Thermal blooming of laser beams propagating through the atmosphere has generally been treated for cases of small wind speed transverse to the beam. The present calculation examines the associated density changes for air moving through a beam at near sonic speeds. The problem is treated for the one-dimensional case only; an exact solution to the nonlinear hydrodynamic equations for the steady state is derived. The solution shows that, at near sonic speeds, the density changes grow drastically with Mach value, while agreeing with the previous results at low wind speeds. In the vicinity of Mach I, the solution becomes invalid, probably due to the nonexistence of a steady state. The effect of the density changes on the beam are not calculated here.

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