Analytical model for the growth of the coastal internal boundary layer during onshore flow

Abstract

A model of near-neutral and convective steady-state internal boundary layer evolution is presented. the model deals with the internal boundary layer that forms over land in coastal and lake areas during onshore winds. Near the ground, the growth of the internal boundary layer is controlled by friction velocity in accordance with surface layer theory. Farther downwind, the growth is determined by the atmospheric stability and friction velocity within the internal boundary layer, and the temperature gradient in the air above. the wind profile inside the internal boundary layer is assumed to follow Obukhov similarity theory. an expression for the strength of the inversion that caps the layer is derived and used in the model. A comparison is carried out with independent experimental observations of internal boundary layer growth in the sea-land transition. Kinematic heat flux through the top of the internal boundary layer is described by the formulation − \documentclass{article}\pagestyle{empty}\begin{document}$ \overline {(w'\theta')} $\end{document}h = 0.2\documentclass{article}\pagestyle{empty}\begin{document}$ \overline {(w'\theta')} $\end{document}s + 2.5 uT/gh + the Zilitinkevich correction. the terms 0.2\documentclass{article}\pagestyle{empty}\begin{document}$ \overline {(w'\theta')} $\end{document}s and 2.5u T/gh account for convective and mechanical turbulence, respectively, and the Zilitinkevich correction is a turbulent kinetic-energy storage term that ensures finite growth rate of the internal boundary layer near the ground. the relative importance of mechanical and convective turbulence as well as the Zilitinkevich correction is discussed. the Zilitinkevich correction dominates the growth process of the internal boundary layer when it is lower than roughly 50m. As the layer grows, the importance of the Zilitinkevich correction diminishes. Then mechanical turbulence dominates the growth process until the internal boundary layer has reached a height of approximately −1.4L. Further growth is controlled mainly by convective turbulence. Conditions of high wind speed and large values of the potential temperature gradient over water result in a deep zone where the growth of the internal boundary layer is controlled by mechanical turbulence. With near-zero potential temperature gradient over water, the zone becomes shallow and may vanish.