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<p>According to the linearized solutions for thermal blooming, the density perturbations become infinite (i.e. \"catastrophic\" defocusing) as the Mach number approaches unity. However, the nonlinearities in the transonic equations cutoff the trend to infinity, and the values of the flow perturbation quantities are finite. The nonlinear equations with heat addition are transformed into simple linear algebraic equations through the specification of the streamline geometry in the heat release region. At a Mach number of unity, streamtube area variation was found to be directly proportional to the change in total temperature. A steady, two-dimensional mixed flow solution has been found for the transonic thermal blooming problem. The solution for the density perturbations within a laser beam at a Mach number of precisely unity is given. For a Gaussian beam with an intensity of 3.333xl0^7 watts/m^2 and an atmospheric absorption of 8.0xlO^-7 cm^-l the maximum fractional density perturbation is 1.028xlO^-6. The transonic thermal blooming problem does not pose as serious a problem as previously anticipated.
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<br>Subjects: Transonic thermal blooming; Subsonic thermal blooming; Supersonic thermal blooming; Atmospheric propagation of laser beam; Sonic flow with heat addition; High energy laser</div>
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Carey, Edwin Fenton, Jr.</div>
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