Hayes J N
Appl Opt. 1974 Sep 1;13(9):2072-4. doi: 10.1364/AO.13.002072.
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.
通常在处理激光束在大气中传播时的热晕效应时，考虑的是风速垂直于光束方向且较小的情况。目前的计算研究了空气以接近声速穿过光束时相关的密度变化。该问题仅针对一维情况进行处理；推导了稳态非线性流体动力学方程的精确解。结果表明，在接近声速时，密度变化随马赫数急剧增大，同时与低风速下的先前结果相符。在马赫数1附近，该解变得无效，可能是由于不存在稳态。此处未计算密度变化对光束的影响。
