Vertical Variations of Mixing Lengths under Neutral and Stable Conditions during CASES-99

2011 ◽  
Vol 50 (10) ◽  
pp. 2030-2041 ◽  
Author(s):  
Jielun Sun
Keyword(s):  
Similarity Theory ◽  
Mixing Length ◽  
Vertical Layer ◽  
Surface Exchange ◽  
Exchange Study ◽  
Von Karman ◽  
Stable Conditions ◽  
Vertical Variations ◽  
Von Kármán ◽  
Neutral Conditions

AbstractAn 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 comparing κz with 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. Here κ is the von Kármán constant and z is 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 MOST κz and can be approximately described by Blackadar’s mixing length, κz/[1 + (κz/l∞)], with l∞ = 15 m for up to z ~ 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 MOST κz and Blackadar’s formula systematically overestimate the mixing length for momentum above ~20 m, leading to overestimates of turbulence.

Evaluation of Boundary Layer Similarity Theory for Stable Conditions in CASES-99

2007 ◽  
Vol 135 (10) ◽  
pp. 3474-3483 ◽  
Author(s):  
Kyung-Ja Ha ◽  
Yu-Kyung Hyun ◽  
Hyun-Mi Oh ◽  
Kyung-Eak Kim ◽  
Larry Mahrt
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Similarity Theory ◽  
Unknown Origin ◽  
Strong Stability ◽  
Surface Exchange ◽  
Stability Functions ◽  
Stable Conditions ◽  
Mean Wind Speed ◽  
Strong Winds

Abstract The Monin–Obukhov similarity theory and a generalized formulation of the mixing length for the stable boundary layer are evaluated using the Cooperative Atmosphere–Surface Exchange Study-1999 (CASES-99) data. The large-scale wind forcing is classified into weak, intermediate, and strong winds. Although the stability parameter, z/L, is inversely dependent on the mean wind speed, the speed of the large-scale flow includes independent influences on the flux–gradient relationship. The dimensionless mean wind shear is found to obey existing stability functions when z/L is less than unity, particularly for the strong and intermediate wind classes. For weak mean winds and/or strong stability (z/L > 1), this similarity theory breaks down. Deviations from similarity theory are examined in terms of intermittency. A case study of a weak-wind night indicates important modulation of the turbulence flux by mesoscale motions of unknown origin.

scholarly journals A New Value of the von Kármán Constant: Implications and Implementation

2009 ◽  
Vol 48 (5) ◽  
pp. 923-944 ◽  
Author(s):  
Edgar L. Andreas
Keyword(s):  
Boundary Layer ◽  
Similarity Theory ◽  
Stable Stratification ◽  
Transfer Coefficients ◽  
Obukhov Length ◽  
Von Karman ◽  
Roughness Lengths ◽  
Experimental Values ◽  
Definition Of ◽  
Von Kármán

Abstract The von Kármán constant k occurs throughout the mathematics that describe the atmospheric boundary layer. In particular, because k was originally included in the definition of the Obukhov length, its value has both explicit and implicit effects on the functions of Monin–Obukhov similarity theory. Although credible experimental evidence has appeared sporadically that the von Kármán constant is different than the canonical value of 0.40, the mathematics of boundary layer meteorology still retain k = 0.40—probably because the task of revising all of this math to implement a new value of k is so daunting. This study therefore outlines how to make these revisions in the nondimensional flux–gradient relations; in variance, covariance, and dissipation functions; and in structure parameters of Monin–Obukhov similarity theory. It also demonstrates how measured values of the drag coefficient (CD), the transfer coefficients for sensible (CH) and latent (CE) heat, and the roughness lengths for wind speed (z0), temperature (zT), and humidity (zQ) must be modified for a new value of the von Kármán constant. For the range of credible experimental values for k, 0.35–0.436, revised values of CD, CH, CE, z0, zT, and zQ could be quite different from values obtained assuming k = 0.40, especially if the original measurements were made in stable stratification. However, for the value of k recommended here, 0.39, no revisions to the transfer coefficients and roughness lengths should be necessary. Henceforth, use the original measured values of transfer coefficients and roughness lengths but do use similarity functions modified to reflect k = 0.39.

