Two dimensional driven nonlinear Rossby wave turbulence with drag

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Two dimensional driven nonlinear Rossby wave
turbulence with drag

• Tomo Iida
• Advised by E.Ott and P.Guzdar

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What is Rossby Wave

• Observed by Carl-Gustav Rossby(1930)
• Stable wave on a layer of fluid, deriving from
  difference of Coriolis force along the latitude.
  (jet stream, ocean current etc.)
• Wave length 500Km with low frequency

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Purpose of this project

• Without Coriollis force

(E.Ott et al)
Log E
E(k)k(-3-const)
Coriolis force
?
0
Log k (wave number)
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Model
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Algorithm

• Change of Method
• 1. Parallel FFT library (MPI FFTW) is reasonably
  fast. (thanks to seaborg)
• 2. Finite difference with Relaxation method is
  less stable in large system.

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Algorithm Deriving Velocity Field.

• Deriving velocity field from Poisson Equation

Real Space
Fourier Space
Finite Difference
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Velocity Field
Red high vorticity Blue low vorticity
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Algorithm Diffusion and Drag Term
latter half (diffusion and drag term) is solved
in Fourier space separately.
Real Space
Fourier Space
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Algorithm
predictor
corrector
diffusion and drag
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Parallelizing

• Use MPI and MPI FFTW libraries.
• Each processor communicate at Finite Difference
  and FFT.
• System is divided into N pieces in Row major
  order.

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Parallelizing
FFT
Poisson
Poisson
FFT
FFT
Reverse FFT
Reverse FFT
Reverse FFT
Predictor
Predictor
Finite difference
Finite difference
Finite difference
Poisson
Poisson
FFT
FFT
FFT
Reverse FFT
Reverse FFT
Reverse FFT
Corrector
Corrector
Finite difference
Finite difference
Finite difference
FFT
FFT
FFT
Diff Drag
Diff Drag
Reverse FFT
Reverse FFT
Reverse FFT
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Some pictures
Static Vorticity Source
Vorticity (red high, blue Low)
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Vorticity with static source
Red high vorticity Blue low vorticity
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So far, Now on

• Done
• Main Program (almost)
• MPI implementation
• Visualize Program
• Todo
• Debug.
• Activate Coriolis force
• Learn how to run the parallel code on Seaborg.
• Post processing