Hartke et al. 1988

Hartke, G.J., V.M. Canuto, and W.P. Dannevik, 1988: A direct interaction approximation treatment of high Rayleigh number convective turbulence and comparison with experiment. Phys. Fluids, 31, 256-262, doi:10.1063/1.866856.

Recently published experimental results [Int. J. Heat Mass Transfer, 23, 738 (1980)] on thermally driven high Rayleigh number turbulent convection have shown that the N proportional to R^(2/7) relation (where N is the Nusselt number and R is the Rayleigh number), which is valid up to R ≈ 5×10⁸, is superceded at this point by the relation N = A_σ*R^(1/3) that holds at least up to R ≈ 10¹¹. For water (Prandtl number σ = 6.6), the experimental value for A_σ was found to be A_σ = 0.0556±0.001. In the present work, the equations for a turbulent fluid driven by thermal convection are solved using the two-point closure prescription of the direct interaction approximation. The theoretical N vs R relation at high R is found to be of the form N = A_σ*R^(1/3) and for σ = 6.6, and the predicted value of the coefficient A_σ is computed to be A_σ ≲ 0.08, in good agreement with the experimental value. Extension of the model to situations other than convection is discussed.

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Hartke, G.J., Canuto, V.M., and Dannevik, W.P.: A direct interaction approximation treatment of high Rayleigh number convective turbulence and comparison with experiment, Phys. Fluids, 31, 256-262, doi:10.1063/1.866856, 1988.

Hartke, G.J., V.M. Canuto, and W.P. Dannevik (1988), A direct interaction approximation treatment of high Rayleigh number convective turbulence and comparison with experiment, Phys. Fluids, 31, 256-262, doi:10.1063/1.866856.

Hartke, G.J., V.M. Canuto, and W.P. Dannevik, 1988: A direct interaction approximation treatment of high Rayleigh number convective turbulence and comparison with experiment. Phys. Fluids, 31, 256-262, doi:10.1063/1.866856.

Hartke, G.J., Canuto, V.M., & Dannevik, W.P. 1988, Phys. Fluids, 31, 256, doi:10.1063/1.866856.

Hartke GJ, Canuto VM, Dannevik WP. A direct interaction approximation treatment of high Rayleigh number convective turbulence and comparison with experiment, Phys Fluids 1988;31:256-262. doi:10.1063/1.866856.

G.J. Hartke, V.M. Canuto, W.P. Dannevik, Phys. Fluids 31, 256-262, doi:10.1063/1.866856 (1988).