91128 Palaiseau, France; CNRS, UMR7648, Laboratoire de Physique des Plasmas, F-91128 Palaiseau, France; and Univ Paris-Sud, UMR7648, Laboratoire de Physique des Plasmas, F-91128 Palaiseau, France.
authors.forename: Ö D
authors.initials: ÖD
authors.lastname: Gürcan