We present numerical simulations of the large‐scale electron density irregularities in the daytime equatorial electrojet driven by the gradient drift instability. The nonlocal nonlinear two‐fluid equations are integrated numerically with scales ranging from about 10 km to less than 100 m directly resolved on a 128×128 grid, while the effects of the smaller subgrid scales are included with the use of anomalous electron mobility and diffusion coefficients [Ronchi et al., 1990a]. The instability evolves to a state in which the perturbations propagate primarily in the east‐west direction with a typical horizontal wavelength of about 2 km. The output of the numerical simulations does not indicate the presence of a significant anisotropy in the power spectrum of the irregularities in the plane perpendicular to the ambient magnetic field, in contrast to the marked differences observed in physical space between the vertical and horizontal dynamics. The one‐dimensional integrated density and electric field power spectra have a power law dependence with a power index ranging between −2.5 and −1.2. The numerical results are compared with in situ rocket observations by probing the simulation region along different flight paths, following both eastward and westward trajectories. Electron vertical turbulent velocity distributions are computed from the code output and are contrasted with radar backscatter data. The features typical of the 3‐m type 2 echoes (such as the broadening and asymmetry in the frequency power spectra) are also present in the computed distributions, indicating that during weak electrojet conditions the small‐scale structures act as tracers of the large‐scale electric field variations. A conclusion of particular note is that a purely linear nonlocal analysis (valid for wavelengths λ ≈ 1 km) leads to the result that all perturbations are eventually damped, either by shear and then diffusion or by recombination. The inclusion of nonlinear effects, however, restores the instability. In the strongly turbulent regime a nonsteady saturated state is reached, whereby the linear convection of energy via shear to high wavenumbers is countered by the nonlinear modification of the equilibrium density and electric field gradients and by mode coupling of shorter wavelengths back to long.
The Farley‐Buneman instability is a collisional two‐stream instability observed in the E region ionosphere at altitudes in the range 90–120 km. While linear theory predicts the dominant wavelengths, it cannot fully describe the behavior of this nonlinearly saturated instability, as observed by radar and rocket measurements. This paper explores the nonlinear behavior of this phenomenon and the resulting waves through simulations and theory. Our two‐dimensional simulations model wave behavior in the plane perpendicular to the Earth's magnetic field, applying a fluid model to describe the electron dynamics and either a particle or a fluid model to describe ion behavior. The results show the growth, saturation, and nonlinear behavior of the instability for a much longer period of time than was possible with the pure particle codes used in previous studies. These simulations show (1) growth of Farley‐Buneman waves, (2) the development of secondary waves which propagate along the extrema and perpendicular to the Farley‐Buneman waves, (3) turning of the primary waves away from the electron drift direction, (4) a saturated wave phase velocity below the one predicted by linear theory but above the acoustic speed and (5) nonlinear electron E×Bo drifting dominates the behavior of the saturated waves. This paper describes both the simulation techniques and fundamental results. Additionally, this paper outlines a theory explaining the dominant nonlinear process seen in this instability.
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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