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In light of some recent experiments on quasi two-dimensional (2D) turbulentchannel flow we provide here a model of the ideal case, for the sake ofcomparison. The ideal 2D channel flow differs from its 3D counterpart by havinga second quadratic conserved variable in addition to the energy, and the latterhas an inverse rather than a direct cascade. The resulting qualitativedifferences in profiles of velocity, V, and energy, K, as a function of thedistance from the wall are highlighted and explained. The most glaringdifference is that the 2D channel is much more energetic, with K in wall unitsincreasing logarithmically with the Reynolds number $\Ret$ instead of being$\Ret$-independent in 3D channels.

Velocity and Energy Profiles In Two- vs. Three-Dimensional Channels: Effects of Inverse vs. Direct Energy Cascade