scholarly journals Reconsideration of the overlap region in smooth shallow open channel flows

2017 ◽  
Vol 44 (3) ◽  
pp. 161-173 ◽  
Author(s):  
Mehdi Heidari ◽  
Ram Balachandar ◽  
Vesselina Roussinova ◽  
Ronald M. Barron
Keyword(s):  
Least Squares ◽  
Channel Flow ◽  
Open Channel ◽  
Open Channel Flow ◽  
Data Sets ◽  
Mixing Length ◽  
Von Karman ◽  
Log Law ◽  
Von Kármán ◽  
Overlap Region

In this paper, data sets for mean velocity distributions in smooth shallow open channel flow are reconsidered to evaluate the characteristics of the overlap region and estimate the friction velocity (u∗). Both new and existing velocity measurements are used in the analysis. The velocity profiles are obtained using laser Doppler velocimetry and particle image velocimetry at typical Reynolds numbers (20 000–60 000) achieved in laboratory flumes. Validation of the estimated u∗ values using different forms of power law is established by comparing these values with the ones available in literature. Also, the Reynolds shear stress distribution based on two-dimensional measurements validate the estimated u∗. The availability of new data sets allows one to verify the usefulness of the log-law and evaluate the log-law constants. Different fitting methods; least squares, derivative, and scattered methods are used to evaluate the value of von Kármán coefficient. It is found that the value of κ obtained from the least squares method varies between 0.35 and 0.51 and depends on the Reynolds number. This refutes the conventional constant value assumption for the von Kármán coefficient (κ = 0.41). By considering the Prandtl’s mixing-length theory, the present values of the von Kármán coefficient are used to evaluate the mixing length distributions. The mixing length distributions in smooth open channel flow are found to depend on Reθ.

scholarly journals An Analysis for the Applicability of Monin–Obukhov Similarity Theory in Stable Conditions

2012 ◽  
Vol 69 (6) ◽  
pp. 1910-1915 ◽  
Author(s):  
Pramod Kumar ◽  
Maithili Sharan
Keyword(s):  
Similarity Theory ◽  
Ground Surface ◽  
Surface Fluxes ◽  
Stability Parameters ◽  
Surface Exchange ◽  
Obukhov Length ◽  
Stable Conditions ◽  
Data Points ◽  
The Stability ◽  
Few Data

Abstract An analysis in a plane of the stability parameters ζ = z/L (where z is a height above the ground surface and L is the Obukhov length) and bulk Richardson number RiB is proposed to examine the applicability of Monin–Obukhov similarity (MOS) theory in stable conditions. In this analysis, the data available from two different experimental datasets [(i) Cooperative Atmosphere–Surface Exchange Study-1999 (CASES-99) and (ii) Cardington] are divided into four quadrants. An unexpected behavior of decreasing ζ with increasing RiB was observed with both datasets in quadrant II characterized by ζ < 1 and RiB > 0.2 and in quadrant IV with ζ > 1 and RiB < 0.2. This is in contrast to a commonly expected monotonically increasing behavior between ζ and RiB. It is shown that the MOS theory is consistent for computing the surface fluxes corresponding to the data points lying in quadrants I (with ζ > 1 and RiB > 0.2) and III (with ζ < 1 and RiB < 0.2), whereas it may not be applicable for the points in quadrants II and IV. Thus, a breakdown of the relationship between observed ζ and RiB with growing stability in these quadrants may limit the applicability of MOS theory in stable conditions. Since quadrant IV has very few data points, the applicability of MOS theory needs to be substantiated further with the availability of sufficient data points in this regime.

scholarly journals Analysis of Turbulence Profiles from Three Tall Towers: Departure from Similarity Theory in Near-Neutral and Stable Conditions

