<p>Wave attractor, a phenomenon of the internal or inertial waves self-focusing, is characterized by a rapid fluid motion velocity increase its trajectory, which causes instability growth in the form of secondary non-linear waves. The latter ones distort the attractor structure and affect its identification as well as visualization. In this paper, we propose a method for visualization of such attractor flows with developed instability in a linearly stratified fluid based on the combined Proper Orthogonal Decomposition (POD) filtering and Hilbert transform amplitude average, and show its efficiency on the examples of various numerical simulation cases.</p>