An official website of the United States government
Abstract A persistent spatial organization of eddies is identified in the lowest portion of the stably stratified planetary boundary layer. The analysis uses flow realizations from published large-eddy simulations (Sullivan et al. in J Atmos Sci 73(4):1815–1840, 2016) ranging in stability from near-neutral to almost z-less stratification. The coherent turbulent structure is well approximated as a series of uniform momentum zones (UMZs) and uniform temperature zones (UTZs) separated by thin layers of intense gradients that are significantly greater than the mean. This pattern yields stairstep-like instantaneous flow profiles whose shape is distinct from the mean profiles that emerge from long-term averaging. However, the scaling of the stairstep organization is closely related to the resulting mean profiles. The differences in velocity and temperature across the thin gradient layers remain proportional to the surface momentum and heat flux conditions regardless of stratification. The vertical thickness of UMZs and UTZs is proportional to height above the surface for near-neutral and weak stratification, but becomes thinner and less dependent on height as the stability increases. Deviations from the logarithmic mean profiles for velocity and temperature observed under neutral conditions are therefore predominately due to the reduction in eddy size with increasing stratification, which is empirically captured by existing Monin–Obukhov similarity relations for momentum and heat. The zone properties are additionally used to explain trends in the turbulent Prandtl number, thus providing a connection between the eddy organization, mean profiles, and turbulent diffusivity in stably stratified conditions.
more »
« less
Understanding Physical Processes Represented by the Monin–Obukhov Bulk Formula for Momentum Transfer
Abstract Physical processes represented by the Monin–Obukhov bulk formula for momentum are investigated with field observations. We discuss important differences between turbulent mixing by the most energetic non-local, large, coherent turbulence eddies and local turbulent mixing as traditionally represented by K-theory (analog to molecular diffusion), especially in consideration of developing surface-layer stratification. The study indicates that the neutral state in a horizontally homogeneous surface layer described in the Monin–Obukhov bulk formula represents a special neutrality regardless of wind speed, for example, the surface layer with no surface heating/cooling. Under this situation, the Monin–Obukhov bulk formula agrees well with observations for heights to at least 30 m. As the surface layer is stratified, stably or unstably, the neutral state is achieved by mechanically generated turbulent mixing through the most energetic non-local coherent eddies. The observed neutral relationship between $$u_*$$ u ∗ (the square root of the momentum flux magnitude) and wind speed V at any height is different from that described by the Monin–Obukhov formula except within several metres of the surface. The deviation of the Monin–Obukhov neutral $$u_*-V$$ u ∗ - V linear relation from the observed one increases with height and contributes to the deteriorating performance of the bulk formula with increasing height, which cannot be compensated by stability functions. Based on these analyses, estimation of drag coefficients is discussed as well.
more »
« less
- Award ID(s):
- 1701278
- PAR ID:
- 10290609
- Date Published:
- Journal Name:
- Boundary-Layer Meteorology
- Volume:
- 177
- Issue:
- 1
- ISSN:
- 0006-8314
- Page Range / eLocation ID:
- 69 to 95
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Harvesting of crops in a weakly sloping Midwestern field during the Stable Atmospheric Variability and Transport (SAVANT) observation campaign allowed for a systematic investigation of the influence of surface roughness and static stability magnitude on the applicability of the Monin–Obukhov similarity (MOST) and hockey-stick transition (HOST) theories during stable boundary layer periods. We analyze momentum flux and turbulent velocity scale V TKE in three regimes, defined using the gradient Richardson number Ri and flux Richardson number Ri f as regime 1 (0 < Ri ≤ 0.1 and 0 < Ri f ≤ 0.1), regime 2 (0.1 < Ri ≤ 0.23 and 0.1 < Ri f ≤ 0.23), and regime 3 (both Ri and Ri f > 0.23). After harvest, in regime 1, stability varied from near-neutral to weakly stable and both MOST and HOST were applicable to estimate the momentum fluxes and V TKE as a function of mean wind speed. In regime 2, the momentum flux deviated from the MOST linear relationship as stability increased. In regimes 1 and 2, a HOST-defined threshold wind speed V s was identified beyond which V TKE increased linearly with wind speed at a rate of 0.26 for all observation heights. Below this threshold wind speed, V TKE behaved independent of mean wind and observation heights. Alternatively, for preharvest periods, MOST was applicable in regimes 1 and 2 for all heights and HOST was applicable with reduced V s for heights above the crop layer. Regime 3 during pre- and postharvest consisted of strongly stable periods and very weak to weak winds, where MOST was found to be invalid and V TKE remained low and independent of wind speed. The results suggest that roughness due to crops enhances the turbulence generation at lower wind speeds.more » « less
-
