An investigation on vertical variations of the mixing lengths for momentum and heat under neutral and stable conditions was conducted using the data collected from the Cooperative Atmosphere–Surface ...Exchange Study in 1999 (CASES-99). By comparingκzwith the mixing lengths under neutral conditions calculated using the observations from CASES-99, the vertical layer where the Monin–Obukhov similarity theory (MOST) is valid was identified. Hereκis the von Kármán constant andzis the height above the ground. On average, MOST is approximately valid between 0.5 and 10 m. Above the layer, the observed mixing lengths under neutral conditions are smaller than the MOSTκzand can be approximately described by Blackadar's mixing length,κz/1 + (κz/l
∞), withl
∞= 15 m for up toz∼ 20 m for the mixing length for momentum and up to the highest observation height for the mixing length for heat. Above ∼20 m, the mixing length for momentum approaches a constant. Both MOSTκzand Blackadar's formula systematically overestimate the mixing length for momentum above ∼20 m, leading to overestimates of turbulence.
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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
∗
(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
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.
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Abstract
An investigation of nocturnal intermittent turbulence during the Cooperative Atmosphere–Surface Exchange Study in 1999 (CASES-99) revealed three turbulence regimes at each observation ...height: 1) regime 1, a weak turbulence regime when the wind speed is less than a threshold value; 2) regime 2, a strong turbulence regime when the wind speed exceeds the threshold value; and 3) regime 3, a moderate turbulence regime when top-down turbulence sporadically bursts into the otherwise weak turbulence regime. For regime 1, the strength of small turbulence eddies is correlated with local shear and weakly related to local stratification. For regime 2, the turbulence strength increases systematically with wind speed as a result of turbulence generation by the bulk shear, which scales with the observation height. The threshold wind speed marks the transition above which the boundary layer approaches near-neutral conditions, where the turbulent mixing substantially reduces the stratification and temperature fluctuations. The preference of the turbulence regimes during CASES-99 is closely related to the existence and the strength of low-level jets. Because of the different roles of the bulk and local shear with regard to turbulence generation under different wind conditions, the relationship between turbulence strength and the local gradient Richardson number varies for the different turbulence regimes. Turbulence intermittency at any observation height was categorized in three ways: turbulence magnitude oscillations between regimes 1 and 2 as wind speed varies back and forth across its threshold value, episodic turbulence enhancements within regime 1 as a result of local instability, and downbursts of turbulence in regime 3.
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The analysis of momentum and heat fluxes from the Cooperative Atmosphere-Surface Exchange Study 1999 (CASES-99) field experiment is extended throughout the diurnal cycle following the investigation ...of nighttime turbulence by Sun et al. (J Atmos Sci 69:338–351,
2012
). Based on the observations, limitations of Monin–Obukhov similarity theory (MOST) are examined in detail. The analysis suggests that strong turbulent mixing is dominated by relatively large coherent eddies that are not related to local vertical gradients as assumed in MOST. The HOckey-Stick Transition (HOST) hypothesis is developed to explain the generation of observed large coherent eddies over a finite depth and the contribution of these eddies to vertical variations of turbulence intensity and atmospheric stratification throughout the diurnal cycle. The HOST hypothesis emphasizes the connection between dominant turbulent eddies and turbulence generation scales, and the coupling between the turbulence kinetic energy and the turbulence potential energy within the turbulence generation layer in determining turbulence intensity. For turbulence generation directly influenced by the surface, the HOST hypothesis recognizes the role of the surface both in the vertical variation of momentum and heat fluxes and its boundary effect on the size of the dominant turbulence eddies.
