From limited observations to the state of turbulence: Fundamental difficulties of flow reconstruction

Is it possible to reconstruct all the scales of turbulence from limited observations? If so, what is the minimum resolution of observations for a successful reconstruction? How much information about a turbulent flow field can be decoded from an isolated, instantaneous measurement? These fundamental questions are addressed using variational data assimilation, where the observations are infused in simulations and are decoded using the Navier-Stokes equations. We highlight the ``dual butterfly effect'' and how the stochasticity of turbulence obfuscates the interpretation of measurements.