Abstract <p>A new universal classification of components of heterogeneous media (liquids, gases, and plasma) flows includes traditional waves and families of ligaments describing the fine structure of distributions of observable physical quantities. The mathematical basis of the classification includes the sets of complete solutions to the system of fundamental equations of fluid mechanics constructed taking into account macro- and microscopic mechanisms of transfer and conversion of energy components. A fluid medium is characterized by equations of state for the Gibbs potential and its derivatives. When solving problems using the algebra of complex numbers, the frequency, which is a measure of energy, preserves its real-valuedness and positive definiteness, and the wave number is chosen to be complex-valued. Complete solutions to linearized and weakly nonlinear equations are found using united perturbation theory. The spatiotemporal parameters of the solutions describing waves and ligaments determine the requirements to experimental techniques as regards the choice of observable physical quantities that permit the assessment of error, the size of the observation area, the sensitivity, as well as the spatial and temporal resolution of instruments. The paper presents complete dispersion relations of propagating periodic surface and internal gravity waves in stratified media. Schlieren methods for visualizations of periodic internal wave beams and ligaments in the depth of a continuously stratified fluid are also considered.</p>