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... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A new mean-field theory of turbulence that treats the effective viscosity as a dynamical degree of freedom is presented on the basis of the stationary action principle, and is shown to reproduce some experiments for the mean flow profile of turbulence in the laboratory. Comparison with eddy viscosity models is also made. Then, with the help of the viscosity expansion method, the theory is applied to a rotating thin fluid disk for the purpose of evaluating the viscosity effect in the dynamics of a spiral galaxy or protoplanetary nebula. We find two types of physically interesting solution. In the first type, the rotation curve at long distances from the disk center is flat as a natural feature of the rotating viscous fluid with neither strong radial motion nor radial pressure gradient. The flow is gravitationally maintained only when a sufficient amount of matter other than viscous fluid is present. In the second type, the rotation is Keplerian with a centrally localized mass distribution. In both types of solution, the effective viscosity tends to act to stabilize perturbation in the region of shorter distances. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subject Index E27, J14, J15, J18

Mean-field theory of turbulence from the variational principle and its application to the rotation of a thin fluid disk