2008 ◽  
Vol 2 (1) ◽  
pp. 106-116 ◽  
Author(s):  
Brent M. Bowen
Keyword(s):  
Similarity Theory ◽  
National Laboratory ◽  
Los Alamos National Laboratory ◽  
Rocky Flats ◽  
Vertical Diffusivity ◽  
Stable Conditions ◽  
Multi Level ◽  
Neutral Conditions ◽  
Good Agreement

Long-term wind and turbulence profiles were analyzed for all stability conditions at three tall, multi-level towers located at the Los Alamos National Laboratory (LANL), Rocky Flats Environmental Plant (RF), and the Boulder Atmospheric Observatory (BAO). The LANL and RF sites are located in complex terrain and the BAO is located over relatively simple terrain, but within 3 to 5 km of an abrupt 20 to 30 m increase in terrain. Results indicate that normalized turbulence parameter profiles at all three sites agree well with widely used empirical relationships during unstable conditions. During near neutral conditions, σu parameter profiles are also well behaved at all three sites while σw increases with height for complex fetch (BAO downwind of bluff, LANL, and RF) while σw remains nearly constant up to 200 m AGL at BAO with simple fetch. The σw /u* values at 10-m AGL are close to one at all sites and they increase by an order of 50% in the lowest 60 to 200 m for complex fetch and remain approximately constant in the lowest 200 m with simple fetch. During very stable conditions, typical values of σu and σ v range between 0.4 to 0.6 ms-1 and increase slightly with height while median σw values nearly double from about 0.1 to 0.2 ms-1 between the 10- and 100 to 200-m levels. A comparison of predicted with measured u* values at two of the sites shows generally good agreement over 6 stability categories. It is suggested that M-O similarity theory will usually greatly underestimate vertical diffusivity and dispersion during very stable conditions, especially at larger heights, based on idealized Kz profiles calculated from measured σw values. Finally, rules of thumb are formulated to describe departure from similarity theory during near-neutral and stable conditions.

scholarly journals The Influence of Swell on the Atmospheric Boundary Layer under Nonneutral Conditions

2018 ◽  
Vol 48 (4) ◽  
pp. 925-936 ◽  
Author(s):  
Zhongshui Zou ◽  
Dongliang Zhao ◽  
Jun A. Zhang ◽  
Shuiqing Li ◽  
Yinhe Cheng ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Similarity Theory ◽  
Complex Problem ◽  
Wind Speeds ◽  
Stable Conditions ◽  
Turbulent Closure ◽  
Low Wind Speeds ◽  
Wind Profiles ◽  
Neutral Conditions ◽  
Wave Boundary

AbstractThe anomalous phenomena induced by the prevailing swell at low wind speeds prevent a complete understanding of air–sea interaction processes. Many studies have considered this complex problem, but most have focused on near-neutral conditions. In this study, the influence of the swell on the atmospheric boundary under nonneutral conditions was addressed by extending the turbulent closure models of Makin and Kudryavtsev and the Monin–Obukhov similarity theory (MOST; Monin and Yaglom) to the existence of swell and nonneutral conditions. It was shown that wind profiles derived from these models were consistent with each other and both departed from the traditional MOST. At low wind speeds, a supergeostrophic jet appeared on the upper edge of the wave boundary layer, which was also reported in earlier studies. Under nonneutral conditions, the influence of buoyancy was significant. The slope of the wind profile increased under stable conditions and became smoother under unstable conditions. Considering the effects of buoyancy and swell, the wind stress derived from the model agreed quantitatively with the observations.

