Magnetohydrodinamic waves inside the sun

Abstract

[eng] In this work, the complex empirical orthogonal function (CEOF) method is used to analyse a numerical simulation of the tachocline. This method extracts information on the waves contained in a two-dimensional field and provides this knowledge in the form of four CEOF functions or measures. Firstly, we construct one- and two-dimensional synthetic signals made of the sum of standing and propagating waves to help interpret the CEOF functions. The CEOF analysis is able to identify each wave component of the field. Also, the amplitude, frequency and wavenumbers are recovered with outstanding accuracy. After testing the method we are able to apply the CEOF analysis to three scalar variables that come from a hydrodynamic numerical simulation of the tachocline: the perturbation of the tachocline thickness, h, and the longitudinal and latitudinal velocity components, u and v. Two physical modes of oscillation present in all variables are found. In addition to the amplitudes of the three variables, their wavenumbers and the frequency, the spatial distribution of h, u and v is also determined. Moreover, the CEOF method also allows to recover some properties of the tachocline di↵erential rotation and reveals the presence of non-linear waves in the numerical simulation.