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Updated: Dec 26, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Slow diffusive structure in Nikolaevskii turbulence
Takayuki Narumi1, Yoshiki Hidaka2
1Graduate School of Sciences and Technology for Innovation, Yamaguchi University, Ube 755-8611, Japan.
Abstract:
Weak turbulence has been investigated in nonlinear-nonequilibrium physics to understand universal characteristics near the transition point of ordered and disordered states. Here the one-dimensional Nikolaevskii turbulence, which is a mathematical model of weak turbulence, is studied theoretically. We calculate the velocity field of the Nikolaevskii turbulence assuming a convective structure and carry out tagged-particle simulations in the flow to clarify the Nikolaevskii turbulence from the Lagrangian description. The tagged particle diffuses in the disturbed flow and the diffusion is superdiffusive in an intermediate timescale between ballistic and normal-diffusive scale. The diffusion of the slow structure is characterized by the power law for the control parameter near the transition point of the Nikolaevskii turbulence, suggesting that the diffusive characteristics of the slow structure remain scale invariant. We propose a simplified model, named two-scale Brownian motion, which reveals a hierarchy in the Nikolaevskii turbulence.
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