Effect of short‐scale turbulence on kilometer wavelength irregularities in the equatorial electrojet

The kilometer scale irregularities in the daytime equatorial electrojet are studied within the framework of a two-fluid, nonlocal theory of the gradient drift instability. A separation of scales is introduced into the equations in order to model the effects of the subgrid, short-wavelength (λ < 100 m) modes. The presence of the short-scale turbulence is included in the large-scale equations through the average nonlinear flux due to the small-scale nonlinear terms. With the use of the linear ion continuity equation the nonlinear flux is expressed in terms of the large-scale quantities and of the small-scale density fluctuation spectrum. It is shown that the small-scale turbulence contributes to the large-scale equations through turbulent mobility and diffusion coefficients. For a particular choice for the small-scale density fluctuation spectrum (modeled after some of the available rocket data), the turbulent mobility is determined as a function of altitude, and its peak equals a few times the classical Pedersen mobility value. The equilibrium solutions of the large-scale equations are also derived in the presence of the short-wavelength turbulence. The localization of the current layer is seen to shift toward higher altitudes, and the current density profile conforms well with some of the available experimental data. Neglecting at this point the large-scale nonlinearities, the local and nonlocal linear growth rates of the long-wavelength modes are also obtained and discussed. The renormalized linear nonlocal equations for the large scales are integrated numerically, and the effects of the turbulent mobility and of velocity shear are observed and discussed. Nonlocal modes with horizontal wavelengths in the kilometer range dominate the linear stage of the instability, thus providing a possible explanation for the experimentally observed predominance of such wavelengths in the electrojet's wave spectrum. The dispersive nature of the large-scale modes is also discussed and reconsidered in the presence of the turbulent mobility term.

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