An analytical study of diurnal wind-structure variations in the boundary layer and the low-level nocturnal jet

Abstract

An analytical framework is proposed for studying variations in the diurnal wind structure in the planetary boundary layer (PBL) and the evolution of the low-level nocturnal jet. A time-dependent eddy-diffusivity coefficient corresponding to solar input is proposed, and an appropriate coordinate transformation ensures that mixing height varies continuously with ground heat-flux changes. The solution exhibits the receding character of the daytime PBL as evening approaches, thereby dividing the PBL into two regimes — the one just above the ground, representing the nocturnal boundary layer, and the region above it. It is assumed that inertial oscillations (IO) are triggered in the upper layer at about the time of sunset when the reversal in the direction of ground heat flux is felt in the upper layer. Two approaches are adopted to determine the characteristic features of IO and the evolution of the nocturnal low-level jet. The first one is based on the physical principle that release of horizontal momentum due to deviation from the geostrophic wind gives rise to the IO. The solution captures all the characteristic features of the IO, such as phase shift and decreasing amplitude of the IO with increasing height. According to this analysis the IO is triggered at a level as soon as the top of the receding boundary layer leaves that level. The solution is discontinuous with respect to the vertical coordinate. In the second approach we solve an initial-value problem to determine the solution in the upper layer, assuming that at about the time of sunset there is a rapid collapse of the daytime PBL to the steady, nocturnal boundary layer. The assumption is based on the mixing-height profiles prepared from climatological data collected at Delhi. The solution for the nocturnal boundary-layer regime is then obtained as a boundary-value problem. The solutions so obtained are continuous throughout the domain of interest and exhibit the characteristic features of an IO. The analysis leads to the conditions under which a low-level nocturnal jet is produced and provides quantitative estimates of the parameters, such as length of night, latitude, mixing height at sunset and nocturnal mixing height, that are conducive to the generation of a jet. The nocturnal wind profile produced by this approach compares well both with typical atmospheric data observed at Delhi and with output from a mesoscale numerical model. There is still some uncertainty related to the time of initiation of the IO as a function of latitude.