2D thermal convection (Benard-Rayleigh problem)

• The left figure is temperature distribution of boussinesq fluid heated from lower boundary (Benard-Rayleigh problem).
• On the lower and upper boundary, temperature is fixed and tangential stress is equal to zero (free-slip boundary condition).
• The horizontal boundary condition is cyclic.
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• Source code

• The same as upper figure but with large horizontal domain.
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• The left figure is temperature distribution of boussinesq fluid heated from lower boundary with constant heat flux.
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• The aspect ratio of convection cell becomes large as time goes on.
• Source code

References

• Chandrasekhar, S., 1961 : Hydrodynamic and Hdromagnetic stability. Oxford University Press.
• Ishiwatari, M., Takehiro, S., Hayashi, Y.-Y., 1994 : The effects of thermal conditions on the cell sizes of two-dimensional convection. J. Fluid Mech., 281, 33--50.