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Observational data from sonic anemometers are commonly rotated from sonic to streamline coordinates, a procedure that is called tilt correction. Tilt corrections are often used to post-process air ...velocity data collected from sonic anemometers to allow objective interpretation of air flow data relative to the Earth. Since streamline coordinates depend on dynamical characteristics of the flow, the tilt correction depends not only on temporal and spatial variations of the flow, but also on local circulations. We found that ensemble- averaged slope flows are approximately parallel to the terrain slope close to the ground within the canopy layer, but not above, due to the influence of the diurnal variation of local vertical circulations. As a result, the diurnal variation of the observed vertical velocity in streamline coordinates at 21.5 m above the ground over 11-m tall forest canopies can be opposite to that calculated from the continuity equation. To estimate CO₂ transport over sloping terrain, a workable reference coordinate system is needed such that multiple sonic anemometers have a common reference relative to the Earth. Streamline coordinate systems can be the choice of the common reference coordinate system only if flow, at least ensemble-averaged flow, is parallel to terrain slopes. The choice of the reference coordinate system and its implication in investigation of CO₂ transport are discussed.
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Flow in a stably stratified environment is characterized by anisotropic and intermittent turbulence and wavelike motions of varying amplitudes and periods. Understanding turbulence intermittency and ...wave‐turbulence interactions in a stably stratified flow remains a challenging issue in geosciences including planetary atmospheres and oceans. The stable atmospheric boundary layer (SABL) commonly occurs when the ground surface is cooled by longwave radiation emission such as at night over land surfaces, or even daytime over snow and ice surfaces, and when warm air is advected over cold surfaces. Intermittent turbulence intensification in the SABL impacts human activities and weather variability, yet it cannot be generated in state‐of‐the‐art numerical forecast models. This failure is mainly due to a lack of understanding of the physical mechanisms for seemingly random turbulence generation in a stably stratified flow, in which wave‐turbulence interaction is a potential mechanism for turbulence intermittency. A workshop on wave‐turbulence interactions in the SABL addressed the current understanding and challenges of wave‐turbulence interactions and the role of wavelike motions in contributing to anisotropic and intermittent turbulence from the perspectives of theory, observations, and numerical parameterization. There have been a number of reviews on waves, and a few on turbulence in stably stratified flows, but not much on wave‐turbulence interactions. This review focuses on the nocturnal SABL; however, the discussions here on intermittent turbulence and wave‐turbulence interactions in stably stratified flows underscore important issues in stably stratified geophysical dynamics in general.
Key Points
Wave‐turbulence interactions in the SABL are poorly understood
New observational strategies are required
Numerical parameterization of wave effects is limited
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Relationships among the horizontal pressure gradient, the Coriolis force, and the vertical momentum transport by turbulent fluxes are investigated using data collected from the 1999 Cooperative ...Atmosphere-Surface Exchange Study (CASES-99). Wind toward higher pressure (WTHP) adjacent to the ground occurred about 50% of the time. For wind speed at 5 m above the ground stronger than 5 m s super(-1), WTHP occurred about 20% of the time. Focusing on these moderate to strong wind cases only, relationships among horizontal pressure gradients, Coriolis force, and vertical turbulent transport in the momentum balance are investigated. The magnitude of the downward turbulent momentum flux consistently increases with height under moderate to strong winds, which results in the vertical convergence of the momentum flux and thus provides a momentum source and allows WTHP.
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Conservation of total, kinetic, and thermal energy in the atmosphere is revisited, and the derived thermal energy balance is examined with observations. Total energy conservation (TEC) provides a ...constraint for the sum of kinetic, thermal, and potential energy changes. In response to air thermal expansion/compression, air density variation leads to vertical density fluxes and potential energy changes, which in turn impact the thermal energy balance as well as the kinetic energy balance due to the constraint of TEC. As vertical density fluxes can propagate through a large vertical domain to where local thermal expansion/compression becomes negligibly small, interactions between kinetic and thermal energy changes in determining atmospheric motions and thermodynamic structures can occur when local diabatic heating/cooling becomes small. The contribution of vertical density fluxes to the kinetic energy balance is sometimes considered but that to the thermal energy balance is traditionally missed. Misinterpretation between air thermal expansion/compression and incompressibility for air volume changes with pressure under a constant temperature would lead to overlooking important impacts of thermal expansion/compression on air motions and atmospheric thermodynamics. Atmospheric boundary layer observations qualitatively confirm the contribution of potential energy changes associated with vertical density fluxes in the thermal energy balance for explaining temporal variations of air temperature.
