Application of the Proper Orthogonal Decomposition to Turbulent Czochralski Convective Flows

The aim of this work is to study the general aspects of the convective flow instabilities in a simulated Czochralski system. We considered the influence of the buoyancy and crystal rotation. Velocity fields, obtained by an ultrasonic technique, the corresponding 2D Fourier spectra and a correlation function, have been used. Steady, quasi-periodic and turbulent flows, are successively recognized, as the Reynolds number was increased, for a fixed Rayleigh number. The orthogonal decomposition method was applied and the numbers of modes, involved in the dynamics of turbulent flows, calculated. As far as we know, this method has been used for the first time to study the Czochralski convective flows. This method provides also information on the most important modes and allows simple theoretical models to be established. The large rotation rates of the crystal were found to stabilize the flow, and conversely the temperature gradients destabilize the flow. Indeed, the increase of the rotation effects reduces the number of involved modes and oscillations, and conversely, as expected, the increase of the buoyancy effects induces more modes to be involved in the dynamics. Thus, the flow oscillations can be reduced either by increasing the crystal rotation rate to the adequate value, as shown in this study or by imposing a magnetic field