Prandtl number dependence of turbulent temperature structure function: A unified theory

1989 ◽  
Vol 1 (6) ◽  
pp. 1021-1026 ◽  
Author(s):  
Hans Effinger ◽  
Siegfried Grossmann
Keyword(s):  
Prandtl Number ◽  
Structure Function ◽  
Temperature Structure ◽  
Unified Theory

Observation of the temperature structure function parameter, C T 2, over the ocean

1978 ◽  
Vol 15 (4) ◽  
pp. 507-523 ◽  
Author(s):  
K. L. Davidson ◽  
T. M. Houlihan ◽  
C. W. Fairall ◽  
G. E. Schacher
Keyword(s):  
Structure Function ◽  
Function Parameter ◽  
Temperature Structure

An empirical expression for on the axis of a slightly heated turbulent round jet

2019 ◽  
Vol 867 ◽  
pp. 392-413 ◽  
Author(s):  
J. Lemay ◽  
L. Djenidi ◽  
R. A. Antonia ◽  
A. Benaïssa
Keyword(s):  
Structure Function ◽  
Dissipation Rate ◽  
Velocity Structure ◽  
Power Laws ◽  
Second Order ◽  
Temperature Structure ◽  
Analytical Expression ◽  
Round Jet ◽  
Mean Temperature ◽  
The Mean

Self-preservation analyses of the equations for the mean temperature and the second-order temperature structure function on the axis of a slightly heated turbulent round jet are exploited in an attempt to develop an analytical expression for$\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}$, the mean dissipation rate of$\overline{\unicode[STIX]{x1D703}^{2}}/2$, where$\overline{\unicode[STIX]{x1D703}^{2}}$is the temperature variance. The analytical approach follows that of Thiessetet al.(J. Fluid Mech., vol. 748, 2014, R2) who developed an expression for$\unicode[STIX]{x1D716}_{k}$, the mean turbulent kinetic energy dissipation rate, using the transport equation for$\overline{(\unicode[STIX]{x1D6FF}u)^{2}}$, the second-order velocity structure function. Experimental data show that complete self-preservation for all scales of motion is very well satisfied along the jet axis for streamwise distances larger than approximately 30 times the nozzle diameter. This validation of the analytical results is of particular interest as it provides justification and confidence in the analytical derivation of power laws representing the streamwise evolution of different physical quantities along the axis, such as:$\unicode[STIX]{x1D702}$,$\unicode[STIX]{x1D706}$,$\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}$,$R_{U}$,$R_{\unicode[STIX]{x1D6E9}}$(all representing characteristic length scales), the mean temperature excess$\unicode[STIX]{x1D6E9}_{0}$, the mixed velocity–temperature moments$\overline{u\unicode[STIX]{x1D703}^{2}}$,$\overline{v\unicode[STIX]{x1D703}^{2}}$and$\overline{\unicode[STIX]{x1D703}^{2}}$and$\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}$. Simple models are proposed for$\overline{u\unicode[STIX]{x1D703}^{2}}$and$\overline{v\unicode[STIX]{x1D703}^{2}}$in order to derive an analytical expression for$A_{\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}}$, the prefactor of the power law describing the streamwise evolution of$\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}$. Further, expressions are also derived for the turbulent Péclet number and the thermal-to-mechanical time scale ratio. These expressions involve global parameters that are most likely to be influenced by the initial and/or boundary conditions and are therefore expected to be flow dependent.

scholarly journals On the Relationship between the TKE Dissipation Rate and the Temperature Structure Function Parameter in the Convective Boundary Layer

2020 ◽  
Vol 77 (7) ◽  
pp. 2311-2326
Author(s):  
Hubert Luce ◽  
Lakshmi Kantha ◽  
Hiroyuki Hashiguchi ◽  
Abhiram Doddi ◽  
Dale Lawrence ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Structure Function ◽  
Convective Boundary Layer ◽  
Dissipation Rate ◽  
Function Parameter ◽  
Mixing Efficiency ◽  
Buoyancy Frequency ◽  
Temperature Structure ◽  
Convective Boundary

AbstractUnder stably stratified conditions, the dissipation rate ε of turbulence kinetic energy (TKE) is related to the structure function parameter for temperature , through the buoyancy frequency and the so-called mixing efficiency. A similar relationship does not exist for convective turbulence. In this paper, we propose an analytical expression relating ε and in the convective boundary layer (CBL), by taking into account the effects of nonlocal heat transport under convective conditions using the Deardorff countergradient model. Measurements using unmanned aerial vehicles (UAVs) equipped with high-frequency response sensors to measure velocity and temperature fluctuations obtained during the two field campaigns conducted at Shigaraki MU observatory in June 2016 and 2017 are used to test this relationship between ε and in the CBL. The selection of CBL cases for analysis was aided by auxiliary measurements from additional sensors (mainly radars), and these are described. Comparison with earlier results in the literature suggests that the proposed relationship works, if the countergradient term γD in the Deardorff model, which is proportional to the ratio of the variances of potential temperature θ and vertical velocity w, is evaluated from in situ (airplane and UAV) observational data, but fails if evaluated from large-eddy simulation (LES) results. This appears to be caused by the tendency of the variance of θ in the upper part of the CBL and at the bottom of the entrainment zone to be underestimated by LES relative to in situ measurements from UAVs and aircraft. We discuss this anomaly and explore reasons for it.

Test of the anomalous scaling of passive temperature fluctuations in turbulent Rayleigh–Bénard convection with spatial inhomogeneity

2014 ◽  
Vol 753 ◽  
pp. 104-130 ◽  
Author(s):  
Xiaozhou He ◽  
Xiao-dong Shang ◽  
Penger Tong
Keyword(s):  
Structure Function ◽  
Temperature Fluctuations ◽  
Thermal Dissipation ◽  
Temperature Structure ◽  
Anomalous Scaling ◽  
Bénard Convection ◽  
Benard Convection ◽  
Turbulent Statistics ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractThe scaling properties of the temperature structure function (SF) and temperature–velocity cross-structure function (CSF) are investigated in turbulent Rayleigh–Bénard convection (RBC). The measured SFs and CSFs exhibit good scaling in space and time and the resulting SF and CSF exponents are obtained both at the centre of the convection cell and near the sidewall. A universal relationship between the CSF exponent and the thermal dissipation exponent is found, confirming that the anomalous scaling of passive temperature fluctuations in turbulent RBC is indeed caused by the spatial intermittency of the thermal dissipation field. It is also found that the difference in the functional form of the measured SF and CSF exponents at the two different locations in the cell is caused by the change of the geometry of the most dissipative structures in the (inhomogeneous) temperature field from being sheetlike at the cell centre to filament-like near the sidewall. The experiment thus provides direct evidence showing that the universality features of turbulent cascade are linked to the degree of anisotropy and inhomogeneity of turbulent statistics.

Measurements of the Temperature Structure-Function Parameters with a Small Unmanned Aerial System Compared with a Sodar

2015 ◽  
Vol 155 (3) ◽  
pp. 417-434 ◽  
Author(s):  
Timothy A. Bonin ◽  
David C. Goines ◽  
Aaron K. Scott ◽  
Charlotte E. Wainwright ◽  
Jeremy A. Gibbs ◽  
...  
Keyword(s):  
Structure Function ◽  
Unmanned Aerial System ◽  
Temperature Structure

Towards a Unified Theory of Immunoglobulin Structure-Function Relations

1986 ◽  
Vol 90 (1) ◽  
pp. 29-48 ◽  
Author(s):  
Thomas Kieder-Emmons ◽  
Heinz Kohler
Keyword(s):  
Structure Function ◽  
Unified Theory
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