THE STRUCTURE OF NONLINEAR CELLULAR SOLUTIONS TO THE BOUSSINESQ EQUATIONS.

A model equation is constructed whose analysis reveals the same features, including stable hexagonal cells, as analysis of genuine approxi mate equations for the thermal convection prob lem. Taking advantage of the relative simplicity of the calculations an attempt is made to clarify certain procedures customarily used in nonlinear stability theory in particular, the basis for the usuaal expansions and the appropriate ness of neglecting terms of fourth and higher order are discussed. It is demonstrated that a whole class of equations lead to hexagonal cells, thereby giving confidence that results on con vection cells found elsewhere in idealized situa tions will remain valid when more realistic situations are studied. Author