The analytical propagation equation of a four-petal Lorentz-Gauss (FPLG) beam propagating through atmospheric turbulence is derived, and the spreading of average intensity is analyzed by using numerical examples. It is found that the FPLG beam propagating through atmospheric turbulence will evolve into Gaussian beam due to the influences of atmospheric turbulence, and the atmospheric turbulence will accelerate the spreading of FPLG beam as the propagation distance increases. It is also found that the FPLG beam with different N or Lorentz widths propagating through atmospheric turbulence will have the same beam spot when the FPLG beam evolves into the Gaussian beam at the same propagation distance.
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