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Assimilating the atmosphere with multifractal entities, nonlinear behaviors in the framework of scale relativity theory regarding its hydrodynamic functionality are established at various scale resolutions. From this perspective, revealing a “hidden” symmetry of the specific multifractal force with the SL(2,R) group leads to synchronization of atmospheric entities on the basis of operational procedures (differential and integral Riemann-type geometries, harmonic mappings from Euclidian to hyperbolic space, variational principles, and others) that imply cellular self-structuring, laminar channels and singularities as turbulence generators. These behaviors can then be assimilated and compared with recent discoveries regarding laminar channels found in atmospheric turbulence through lidar data processing.