Estimation of upper bounds for the applicability of non-linear similarity functions for non-dimensional wind and temperature profiles in the surface layer in very stable conditions

2010 ◽  
Vol 467 (2126) ◽  
pp. 473-494 ◽  
Author(s):  
Maithili Sharan ◽  
Pramod Kumar
Keyword(s):  
Surface Layer ◽  
Similarity Theory ◽  
Upper Bounds ◽  
Surface Fluxes ◽  
Similarity Function ◽  
Temperature Profiles ◽  
Similarity Functions ◽  
Surface Exchange ◽  
Stable Conditions ◽  
Non Linear

The computation of surface fluxes by Monin–Obukhov similarity theory with different linear/non-linear similarity functions for non-dimensional wind and temperature profiles becomes limited to specific ranges of ζ = z / L (where z is the height above ground and L is the Obukhov length) and bulk Richardson number ( Ri B ) under very stable conditions. A systematic mathematical analysis is carried out to estimate the upper bounds of ζ and Ri B for the extent of applicability of different non-linear similarity functions in the surface layer under these conditions. A generalized methodology is proposed on the basis of momentum drag coefficient ( C D ) and heat exchange coefficient ( C H ) and applied to various non-linear similarity functions available in the literature. A theoretically derived criterion for the applicability of each of the non-linear similarity function is evaluated with observations from Cooperative Atmosphere-Surface Exchange Study-99 and UK Meteorological Office’s Cardington datasets. The evaluation with both datasets for each non-linear similarity function confirms the validity of proposed theoretical results under very stable conditions.

Turbulence and Vertical Fluxes in the Stable Atmospheric Boundary Layer. Part II: A Novel Mixing-Length Model

2013 ◽  
Vol 70 (6) ◽  
pp. 1528-1542 ◽  
Author(s):  
Jing Huang ◽  
Elie Bou-Zeid ◽  
Jean-Christophe Golaz
Keyword(s):  
Large Eddy Simulations ◽  
Mixing Length ◽  
New Model ◽  
Vertical Fluxes ◽  
Stable Conditions ◽  
Large Eddy ◽  
Single Column ◽  
Single Column Model ◽  
Stable Atmospheric Boundary Layer ◽  
Neutral Conditions

Abstract This is the second part of a study about turbulence and vertical fluxes in the stable atmospheric boundary layer. Based on a suite of large-eddy simulations in Part I where the effects of stability on the turbulent structures and kinetic energy are investigated, first-order parameterization schemes are assessed and tested in the Geophysical Fluid Dynamics Laboratory (GFDL)’s single-column model. The applicability of the gradient-flux hypothesis is first examined and it is found that stable conditions are favorable for that hypothesis. However, the concept of introducing a stability correction function fm as a multiplicative factor into the mixing length used under neutral conditions lN is shown to be problematic because fm computed a priori from large-eddy simulations tends not to be a universal function of stability. With this observation, a novel mixing-length model is proposed, which conforms to large-eddy simulation results much better under stable conditions and converges to the classic model under neutral conditions. Test cases imposing steady as well as unsteady forcings are developed to evaluate the performance of the new model. It is found that the new model exhibits robust performance as the stability strength is changed, while other models are sensitive to changes in stability. For cases with unsteady forcings, which are very rarely simulated or tested, the results of the single-column model and large-eddy simulations are also closer when the new model is used, compared to the other models. However, unsteady cases are much more challenging for the turbulence closure formulations than cases with steady surface forcing.

scholarly journals Investigation of feasibility of wind turbulence measurement by a pulsed coherent doppler lidar in the atmospheric boundary layer

2018 ◽  
Vol 176 ◽  
pp. 06016
Author(s):  
Igor Smalikho ◽  
Viktor Banakh
Keyword(s):  
Stream Line ◽  
Doppler Lidar ◽  
Atmospheric Conditions ◽  
Turbulence Measurement ◽  
Von Karman ◽  
Coherent Doppler Lidar ◽  
Stable Conditions ◽  
Lidar Measurements ◽  
Wind Turbulence ◽  
Von Kármán

Feasibilities of determination of the wind turbulence parameters from data measured by the Stream Line coherent Doppler lidar under different atmospheric conditions have been studied experimentally. It has been found that the spatial structure of the turbulence is described well by the von Karman model in the layer of intensive mixing. From the lidar measurements at night under stable conditions the estimation of the outer scale of turbulence with the use of the von Karman model is not possible.

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