Kinetic theory of fluctuations near a convective instability

The kinetic theory of density and velocity fluctuations below and above the first convective instability in a Benard cell is presented. Results are given in a form valid for all fluid densities. In particular, the singular behavior near the instability point is computed and a detailed comparison with that near a critical point is made. Mode coupling effects, involving the viscous and the heat mode, that determine the singular behavior of the thermal conductivity near the critical point, are also responsible for the singular behavior of the pair correlation function and in particular the density-density correlation function near the instability point. The anomalous density fluctuations could be measured directly by microwave scattering experiments, while the velocity fluctuation could be measured by laser Doppler velocimetry.