Phase correlation of lage amplitude MHD waves in the earth's foreshock

Large amplitude MHD turbulence is commonly found in the earth's foreshock. They can be written as a superposition of MHD Fourier modes with characteristic frequency, amplitude, and phase. Nonlinear interaction between the Fourier modes are likely to produce finite correlation among the wave phases. It is fundamentally important to identify whether the observed wave phases are completely random (as assumed in quasi-linear theories) or they are correlated above a level statistically significant. Using a method based on a surrogate data composition and a fractal analysis, we analyzed Geotail magnetic field data and found that the correlation of wave phases does exist, indicating that the nonlinear interactions between the waves is in progress. We will discuss details of our results in the presentation.