Experimental studies of the fine structure of the perturbation pattern in a continuously stratified fluid (an aqueous solution of table salt) generating at a uniform motion of obstacles of different shapes (plate, horizontal cylinder and sphere) were conducted using high-resolution schlieren and electrolytic techniques at the laboratory facilities of the Unique Research Facility, Hydrophysical Complex, Ishlinsky Institute for Problems in Mechanics RAS. These experiments were based on properties of the complete analytical and numerical solutions of a reduced fundamental equations system (FES). Describing the dynamics and structure of incompressible, heterogeneous fluids flows is based on equations for density distribution (replacing the state equation), continuity, Navier-Stokes, and diffusion system. The analysis of the system performed by singular perturbation theory and numerical simulation shows that the well-known large-scale components (the upstream perturbation, attached internal waves, wake and vortices) are complemented by the ligaments (families of singular solutions). In experiments, thin interfaces and fibers, mathematically represented as ligaments, were identified in patterns of flow past various types of obstacles. The results from observations and calculations based on complete solutions to the FES agree both quantitatively and qualitatively.