Thermally driven convections such as Boussinesq equations, are an active area of research, at present, with various applications from geophysics, ocean circulation clued dynamics, inner core of the planets to astrophysics. These equations are one of the most commonly used fluid models in the atmospheric sciences to model Jet streams as a narrow fast flowing air currents, cold front (as a transition zone replacing cold and warm air), thermohaline circulation and the El Nino Southern Oscillationas.

Papers:

G. R. Kirchhoff. Vorlesungen, uber Mathematische Physik, Mechanik. Teubner, Leipzig, 1876.

J. Boussinesq, Theorie Analitique de la Chaleur, vol. 2, Gauthieraux Villars, Paris, 1903.

Ting. Lu, and Chee. Tung, Motion and decay of a vortex in a nonuniform stream, The Physics of Fluids, 8 (1965), 1039-1051.

Thierry. Gallay and C. Eugene. Wayne, Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations, Arch. Ration. Mech. Anal., 163 (2002), 209–258.