A Refinement of the Millionshchikov Quasi-Normality Hypothesis for Convective Boundary Layer Turbulence

Gryanik, Vladimir M.; Hartmann, Jörg; Raasch, Siegfried; Schröter, M.

doi:10.1175/jas3457.1

Cited by 41 publications

(89 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A quasi-normal FOM even when TOM is non-zero, agrees with the hypothesis of Millionshchikov (1941) which forms the basis for a large number of closure models (see Gryanik et al, 2005, for an overview). 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).…”

Section: Discussionsupporting

confidence: 82%

“…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%

See 1 more Smart Citation

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

View full text Add to dashboard Cite

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...

show abstract

Section: Discussionsupporting

confidence: 82%

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

View full text Add to dashboard Cite

show abstract

“…Our model indicates a different origin for the strong localized events, associated with a positive feedback in the vertical between nonlinear steepening and wave motions, and is consistent with the simulations that indicate that a more stably stratified flow has stronger bursts in a plage of parameters. This study may thus lead to more useful parametrizations of stably stratified flows in weather and climate models, by formulating a stochastic eddy-noise [27] which explicitly incorporates the non-linear coupling described herein (for a quasi-normal closure, see [28]). …”

mentioning

confidence: 99%

Turbulence comes in bursts in stably stratified flows

2014

View full text Add to dashboard Cite

There is a clear distinction between simple laminar and complex turbulent fluids. But in some cases, as for the nocturnal planetary boundary layer, a stable and well-ordered flow can develop intense and sporadic bursts of turbulent activity which disappear slowly in time. This phenomenon is ill-understood and poorly modeled; and yet, it is central to our understanding of weather and climate dynamics. We present here a simple model which shows that in stably stratified turbulence, the stronger bursts can occur when the flow is expected to be more stable. The bursts are generated by a rapid non-linear amplification of energy stored in waves, and are associated with energetic interchanges between vertical velocity and temperature (or density) fluctuations. Direct numerical simulations on grids of 2048 3 points confirm this somewhat paradoxical result of measurably stronger events for more stable flows, displayed not only in the temperature and vertical velocity derivatives, but also in the amplitude of the fields themselves.PACS numbers: 47.55. Hd, 47.35.Bb, 47.27.ek Large fluctuations are common in physical systems with long-range correlations, and have been found to be linked to so-called "1/f" noise [1]. They take the form of sporadic and localized events, as observed in many instances in critical phenomena and in turbulent flows, and are diagnosed through non-Gaussian Probability Distribution Functions (PDFs) [2]. In turbulence, strong events occur in field gradients, with the velocity itself being nearly Gaussian. There are however exceptions to this last rule for shear flows [3,4], quantum fluids [6,7], and subtropical current systems [5]. Extreme events associated with random plumes have also been diagnosed in the atmospheric convective boundary layer [8], or when linked with coherent structures, e.g., storm tracks.The occurrence of intermittent strong activity is a signature of fully developed turbulence and is therefore more surprising in stable flows. Intermittency makes the stable nocturnal planetary boundary layer (PBL) highly unpredictable: as night sets in, this layer between the atmosphere and land or sea stabilizes due to the radiative cooling of the land and ocean masses. It is still unclear how stable the nocturnal PBL becomes. Three regimes have been observed [9]: very stable, weakly stable with turbulent motions persisting and competing with internal gravity waves, and transitory. Even in the very stable case, the PBL is subject to intense sporadic bursts of turbulence which die out after many wave periods [9,10].Numerical simulations play an increasing role in the understanding of these complex processes, and in quantifying the dual problem of the increased stability [11] and the spontaneous generation of bursts. However, modeling of the PBL in weather and climate codes is often inadequate, resulting, for example, in an inaccurate evaluation of the extension of the ice sheet, as is the case over Greenland [12], and in a faulty estimate of the overall energy balance in long-term climate syste...

show abstract

“…For this case a number of analytical relations exists between higher order moments. As they were found to scale very well with Reynolds averages, GH2002 and Gryanik et al (2005) suggested to replace the quasi-normal (QN) model with a new set of closures (see Kupka & Robinson 2007 for a discussion).…”

Section: Models For Third and Fourth Order Momentsmentioning

confidence: 99%

Coherent structures in granulation convection and their importance for higher order closure models

Kupka

Robinson

2006

Proc. IAU

View full text Add to dashboard Cite

Abstract. We use numerical simulations of granulation in the Sun and a K dwarf to study the effects of coherent structures on higher order moments. The latter need to be calculated in non-local Reynolds stress models of turbulent convection. Models that explicitly account for the asymmetry between up-and downflows as well as hot and cold drafts provide a substantial improvement over traditional ones, such as the quasi-normal approximation, which is only able to provide order of magnitude estimates for this type of flow.

show abstract

A Refinement of the Millionshchikov Quasi-Normality Hypothesis for Convective Boundary Layer Turbulence

Cited by 41 publications

References 13 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

Turbulence comes in bursts in stably stratified flows

Coherent structures in granulation convection and their importance for higher order closure models

Contact Info

Product

Resources

About