Random acoustic fields and their energetic quantities (acoustic active and reactive intensities, potential and kinetic energy densities) are described in terms of the mutual coherences between sources. Conditions to correctly construct the coherence matrix of sources in a multivariate random process are given. It is shown that the description of a sound field using the coherence matrix of source is equivalent to the superposition of a number of independent coherent fields, which do not correspond to the original localized sources. A method based on processing the principal components of the coherence matrix of sources is given to reduce the number of necessary fields. The coherence function between acoustic pressure and particle velocity and the curl of active intensity are proposed as two indicators for estimating the degree of coherence and the polarization of acoustic fields. These indicators are analyzed theoretically and experimentally. The description of the structure of partially coherent fields is generalized by the definition of the field matrix whose rank is an indicator of the local complexity of an acoustic field.