Scaling the Decay of Turbulence Kinetic Energy in the Free-Convective Boundary Layer

We investigate the scaling for decaying turbulence kinetic energy (TKE) in the free-convective boundary layer, from the time the surface heat flux starts decaying, until a few hours after it has vanished. We conduct a set of large-eddy simulation experiments, consider various initial convective situations, and prescribe realistic decays of the surface heat flux over a wide range of time scales. We find that the TKE time evolution is dictated by the decaying magnitude of the surface heat flux up to \(0.7 \tau \) approximately, where \(\tau \) is the prescribed duration from maximum to zero surface heat flux. During the time period starting at zero surface heat flux, we search for potential power-law scaling by examining the log–log presentation of TKE as a function of time. First, we find that the description of the decay highly depends on whether the time origin is defined as the time when the surface heat flux starts decaying (traditional scaling framework), or the time when it vanishes (proposed new scaling framework). Second, when varying \(\tau \), the results plotted in the traditional scaling framework indicate variations in the power-law decay rates over several orders of magnitude. In the new scaling framework, however, we find a unique decay exponent in the order of 1, independent of the initial convective condition, and independent of \(\tau \), giving support for the proposed scaling framework.