We introduce an analytical model that describes the vertical structure of Ekman boundary layer flows coupled to the Monin-Obukhov Similarity Theory (MOST) surface layer repre- sentation, which is valid for conventionally neutral (CNBL) and stable (SBL) atmospheric conditions. The model is based on a self-similar profile of horizontal stress for both CNBL and SBL flows that merges the classic 3/2 power law profile with a MOST-consistent stress profile in the surface layer. The velocity profiles are then obtained from the Ekman momentum balance equation. The same stress model is used to derive a new self-consistent Geostrophic Drag Law (GDL). We determine the ABL height (h) using an equilibrium boundary layer height model and parameterize the surface heat flux for quasi-steady SBL flows as a function of a prescribed surface temperature cooling rate. The ABL height and GDL equations can then be solved together to obtain the friction velocity (u∗) and the cross-isobaric angle (α0) as a function of known input parameters such as the Geostrophic wind speed and surface roughness (z0). We show that the model predictions agree well with simulation data from the literature and newly generated Large Eddy Simulations (LES). These results indicate that the proposed model provides an efficient and relatively accurate self-consistent approach for predicting the mean wind velocity distribution in CNBL and SBL flows.more » « less
-
Abstract In this work, we seek to address the validity of Monin–Obukhov similarity theory (MOST) in the wave-affected surface boundary layer of the atmosphere. While bulk flux formulas which rely on MOST have been tested with and applied to measurements and models of air/sea interaction for several decades, the influences of surface wave–mediated fluxes on MOST have not been thoroughly quantified. We assess several months of direct covariance data from a stationary tower deployed with instruments inside the wave-affected surface layer. These measurements are analyzed in the context of the turbulent kinetic energy (TKE) equation and MOST, extending previous work due to the inclusion of directly estimated wave-coherent energy fluxes. Scaled TKE dissipation rates are reduced from what is predicted by MOST during events with large wave-coherent surface fluxes, resulting in a dissipation deficit in the energy budget (roughly 30%). However, we find that shear is much less impacted by these wave events showing much smaller deviations from baselines (less than 10%). During much of the experiment, the dissipation deficit is balanced by the wave-coherent pressure work, suggesting a general understanding of the combined turbulent and wave-driven energetics. However, several large storms in the fall of 2022 yielded much larger dissipation deficits than can be explained by the wave-coherent pressure work, highlighting that more work is needed to understand energetics in the wave-affected surface layer more generally. Significance StatementThe exchanges of heat, momentum, and gases between the air and the ocean are important for weather and climate prediction, ocean simulation, and wave models that are important for safe operations at sea. A current theory for these exchanges was designed for use over land but has been applied successfully over the ocean for several decades. One reason the overland theory [Monin–Obukhov similarity theory (MOST)] may not work as well is due to ocean waves, which change the nature of the surface in comparison with unmoving overland features like hills, mountains, and other topography. In particular, ocean waves grow with the wind, which means that they must draw down momentum and energy from the air above. In this paper, we work to understand why this theory for heat and momentum exchange at the surface (MOST) works well over ocean waves despite the unique physics when compared to wind over land. We find that the influence of waves is visible in some parts of the theory but that for the majority of conditions, the predictions from MOST should work well.more » « less
-
Sensitivity of large eddy simulations of tropical cyclone to sub-grid scale mixing parameterization.The surface wind structure and vertical turbulent transport processes in the eyewall of hurricane Isabel (2003) are investigated using six large-eddy simulations (LESs) with different horizontal grid spacing and three-dimensional (3D) sub-grid scale (SGS) turbulent mixing models and a convection permitting simulation that uses a coarser grid spacing and one-dimensional vertical turbulent mixing scheme. The mean radius-height distribution of storm tangential wind and radial flow, vertical velocity structure, and turbulent kinetic energy and momentum fluxes in the boundary layer generated by LESs are consistent with those derived from historical dropsonde composites, Doppler radar, and aircraft measurements. Unlike the convection permitting simulation that produces storm wind fields lacking small-scale disturbances, all LESs are able to produce sub-kilometer and kilometer scale eddy circulations in the eyewall. The inter-LES differences generally reduce with the decrease of model grid spacing. At 100-m horizontal grid spacing, the vertical momentum fluxes induced by the model-resolved eddies and the associated eddy exchange coefficients in the eyewall simulated by the LESs with different 3D SGS mixing schemes are fairly consistent. Although with uncertainties, the decomposition in terms of eddy scales suggests that sub-kilometer eddies are mainly responsible for the vertical turbulent transport within the boundary layer (~1 km depth following the conventional definition) whereas eddies greater than 1 km become the dominant contributors to the vertical momentum transport above the boundary layer in the eyewall. The strong dependence of vertical turbulent transport on eddy scales suggests that the vertical turbulent mixing parameterization in mesoscale simulations of tropical cyclones is ultimately a scale-sensitive problem.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s10546-020-00546-5
