High-latitude ionospheric electrostatic turbulence studied by means of the wavelet transform

Abstract : The wavelet transform, after performing a time-scale decomposition by means of wavelet coefficients, displays the energy of a signal simultaneously in time and frequency. According to the uncertainty principle, at each frequency an optimal compromise between time resolution and frequency resolution is provided. The Morlet (complex-valued) wavelet is applied to the study of high-latitude electrostatic turbulence recorded onboard the AUREOL-3 satellite. The transforms of electron density and of one electric field component (approximately perpendicular to the Earth's magnetic field) are presented. The modulus of wavelet coefficients show vertical structures that are due to intensifications of the signal at a high frequency occurring at the same lime as at a low frequency. At each frequency, the duration of a turbulent event is of the order of a few periods, which implies that electrostatic turbulence is highly inhomogeneous. We can compare the two signals by calculating the ratio of the modulus of their wavelet transform and the phase difference. This comparison illustrates the differences between the frequency-time behaviours of the two fields, which are probably related to the nonlinear regime of turbulence.