X X Y Y Y ZX rX - - PowerPoint PPT Presentation

 

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  Plan B

hot cold

 Start with Navier-Stokes Equations  Ansatz for Disturbance…  …and Temperature field

2

1 Pr u u w w u w u w t z x z x x z x                                              

u w Ra w t x z                

       

 

1

, , sin cos 2 1

mn m n

x z t t mqx n z   

   

 



       

 

     

1 1

, , cos cos 2 1 cos sin 2

a b mn mn m n m n

x z t t mqx n z t mqx nz     

       

  

 

 Apply Galerkin Method  Make Transformations  Result: System of ODEs for amplitudes

       

 

1

, , sin cos 2 1

mn m n

x z t t mqx n z   

   

 



 

i i

X f X  

 Prandtl number  Rayleigh Number

viscous effects Pr thermal effects    buoyancy effects Ra thermal effects r  

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

Theory

 Research scan  Calculating the equations: Transition from

Maple to Matlab (Maple)

 Simulating the resulting Flow and

Temperature field

 Go on: Analysis …