Theory of the nonlinear spectrum of the gradient drift instability in the equatorial electrojet

A set of nonlinear coupled differential equations is derived from the fluid equations to describe the two-dimensional nonlinear behavior of the gradient drift instability. The divergence of the nonlinear electron flux, large only if more than one spatial dimension is considered, is identified as the dominant nonlinearity. This term causes saturation of the instability and cascading of energy to smaller wavelengths. Saturated amplitudes and spectra of density and electric field fluctuations are calculated, and both analytical and numerical results are given. Applying the results to nighttime rocket observations in the equatorial electrojet yields the observed density fluctuations of ∼10% and also reproduces the observed steepening of the density wave form in the vertical x direction. The nighttime density spectrum is found to be dominated by irregularities that vary only in this x direction.