Fig. 1. (a) Representative phase screen with structure constant Cn2=10−13  cm−2/3 and distance Δz=1  m; (b) structure function of phase fluctuations. Black line refers to simulation result and red line corresponds to theoretical prediction.

Fig. 2. Three cases of the simulation: (a) turbulence is introduced prior to filament formation; (b) turbulence is introduced after filament formation; (c) axicon is used as focusing optics.

Fig. 3. Spatial displacements of a single filament center in turbulent air obtained with 30 statistically independent chains of random phase screens but the same turbulent structure constant Cn2=6.4×10−13  cm−2/3 for three different conditions: (a) turbulence is introduced prior to filament formation; (b) turbulence is introduced after filament formation; (c) axicon is used as focusing optics.

Fig. 4. (a) Averaged transverse displacement of a single filament as a function of the square root of the turbulent structure constant; (b) averaged transverse displacement of a single filament versus filament length in turbulent air (Cn2=6.4×10−13  cm−2/3, solid circles) and the fitting (solid line).