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We discuss the accuracy requirements for measuring mesoscale (roughly horizontal scales > 10 km or 5 to 10 times the planetary boundary-layer (PBL) depth) fluxes in the convective PBL, and the ...ability of current research aircraft to achieve this accuracy. We conclude that aircraft equipped with inertial nagivation systems capable of < 3 km hr-¹ navigational accuracy are able to resolve mesoscale fluctuations in velocity, and thus variances and fluxes on the mesoscale. We then discuss measurements of velocity and scalar spectra, and cospectra of vertical velocity with horizontal velocity components and scalars, obtained from long flight legs with the National Center for Atmospheric Research Electra aircraft over the boreal forest of Canada in summer during the BOreal Ecosystem-Atmosphere Study (BOREAS), over the tropical Pacific Ocean from the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE), and over the East China Sea during wintertime cold-air outbreaks from the Air Mass Transformation Experiment (AMTEX). Each of these studies has somewhat different forcings and boundary conditions, so we can compare their consequences on the spectra and cospectra. On average, we found no significant scalar or momentum fluxes for horizontal scales > 10 km. We also develop a simple model based on observed thermal structure to explain the phase angle between vertical velocity and the along-wind horizontal velocity as a function of height, which shows good agreement with the observed phase angle in AMTEX.
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Abstract
The light-wind, clear-sky, very stable boundary layer (vSBL) is characterized by large values of bulk Richardson number. The light winds produce weak shear, turbulence, and mixing, and ...resulting strong temperature gradients near the surface. Here five nights with weak-wind, very stable boundary layers during the Cooperative Atmosphere–Surface Exchange Study (CASES-99) are investigated. Although the winds were light and variable near the surface, Doppler lidar profiles of wind speed often indicated persistent profile shapes and magnitudes for periods of an hour or more, sometimes exhibiting jetlike maxima. The near-surface structure of the boundary layer (BL) on the five nights all showed characteristics typical of the vSBL. These characteristics included a shallow traditional BL only 10–30 m deep with weak intermittent turbulence within the strong surface-based radiation inversion. Above this shallow BL sat a layer of very weak turbulence and negligible turbulent mixing. The focus of this paper is on the effects of this quiescent layer just above the shallow BL, and the impacts of this quiescent layer on turbulent transport and numerical modeling. High-frequency time series of temperature T on a 60-m tower showed that 1) the amplitudes of the T fluctuations were dramatically suppressed at levels above 30 m in contrast to the relatively larger intermittent T fluctuations in the shallow BL below, and 2) the temperature at 40- to 60-m height was nearly constant for several hours, indicating that the very cold air near the surface was not being mixed upward to those levels. The presence of this quiescent layer indicates that the atmosphere above the shallow BL was isolated and detached both from the surface and from the shallow BL.
Although some of the nights studied had modestly stronger winds and traveling disturbances (density currents, gravity waves, shear instabilities), these disturbances seemed to pass through the region without having much effect on either the SBL structure or on the atmosphere–surface decoupling. The decoupling suggests that under very stable conditions, the surface-layer lower boundary condition for numerical weather prediction models should act to decouple and isolate the surface from the atmosphere, for example, as a free-slip, thermally insulated layer.
A multiday time series of ozone from an air quality campaign in Tennessee, which exhibited nocturnal behavior typical of polluted air, showed the disappearance of ozone on weak low-level jets (LLJ) nights. This behavior is consistent with the two-stratum structure of the vSBL, and with the nearly complete isolation of the surface and the shallow BL from the rest of the atmosphere above, in contrast to cases with stronger LLJs, where such coupling was stronger.
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