Synchronization of wall turbulence

The reconstruction of turbulence from limited observations does not guarantee that the estimated state is synchronized with the true trajectory (M. Wang and T. Zaki, 2021, J. Fluid Mech. 917, A9). Furthermore, the design of the observations that ensure synchronization has not been systematically examined in wall-bounded flows. We first investigate the synchronization of a horizontal layer of turbulence in channel flow, when the observations are the fully resolved fields outside that layer. Synchronization of the emergent turbulence to the true flow trajectory is only possible when that horizontal layer smaller than a critical thickness on the order of the Taylor microscale. We proceed to analyze synchronization of different configurations, including multiple missing volumes within the channel and the case where the observations are limited to surface values.