Production and flow of turbulence kinetic energy in convective boundary layers

According to the usual interpretation, the `shear production' term in the RANS equation for turbulence kinetic energy represents a local transfer of kinetic energy from the mean flow to the turbulence in any turbulent shear flow where momentum is transferred. No explanation has been offered for the dynamics of the eddy processes causing this interaction. Recently Laubach and McNaughton (2009) developed a model of eddy processes in convective boundary layers (CBLs); they found no process that corresponds to local shear production. Their model emphasizes the external origins of the energy found in the CBL and its flow through the system. In support of this interpretation, a simple derivation using the RANS formalism shows that `shear production' is, in fact, a part of the divergence in the flux of kinetic energy. Here we trace `shear production' back to its origins in Osborne Reynolds' paper of 1895. It is found that his description is based on a false analogy with the transfer of eddy energy to heat energy at the smallest scales, and with Reynolds' own misunderstanding of the cause of the transition to turbulence in pipes, as characterized by his [Reynolds] number. More modern works, which have simply adopted Reynolds' own interpretation, are similarly mistaken.