Prog. Theor. Phys. Vol. 90 No. 6 (1993) pp. 1229-1240
Theory of Eddy Viscosity Coefficient for Two-Dimensional Inviscid Barotropic Fluid
Department of Physics, Kyushu University, Fukuoka 812
(Received August 25, 1993)
According to Mori's theory, the spectral form of the vorticity equation for two-dimensional inviscid barotropic fluid is reduced to the generalized Langevin equation for the vorticity. The damping term in the Langevin equation is interpreted as the eddy viscosity damping term. A formula for the eddy viscosity coefficient is derived by using the fluctuation-dissipation theorem. The eddy viscosity coefficient thus obtained depends on the length scale of a phenomenon of interest. Under Cheju Island scale, the theory derives that the eddy viscosity coefficient is about eight orders of magnitude larger than that of the molecular viscosity coefficient of the air. This value is of the same order as the eddy viscosity coefficient obtained by applying the Reynolds' law of similarity to atmospheric Kármán vortices generated on the leeward of Cheju Island. It is theoretically derived that the reason for the enormousness of the atmospheric eddy viscosity coefficient comes from that of the length scale of interest.
DOI : 10.1143/PTP.90.1229
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Citing Article(s) :
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