A Numerical Study of the Stratified Planetary Boundary Layer: the long-time response to a stabilizing surface buoyancy flux

Numerical simulations of a stable boundary layer are performed to study the flow evolution at long time in response to different values of a stabilizing buoyancy flux. DNS is used to simulate cases with moderate Reynolds number (Re* = 1120) and LES is ongoing to access the high-Re regime. The boundary condition of imposed buoyancy flux is different from the constant boundary temperature employed in the recent DNS of [1]. Our DNS results show that, after an initial transient of cyclic collapse and rebirth of turbulence, a regime of continuous but globally intermittent turbulence with interspersed laminar and turbulent patches is eventually reached. Flow visualization shows that the organization of fluctuations fields on horizontal planes does not change qualitatively at this state, however flow statistics are not quantitatively at steady state even after 5 inertial periods. In all simulated cases, a Low Level Jet (LLJ) emerges in the streamwise mean velocity (Figure 1a) and, as the stability increases, the LLJ velocity strengthens and the height of the maximum in the velocity profile decreases. The turbulent kinetic energy (TKE) profile (Figure 1b) shows a two-layer structure in the vertical with minimum intensity of TKE at the LLJ nose height and two local maxima, one below and the other above the LLJ nose level, the former located at a height of about one-fifth the LLJ nose height, and the latter located at approximately three times the height of nose. Atmospheric observations of a LLJ over the Baltic Sea showed similar findings regarding these maxima locations and TKE values [6]. The temperature evolves with time and its eventual structure (Figure 1c) is of interest. In all simulated cases, a new boundary layer is formed with a thermal inversion that is capped by a thermocline. Interestingly, although the case with highest surface buoyancy rate eventually exhibits a large stable temperature gradient concentrated near the surface, a turbulent layer with relatively low stratification develops during the evolution and a thermocline forms to cap the turbulent layer. The root-mean-square of temperature fluctuations peaks at the thermocline in agreement with previous work, e.g. numerical studies [2,4] and an observational study [6] (Figure 1d). The transport equations of TKE and temperature variance are evaluated to understand the turbulence profiles obtained in these simulations. In ongoing work, we are analyzing the DNS results to compare previous stratified boundary layer theory [3,5,7] to the long-time behavior found here. We are also performing LES to access the regime of higher Reynolds number. Results from the ongoing work will also be presented. Figure 1: Profiles of normalized statistics at long time against normalized height: (a) Velocities; (b) Turbulent kinetic energy; (c) Potential temperature; (d) Variance of temperature fluctuations. Here all the stratified cases with high (solid red line), moderate (dot dash blue line), weak (dash magenta line) stratification rate are plotted. The unstratified case is also shown in solid black. References: [1] Ansorge C, Mellado J (2014) Global intermittency and collapsing turbulence in the stratified planetary boundary layer. Boundary-Layer Meteorology 153(1):89–116 [2] Cuxart J, Jimenez MA (2007) Mixing processes in a nocturnal low-level jet: an LES study. Journal of Atmospheric Science 64:1666–1679 [3] Derbyshire SH (1990) Nieuwstadt's stable boundary layer revisited. Quarterly Journal of the Royal Meteorological Society 116:127–158 [4] Deusebio E, Brethouwer G, Schlatter P, Lindborg E (2014) A numerical study of the unstratified and stratified Ekman layer. Journal of Fluid Mechanics 755:672–704 [5] Nieuwstadt (1984) The turbulent structure of stable, nocturnal boundary layer. Journal of Atmospheric Science 41:2202–2216 [6] Smedman AS, Tjernstrom M, Hogstrom U (1993) Analysis of the turbulence structure of a marine low-level jet. Boundary-Layer Meteorology 66(1-2):105–126 [7] de Wiel BJHV, Moene GJAF, Steeneveld P, Baas FC, A BA, Holtslag M (2012) The cessation of continuous turbulence as precursor of the very stable nocturnal boundary layer. Journal of Atmospheric Science 69:3097–3115