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This work investigates steady-state thermal blooming of a high-energy laser in the presence of laser-driven convection. While thermal blooming has historically been simulated with prescribed fluid velocities, the model introduced here solves for the fluid dynamics along the propagation path using a Boussinesq approximation to the incompressible Navier–Stokes equations. The resultant temperature fluctuations were coupled to refractive index fluctuations, and the beam propagation was modeled using the paraxial wave equation. Fixed-point methods were used to solve the fluid equations as well as to couple the beam propagation to the steady-state flow. The simulated results are discussed relative to recent experimental thermal blooming results [Opt. Laser Technol. 146, 107568 (2022) OLTCAS0030-399210.1016/j.optlastec.2021.107568], with half-moon irradiance patterns matching for a laser wavelength at moderate absorption. Higher energy lasers were simulated within an atmospheric transmission window, with the laser irradiance exhibiting crescent profiles.

This research investigates laser-induced convection through a stream function-vorticity formulation. Specifically, this paper considers a solution to the steady Boussinesq Navier–Stokes equations in two dimensions with a slip boundary condition on a finite box. A fixed-point algorithm is introduced in stream function-vorticity variables, followed by a proof of the existence of steady solutions for small laser amplitudes. From this analysis, an asymptotic relationship is demonstrated between the nondimensional fluid parameters and least upper bounds for laser amplitudes that guarantee existence, which accords with numerical results implementing the algorithm in a finite difference scheme. The findings indicate that the upper bound for laser amplitude scales by O(Re−2Pe−1Ri−1) when Re≫Pe, and by O(Re−1Pe−2Ri−1) when Pe≫Re. These results suggest that the existence of steady solutions is heavily dependent on the size of the Reynolds (Re) and Peclet (Pe) numbers, as noted in previous studies. The simulations of steady solutions indicate the presence of symmetric vortex rings, which agrees with experimental results described in the literature. From these results, relevant implications to thermal blooming in laser propagation simulations are discussed.