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X X Y Y Y ZX rX Z bZ XY Introduction of the Topic Derivation Explanation Project Outline The First Steps Current Status Next Steps

  4.        X X Y      Y Y ZX rX     Z bZ XY

  6.  Introduction of the Topic  Derivation  Explanation  Project Outline  The First Steps  Current Status  Next Steps  Plan B

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  11.  Start with Navier-Stokes Equations                1 u u w w            2       u w u w               Pr t z x z x x z x              u w Ra w    t x z  Ansatz for Disturbance…                   x z t , , t sin mqx cos 2 n 1 z mn   m 1 n 0  …and Temperature field                               a b x z t , , t cos mqx cos 2 n 1 z t cos mqx sin 2 nz mn mn     m 1 n 0 m 0 n 1

  12.  Apply Galerkin Method                   x z t , , t sin mqx cos 2 n 1 z mn   m 1 n 0  Make Transformations  Result: System of ODEs for amplitudes     X f X i i

  13.  Prandtl number viscous effects    Pr thermal effects  Rayleigh Number buoyancy effects   Ra r thermal effects

  14.  Extend number of modes  Analyze emerging Dynamical System  Extract Poincare Return Map  Analyze PRM with means of Information Theory

  18.  Research scan  Calculating the equations: Transition from Maple to Matlab (Maple)  Simulating the resulting Flow and Temperature field  Go on: Analysis …

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