Observations of the spatial sample covariance matrix (SCM) reveal that the ordered noise eigenvalues of the SCM decay steadily. Using a stochastic model for the sample covariance matrix, the empirical eigenvalue distribution can be derived using random matrix theory. The eigenvalue spectrum is directly related to the quantile function of the empirical eigenvalue distribution. These ordered eigenvalues have a decay that resembles what is observed in real data. Noise on the array is considered either incoherent self-noise or propagating acoustic noise that is coherent across the array. Using conventional 2D or 3D isotropic noise models, realizations of the SCM eigenvalues are generated using random matrix theory. Deep-water towed-array data are analyzed and it is shown that the eigenvalues of the SCM and compares well with theory.