Distortion of a narrow radio beam in a convective medium

In considering the basic mechanism of heat exchange by convective circulation in the atmosphere it is apparent that the resultant thermal cell structures, as proposed by Benard, may possess refractive index properties which will influence the cross-sectional shape of a narrow conical radio beam. A simplified classical toroidal cell is considered for the purpose of analysis to show that the core of such a cell in the atmosphere may act as a cylindrical concave lens. The resultant distortion of a narrow beam is then discussed. The concept if then developed further to show that trans-horizon propagation may result from an in-line array of thermal cells.