A Turbulence Closure for the Convective Boundary Layer Based on a Two-Scale Mass-Flux Approach

Gryanik, Vladimir M.; Hartmann, Jörg

doi:10.1175/1520-0469(2002)059<2729:atcftc>2.0.co;2

Cited by 80 publications

(181 citation statements)

References 43 publications

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“…However, some recent theoretical studies, measurement data, and LES data suggest that this hypothesis would not be valid for temperature in the CBL (also see Gryanik et al, 2005, for an overview). Gryanik and Hartmann (2002) suggested furthermore a parameterization between the FOM, skewness, and variance of turbulent temperature fluctuations which can be tested as soon as a larger number of measurement cases on turbulent temperature fluctuations with rotational Raman lidar have become available.…”

Section: Discussionmentioning

confidence: 99%

Profiles of second- to fourth-order moments of turbulent temperature fluctuations in the convective boundary layer: first measurements with rotational Raman lidar

et al. 2015

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Abstract. The rotational Raman lidar (RRL) of the University of Hohenheim (UHOH) measures atmospheric temperature profiles with high resolution (10 s, 109 m). The data contain low-noise errors even in daytime due to the use of strong UV laser light (355 nm, 10 W, 50 Hz) and a very efficient interference-filter-based polychromator. In this paper, the first profiling of the second-to fourth-order moments of turbulent temperature fluctuations is presented. Furthermore, skewness profiles and kurtosis profiles in the convective planetary boundary layer (CBL) including the interfacial layer (IL) are discussed. The results demonstrate that the UHOH RRL resolves the vertical structure of these moments. The data set which is used for this case study was collected in western Germany (50 • 53 50.56 N, 6 • 27 50.39 E; 110 m a.s.l.) on 24 April 2013 during the Intensive Observations Period (IOP) 6 of the HD(CP) 2 (High-Definition Clouds and Precipitation for advancing Climate Prediction) Observational Prototype Experiment (HOPE). We used the data between 11:00 and 12:00 UTC corresponding to 1 h around local noon (the highest position of the Sun was at 11:33 UTC). First, we investigated profiles of the total noise error of the temperature measurements and compared them with estimates of the temperature measurement uncertainty due to shot noise derived with Poisson statistics. The comparison confirms that the major contribution to the total statistical uncertainty of the temperature measurements originates from shot noise. The total statistical uncertainty of a 20 min temperature measurement is lower than 0.1 K up to 1050 m a.g.l. (above ground level) at noontime; even for single 10 s temperature profiles, it is smaller than 1 K up to 1020 m a.g.l. Autocovariance and spectral analyses of the atmospheric temperature fluctuations confirm that a temporal resolution of 10 s was sufficient to resolve the turbulence down to the inertial subrange. This is also indicated by the integral scale of the temperature fluctuations which had a mean value of about 80 s in the CBL with a tendency to decrease to smaller values towards the CBL top. Analyses of profiles of the second-, third-, and fourth-order moments show that all moments had peak values in the IL around the mean top of the CBL which was located at 1230 m a.g.l. The maximum of the variance profile in the IL was 0.39 K 2 with 0.07 and 0.11 K 2 for the sampling error and noise error, respectively. The third-order moment (TOM) was not significantly different from zero in the CBL but showed a negative peak in the IL with a minimum of −0.93 K 3 and values of 0.05 and 0.16 K 3 for the sampling and noise errors, respectively. The fourth-order moment (FOM) and kurtosis values throughout the CBL were not significantly different to those of a Gaussian distribution. Both showed also maxima in the IL but these were not statistically significant taking the measurement uncertainties into account. We conclude that these measurements permit the validation of large eddy simulation results and the...

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Section: Discussionmentioning

confidence: 99%

Profiles of second- to fourth-order moments of turbulent temperature fluctuations in the convective boundary layer: first measurements with rotational Raman lidar

et al. 2015

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“…K w = 3. Then, Gryanik & Hartmann (2002) proposed to modify Eq. (61) as follows: Figure 8 shows that the FOM based on Eq.…”

Section: Closure Models and Anisotropymentioning

confidence: 99%

Stochastic Excitation of Acoustic Modes in Stars

Samadi

2011

The Pulsations of the Sun and the Stars

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Abstract. For more than ten years, solar-like oscillations have been detected and frequencies measured for a growing number of stars with various characteristics (e.g. different evolutionary stages, effective temperatures, gravities, metal abundances ...).Excitation of such oscillations is attributed to turbulent convection and takes place in the uppermost part of the convective envelope. Since the pioneering work of Goldreich & Keely (1977), more sophisticated theoretical models of stochastic excitation were developed, which differ from each other both by the way turbulent convection is modelled and by the assumed sources of excitation. We review here these different models and their underlying approximations and assumptions.We emphasize how the computed mode excitation rates crucially depend on the way turbulent convection is described but also on the stratification and the metal abundance of the upper layers of the star. In turn we will show how the seismic measurements collected so far allow us to infer properties of turbulent convection in stars.

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“…The third model ('full TOM') is just a variant of this approach with a damping factor 1/(1 + 0.0008N 4 τ 4 ) as used in Kupka & Montgomery (2002), because of its more smooth behaviour near the convective boundary (its coefficient was determined using the simulation '3J' shown here). Finally, we show the result of using the Gryanik & Hartmann (2002) approximation (GH2002; see Kupka & Robinson 2007) for wθ 2 in consistency tests (see middle row of Fig. 1).…”

Section: Third Order Moment Modelsmentioning

confidence: 99%

Probing Reynolds stress models of convection with numerical simulations: II. Non-locality and third order moments.

Kupka

Muthsam

2006

Proc. IAU

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A Turbulence Closure for the Convective Boundary Layer Based on a Two-Scale Mass-Flux Approach

Cited by 80 publications

References 43 publications

Profiles of second- to fourth-order moments of turbulent temperature fluctuations in the convective boundary layer: first measurements with rotational Raman lidar

Profiles of second- to fourth-order moments of turbulent temperature fluctuations in the convective boundary layer: first measurements with rotational Raman lidar

Stochastic Excitation of Acoustic Modes in Stars

Probing Reynolds stress models of convection with numerical simulations: II. Non-locality and third order moments.

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