Nested traveling waves underlying elastoinertial turbulence: simulations, SPOD analysis, theory, and reduced order model

Polymer additives are commonly used in pipeline transport of liquids such as crude oil transport, water heating and cooling systems, and airplane tank filling to reduce turbulent drag. The emergence of elastoinertial turbulence (EIT), a chaotic flow state resulting from the interplay between inertia and elasticity, sets a limit on the achievable drag reduction using polymer additives. We investigate the dynamics of simulated 2D EIT in a FENE-P fluid using Spectral Proper Orthogonal Decomposition (SPOD) and discover that the dynamics of EIT are predominantly made of a collection of self-similar nested traveling waves that exhibit wall-mode structure and shift-reflect symmetry similar to the Tollmien–Schlichting wave. A scaling theory quantitatively captures the distribution of dominant wave speeds. We also developed a data-driven reduced-order model of EIT which captures the dominant structures and dynamics O(10⁶) times faster than the direct numerical simulation. The reduced-order model can be used to further investigate and also design control to manipulate its dynamics.