Correlations and instabilities of phase density fluctuations in models of open star clusters

The investigation of dynamical evolution of 6 open cluster models is carried out on data about phase coordinates of stars received by numerical integration of stellar motion equations. To attain the aim the phase coordinates of stars for 100 equidistant moments of time from the initial $t=0$ to $t_m \simeq 5.1 \tau_{vr}$ ($\tau_{vr}$ is the initial time of cluster violent relaxation), are used. Over the interval of time the rounding-off errors and errors because of exponential growth of initial coordinates perturbations do not affect statistical conclusions about motion behavior of cluster stars. The investigation method is based on calculations of mutual correlation functions $C_{1,2}=C_{1,2}(\tau, r)$ ($\tau$ is the time delay, $r$ is the distance between the points) for phase density fluctuations and application of Fourier transformations of functions $C_{1,2}$ in order to calculate frequency spectra and dispersion relations. The analysis of graphics $C_{1,2}$, frequency spectra and dispersion curves confirms the existence of phase density waves in cluster models, allows to get a complete spectrum of phase density radial oscillations, to separate stable and unstable oscillations, to calculate the periods of phase density oscillations and increments of unstable phase density oscillations. The theoretical estimations of periods of known unstable homological core oscillations of cluster models are confirmed. Pointed out are some astrophysical applications of results received: the origin of irregular structures in open clusters, weak turbulence of cluster star motions.