Frequency spectrum in drift wave turbulence

Abstract

The frequency spectrum of drift wave turbulence is examined, with emphasis on the underlying dynamics, the nonlinear frequency shift, and the reliability of analytical techniques. It is found that the frequency spectrum can depend on three different effects, each of which contribute both a broadening and shift to the spectrum. First is the usual ‘‘eddy-damping’’ mechanism, which is derived here from a direct interaction approximation (DIA) analysis. Spectral broadening from the eddy-damping mechanism tends to be important at longer wavelengths, and gives a frequency broadening and a downshift, coming, respectively, from the real and imaginary parts of the renormalized diffusivity. A second effect that contributes to the frequency spectrum is the incoherent nonlinear drive, revealed by a DIA solution but often neglected in Markovian approximations. The nonlinear drive also tends to be important at longer wavelengths, and contributes both to the spectral width (from broadband driving), and a frequency downshift (from off-frequency driving). A third effect comes from turbulent fluctuations of the density gradient, which add to the equilibrium density gradient and thereby cause fluctuations in the linear drift frequency. This mechanism tends to become important at short wavelengths, contributing both a frequency broadening as revealed by a DIA analysis, and a frequency upshift, as revealed by a weak turbulence analysis. The relation of these results to the fluctuation–dissipation theorem, and the impact on drift wave stability are discussed.