Nonlinear dynamics of Rossby-Khantadze electromagnetic planetary waves in the weakly ionized ionospheric E-layer is investigated. Along with the prevalent effect of Hall conductivity for these waves, the latitudinal inhomogeneity of both the Earth's angular velocity and the geomagnetic field becomes essential. It is shown that such short wavelength turbulence of Rossby-Khantadze waves is unstable with respect to the excitation of low-frequency and large-scale perturbations of the zonal flow and magnetic field. The nonlinear mechanism of the instability is driven by the advection of vorticity, leading to the inverse energy cascade toward the longer wavelength. The growth rate of the corresponding instability is found. It is shown that the generation of the intense mean magnetic field is caused by the latitudinal gradient of the geomagnetic field.
It is shown that in the earth's conductive ionospheric E-region, large-scale ultra low-frequency Rossby and Khantadze electromagnetic waves can propagate. Along with the prevalent effect of Hall conductivity for these waves, the latitudinal inhomogeneity of both the earth's angular velocity and the geomagnetic field becomes essential. Action of these effects leads to the coupled propagation of electromagnetic Rossby and Khantadze modes. Linear propagation properties of these waves are given in detail. It is shown that the waves lose the dispersing property for large values of wave numbers. Corresponding nonlinear solitary vortical structures are constructed. Conditions for such self-organization are given. It is shown that nonlinear large-scale vortices generate the stronger pulses of the geomagnetic field than the corresponding linear waves. Previous investigations are revised.
[1] Planetary-scale waves and vortices in the weakly ionized ionospheric E layer are dominated by the Hall conductivity that couples the Rossby and Alfvén dynamics giving rise to what are called Rossby-Alfvén-Khantadze electromagnetic structures. At finite amplitudes we show that the nonlinearities in the dynamics generate sheared zonal-flow velocities and zonal magnetic field fluctuations. The zonal-flow mechanism is based on the parametric excitation of the zonal variations through three-wave mode coupling in the planetary-scale waves. The coupled dynamics of the nonlinear 3-D incompressible flows and the magnetic field fluctuations are derived and used to derive the structure and growth rates for the zonal flows and zonal magnetic fields. Large-amplitude planetary waves are shown to drive up magnetic fluctuations up to 100 nT.
We review the generation of zonal flow and magnetic field by coupled electromagnetic ultra-low-frequency waves in the Earth’s ionospheric E-layer. It is shown that, under typical ionospheric E-layer conditions, different planetary low-frequency waves can couple with each other. Propagation of coupled internal-gravity–Alfvén, coupled Rossby–Khantadze and coupled Rossby–Alfvén–Khantadze waves is revealed and studied. A set of appropriate equations describing the nonlinear interaction of such waves with sheared zonal flow is derived. The conclusion on the instability of short-wavelength turbulence of such coupled waves with respect to the excitation of low-frequency and large-scale perturbation of the sheared zonal flow and sheared magnetic field is deduced. The nonlinear mechanism of the instability is based on the parametric triple interaction of finite-amplitude coupled waves leading to the inverse energy cascade towards longer wavelength. The possibility of generation of an intense mean magnetic field is shown. Obtained growth rates are discussed for each case of the considered coupled waves.
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