Velocity and Energy Profiles In Two- vs. Three-Dimensional Channels: Effects of Inverse vs. Direct Energy Cascade
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In light of some recent experiments on quasi two-dimensional (2D) turbulent channel flow we provide here a model of the ideal case, for the sake of comparison. The ideal 2D channel flow differs from its 3D counterpart by having a second quadratic conserved variable in addition to the energy, and the latter has an inverse rather than a direct cascade. The resulting qualitative differences in profiles of velocity, V, and energy, K, as a function of the distance from the wall are highlighted and explained. The most glaring difference is that the 2D channel is much more energetic, with K in wall units increasing logarithmically with the Reynolds number $\Ret$ instead of being $\Ret$-independent in 3D channels.
Theoretical; 4 pages, 3 figures (8 plots); Submitted to Physical Review Letters on 16 February 2009
Theoretical; 4 pages, 3 figures (8 plots); Submitted to Physical Review Letters on 16 February 2009