Velocity and energy profiles in two- versus three-dimensional channels: Effects of an inverse- versus a direct-energy cascade.
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 three-dimensional (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 Re_{tau} instead of being Re_{tau} independent in 3D channels.
L'vov
Victor S
VS
Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.
Procaccia
Itamar
I
Rudenko
Oleksii
O