A theory that accounts for the generation of short‐wavelength irregularities in the equatorial electrojet for an electron drift velocity below the ion‐acoustic speed is presented. Long‐wavelength (tens of meters) horizontally propagating waves driven unstable by the ambient ionization density gradient are found not to steepen very much, even though they are nondispersive. However, the local vertical velocity and horizontal density gradient associated with these waves are capable of generating the meter‐wavelength obliquely propagating irregularities detected in radar observations.

A nonlinear unified theory of type I and II irregularities is presented that explains their principal observed characteristics. The power spectrum is predicted by using Kolmogoroff‐type conservation law for the power flow in cascading eddies.

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The ion-temperature-gradient-driven instability is considered in this paper. Physical pictures are presented to clarify the nature of the instability. The saturation of a single eddy is modeled by a simple nonlinear equation. It is shown that eddies that are elongated in the direction of the temperature gradient are the most unstable and have the highest saturation amplitudes. In a sheared magnetic field, such elongated eddies twist with the field lines. This structure is shown to be an alternative to the usual Fourier mode picture in which the mode is localized around the surface where k∥ =0. These elongated twisting eddies, which are an integral part of the ‘‘ballooning mode’’ structure, could survive in a torus. The elongated eddies are shown to be unstable to secondary instabilities that are driven by the large gradients in the long eddy. It is argued that the ‘‘mixing length’’ is affected by this nonlinear process, and is unlikely to be a linear eigenmode width.

The following macroscopic equation is shown to govern the time development of a nonlinear ion acoustic wave: ∂n∂τ + α2n ∂n∂ξ + α3 ∂3n∂ξ3 + α1(8π)1/2 P  ∫ −∞+∞ ∂n∂ξ′ dξ′ξ − ξ′ = 0, where n, ξ, and τ are normalized wave amplitude, space, and time coordinates, and α1, α2, α3 are parameters which depend on the relative strengths of Landau damping, nonlinearity, and dispersion. The first three terms constitute the Korteweg-deVries equation, and the last term represents the effect of Landau damping. The equation conserves the number of particles but the wave energy can be shown to decay always. It is demonstrated that an initial waveform may either steepen or not depending on the relative size of the nonlinearity as compared to Landau damping. It is also shown that the Landau damping term causes the amplitude of a solitary wave to decay with time as (τ+τ0)−2.