  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.
