The Flow of Mechanical Energy in Convective Boundary Layers

There are two frameworks within which we can discuss turbulence energy in convective boundary layers. The first is the one provided by the Reynolds-averaged Navier–Stokes (RANS) energy equations, as interpreted by Osborne Reynolds in the late nineteenth century. The other, much newer framework is that provided by complex dynamical systems. The former gives prominence to the interpretation of local budgets of turbulence kinetic energy while the latter emphasizes the energy flows necessary to maintain turbulence in a statistically-steady state. It is argued that these frameworks constitute two incompatible paradigms, since the first localizes physical interpretation of the RANS kinetic energy budget while the second denies such a simple view. The local interpretation traces back to the way Reynolds himself interpreted his RANS energy equations, which interpretation is examined here and found to be faulty. We present a schematic model for energy flow in convective boundary layers from a complex dynamical systems’ perspective, and use it to re-interpret the RANS energy equation.