Experimental evidence for the continuous transition between elastic and elastoinertial turbulence.

Elastic turbulence (ET) and elastoinertial turbulence (EIT) of viscoelastic fluids are unique flow states with features distinct from the inertial turbulence of Newtonian fluids. Whether these two states are connected or entirely decoupled remains controversial. We here resolve this controversy by providing experimental evidence of a continuous transition between ET and EIT in Taylor-Couette flow. Through experimentally quantifying the roles of elasticity and inertia in flow stability, we find that elasticity is the primary driving mechanism for both elastic and elastoinertial instabilities, and inertia plays a secondary role in the latter. Remarkably, the critical condition for these instabilities can be described by a unified function derived from stability analysis, revealing that the transition between elastic instability to elastoinertial instability is continuous. Moreover, we show that the flow structures and the energy spectrum evolve seamlessly from ET to elasticity-dominated EIT, transitional EIT, and inertia-modulated EIT, with inertia playing an increasingly important role in the last three regimes. Our results offer insights into the fundamental nature of turbulence in viscoelastic flows and would have implications for applications involving drag reduction and polymer processing.