au'aw' ax az -+-=oThe natural boundary conditions at z z 1 areThe Fourier decomposition proceeds as before, except that K , = 0 and K , = K . Equations (2.6) and (2.7) becomeEquations (2.8b) and (2.9) become 2 1whereas (2.8a) remains the same. Instead of (2.10), Equations (A8b) and (A8c) become
.-The solution technique for p is the same as before, only the boundary conditions to use are (A13), (A12), (2.11) and (A8a), and a slightly modified (2.4b) : JW' 32 -( 0 ) = ~' ( 0 ) = cp(0) x w ' ( 1 ) = 0 (A14) One point on the stability boundary, Ra = 150, Re = 35, was calculated using this technique. It was assumed that K and ?L retain the same values as when w = 1. Although this was not verified the independence of ?.opt and KOpt was well established. The new stability point is at MU = 31.1 (at w = 2 compared to Ma = 22.2 (at w = 1). While the stability boundary is raised significantly, note that it still falls below that for transverse disturbances.this area fall into two groups. In the first, enhancement