Synchronization of turbulence in channel flow

TL;DR

This paper demonstrates that turbulence in channel flow can be accurately reconstructed through continuous data assimilation, with synchronization depending on the size and orientation of missing regions, even with limited velocity data.

Contribution

It introduces conditions for turbulence synchronization in channel flow using partial velocity data, advancing understanding of flow reconstruction via data assimilation.

Findings

Horizontal layers synchronize if less than 30 wall units thick.

Vertical layers synchronize when spanwise width is near the near-wall Taylor microscale.

Synchronization is achievable with planar velocity data under certain conditions.

Abstract

Synchronization of turbulence in channel flow is investigated using continuous data assimilation. The flow is unknown within a region of the channel. Beyond this region the velocity field is provided, and is directly prescribed in the simulation, while the pressure is unknown throughout the entire domain. Synchronization takes place when the simulation recovers the full true state of the flow, or in other words when the missing region is accurately re-established, spontaneously. Successful synchronization depends on the orientation, location and size of the missing layer. For friction Reynolds numbers up to one thousand, wall-attached horizontal layers can synchronize as long as their thickness is less than approximately thirty wall units. When the horizontal layer is detached from the wall, the critical thickness increases with height and is proportional to the local wall-normal Taylor microscale. A flow-parallel, vertical layer that spans the height of the channel synchronizes when its spanwise width is on the order of the near-wall Taylor microscale, while the criterion for a crossflow vertical layer is set by the advection distance within a Lyapunov timescale. Finally, we demonstrate that synchronization is possible when only planar velocity data are available, rather than the full outer state, as long as the unknown region satisfies the condition for synchronization in one direction. These numerical experiments demonstrate the capacity of accurately reconstructing, or synchronizing, the missing scales of turbulence from observations, using continuous data assimilation.