Intermittent direction reversals of moving spatially localized turbulence observed in two-dimensional Kolmogorov flow

Abstract

We have found that in two-dimensional Kolmogorov flow a single spatially-localized turbulence (SLT) exists stably and travels with a constant speed on average switching the moving direction randomly and intermittently for moderate values of control parameters: Reynolds number and the flow rate. We define the coarse-grained position and velocity of an SLT and separate the motion of the SLT from its internal turbulent dynamics by introducing a co-moving frame. The switching process of an SLT represented by the coarse-grained velocity seems to be a random telegraph signal. Focusing on the asymmetry of the internal turbulence we introduce two coarse-grained variables characterizing the internal dynamics. These quantities follow the switching process reasonably. This suggests that the twin attracting invariant sets each of which corresponds to a one-way traveling SLT are embedded in the attractor of the moving SLT and the connection of the two sets is too complicated to be represented by a few degrees of freedom but the motion of an SLT is controlled by the internal turbulent dynamics.

Subcritical laminar-turbulence transition with wide domains in simple two-dimensional Navier-Stokes flow without walls

“…This advection effect disturbs an efficient supply of kinetic energy for disturbances to grow. This interpretation is consistent with the fact that the tails of SLT do not develop for large U y flows [43,44]. These kinds of effects can be seen in wallbounded flow but not be controlled.…”

“…Kolmogorov flow is used to obtain many characteristics of solutions of Navier-Stokes equation and as a test field of novel idea of understanding complex solutions [38][39][40][41]. Recently, solutions in which spatially-localized chaotic regions and steady regions coexist were found even in 2D Kolmogorov flow [42][43][44].…”

Symmetry-reduced dynamic mode decomposition of near-wall turbulence

“…(2015 b ) demonstrated that such a first Fourier mode slice can be used to reduce the translation symmetry of the flow for all dynamics of interest. Later, the method was adapted successfully to two-dimensional Kolmogorov flows (Farazmand 2016; Hiruta & Toh 2017) and three-dimensional pipe flows (Willis, Short & Cvitanović 2016; Budanur et al. 2017; Budanur & Hof 2018); see Budanur, Borrero-Echeverry & Cvitanović (2015 a ) for a pedagogical introduction.…”