Estimation of turbulence energy dissipation rate and vertical eddy diffusivity with the MU radar RASS

Hermawan, Eddy; Tsuda, Toshitaka

doi:10.1016/s1364-6826(99)00075-9

Cited by 17 publications

(12 citation statements)

References 22 publications

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“…These values are somewhat larger than the widely accepted in the oceanographic literature estimate of 0.2 (Osborn 1980;Gregg et al 2003;Wunsch and Ferrari 2004;Palmer et al 2008). However, they are well in line with the atmospheric data where was found in the range between 0.33 and 1 (Lilly et al 1974;Pardyjak et al 2002;Hermawan and Tsuda 1999;Bishop et al 2004;Clayson and Kantha 2008). Note that derived from observations may differ from these values due to, e.g., contribution of double diffusion processes (Canuto et al 2008a) or lateral stirring by mesoscale fluctuations (Smith and Ferrari 2009).…”

Section: The Richardson Diffusion Law Formatsupporting

confidence: 89%

Geophysical flows with anisotropic turbulence and dispersive waves: flows with stable stratification

Galperin

Sukoriansky

2010

Ocean Dynamics

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The quasi-normal scale elimination (QNSE) is an analytical spectral theory of turbulence based upon a successive ensemble averaging of the velocity and temperature modes over the smallest scales of motion and calculating corresponding eddy viscosity and eddy diffusivity. By extending the process of successive ensemble averaging to the turbulence macroscale one eliminates all fluctuating scales and arrives at models analogous to the conventional Reynolds stress closures. The scale dependency embedded in the QNSE method reflects contributions from different processes on different scales. Two of the most important processes in stably stratified turbulence, internal wave propagation and flow anisotropization, are explicitly accounted for in the QNSE formalism. For relatively weak stratification, the theory becomes amenable to analytical processing revealing just how increasing stratification modifies the flow field via growing anisotropy and gravity wave radiation. The QNSE theory yields the dispersion relation for internal waves in the presence of turbulence and provides a theoretical reasoning for the Gargett et al. (J Phys Oceanogr 11:1258-1271 scaling of the vertical shear spectrum. In addition, it shows that the internal wave breaking and flow anisotropization void the notion of the critical Richardson number at which turbulence is fully suppressed. The isopycnal and diapycnal viscosities and diffusivities can be expressed in the form of the Richardson diffusion laws thus providing a theoretical framework for the Okubo dispersion diagrams. Transitions in the spectral slopes can be associated with the turbulence-and wave-dominated ranges and have direct implications for the transport processes. We show that only quasi-isotropic, turbulence-dominated scales contribute to the diapycnal diffusivity. On larger, buoyancy dominated scales, the diapycnal diffusivity becomes scale independent. This result underscores the well-known fact that waves can only transfer momentum but not a scalar and sheds a new light upon the Ellison-Britter-Osborn mixing model. It also provides a general framework for separation of the effects of turbulence and waves even if they act on the same spatial and temporal scales. The QNSE theory-based turbulence models have been tested in various applications and demonstrated reliable performance. It is suggested that these models present a viable alternative to conventional Reynolds stress closures.

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Section: The Richardson Diffusion Law Formatsupporting

confidence: 89%

Geophysical flows with anisotropic turbulence and dispersive waves: flows with stable stratification

Galperin

Sukoriansky

2010

Ocean Dynamics

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“…In many studies, this spectrum has been identified with the saturated spectrum of IGWs and its exponent obtained based upon parametrization of breaking waves and dimensional considerations (see [115][116][117][118][119][120][121][122][123][124][125], and references therein). An often used estimate of C B throughout the atmosphere is 1 6 [70,115,126,127], which is close to the QNSE-derived value of 0.2.…”

Section: Energy and Temperature Spectra (A) Vertical Spectrum Of The supporting

confidence: 78%

An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

Sukoriansky

Galperin

2013

Phil. Trans. R. Soc. A.

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The buoyancy subrange of stably stratified turbulence is defined as an intermediate range of scales larger than those in the inertial subrange. This subrange encompasses the crossover from internal gravity waves (IGWs) to small-scale turbulence. The energy exchange between the waves and small-scale turbulence is communicated across this subrange. At the same time, it features progressive anisotropization of flow characteristics on increasing spatial scales. Despite many observational and computational studies of the buoyancy subrange, its theoretical understanding has been lagging. This article presents an investigation of the buoyancy subrange using the quasi-normal scale elimination (QNSE) theory of turbulence. This spectral theory uses a recursive procedure of small-scale modes elimination based upon a quasi-normal mapping of the velocity and temperature fields using the Langevin equations. In the limit of weak stable stratification, the theory becomes completely analytical and yields simple expressions for horizontal and vertical eddy viscosities and eddy diffusivities. In addition, the theory provides expressions for various one-dimensional spectra that quantify turbulence anisotropization. The theory reveals how the dispersion relation for IGWs is modified by turbulence, thus alleviating many unique waves' features. Predictions of the QNSE theory for the buoyancy subrange are shown to agree well with various data.

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“…Radar wind profilers were used to study the vertical CBL wind profile and its variance (e.g., Angevine et al, 1994;Eng et al, 2000;Campistron et al, 2002). A radio-acoustic sounding system (RASS) provides profiles of virtual temperature which can be used as a scaling parameter for turbulence studies also in higher altitudes (e.g., Hermawan and Tsuda, 1999;Furomoto and Tsuda, 2001). But temperature and moisture fluctuations cannot be separated with RASS.…”

Section: A Behrendt Et Al: Profiles Of Second-to Fourth-order Momenmentioning

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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Estimation of turbulence energy dissipation rate and vertical eddy diffusivity with the MU radar RASS

Cited by 17 publications

References 22 publications

Geophysical flows with anisotropic turbulence and dispersive waves: flows with stable stratification

Geophysical flows with anisotropic turbulence and dispersive waves: flows with stable stratification

An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

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

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