Spectral modelling of high Reynolds number unstably stratified homogeneous turbulence

2015 ◽  
Vol 765 ◽  
pp. 17-44 ◽  
Author(s):  
A. Burlot ◽  
B.-J. Gréa ◽  
F. S. Godeferd ◽  
C. Cambon ◽  
J. Griffond
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Isotropic Turbulence ◽  
Spectral Energy Distribution ◽  
Homogeneous Turbulence ◽  
Spectral Energy ◽  
Characteristic Relaxation Time ◽  
Background Density ◽  
Self Similar ◽  
High Reynolds

AbstractWe study unconfined homogeneous turbulence with a destabilizing background density gradient in the Boussinesq approximation. Starting from initial isotropic turbulence, the buoyancy force induces a transient phase toward a self-similar regime accompanied by a rapid growth of kinetic energy and Reynolds number, along with the development of anisotropic structures in the flow in the direction of gravity. We model this with a two-point statistical approach using an axisymmetric eddy-damped quasi-normal Markovian (EDQNM) closure that includes buoyancy production. The model is able to match direct numerical simulations (DNS) in a parametric study showing the effect of initial Froude number and mixing intensity on the development of the flow. We further improve the model by including the stratification timescale in the characteristic relaxation time for triple correlations in the closure. It permits the computation of the long-term evolution of unstably stratified turbulence at high Reynolds number. This agrees with recent theoretical predictions concerning the self-similar dynamics and brings new insight into the spectral energy distribution and anisotropy of the flow.

scholarly journals Circulation in High Reynolds Number Isotropic Turbulence is a Bifractal

2019 ◽  
Vol 9 (4) ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P. K. Yeung
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Isotropic Turbulence ◽  
High Reynolds

Spectral energy transfer in high Reynolds number turbulence

1977 ◽  
Vol 79 (2) ◽  
pp. 337-359 ◽  
Author(s):  
K. N. Helland ◽  
C. W. Van Atta ◽  
G. R. Stegen
Keyword(s):  
Reynolds Number ◽  
Energy Transfer ◽  
Energy Spectrum ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Second Order ◽  
Spectral Energy ◽  
Local Isotropy ◽  
High Reynolds ◽  
Good Agreement

The spectral energy transfer of turbulent velocity fields has been examined over a wide range of Reynolds numbers by experimental and empirical methods. Measurements in a high Reynolds number grid flow were used to calculate the energy transfer by the direct Fourier-transform method of Yeh & Van Atta. Measurements in a free jet were used to calculate energy transfer for a still higher Reynolds number. An empirical energy spectrum was used in conjunction with a local self-preservation approximation to estimate the energy transfer at Reynolds numbers beyond presently achievable experimental conditions.Second-order spectra of the grid measurements are in excellent agreement with local isotropy down to low wavenumbers. For the first time, one-dimensional third-order spectra were used to test for local isotropy, and modest agreement with the theoretical conditions was observed over the range of wavenumbers which appear isotropic according to second-order criteria. Three-dimensional forms of the measured spectra were calculated, and the directly measured energy transfer was compared with the indirectly measured transfer using a local self-preservation model for energy decay. The good agreement between the direct and indirect measurements of energy transfer provides additional support for both the assumption of local isotropy and the assumption of self-preservation in high Reynolds number grid turbulence.An empirical spectrum was constructed from analytical spectral forms of von Kármán and Pao and used to extrapolate energy transfer measurements at lower Reynolds number to Rλ = 105 with the assumption of local self preservation. The transfer spectrum at this Reynolds number has no wavenumber region of zero net spectral transfer despite three decades of $k^{-\frac{5}{3}}$. behaviour in the empirical energy spectrum. A criterion for the inertial subrange suggested by Lumley applied to the empirical transfer spectrum is in good agreement with the $k^{-\frac{5}{3}}$ range of the empirical energy spectrum.

Efficient Generation of High-Reynolds-Number Homogeneous Turbulence by Disturbances Composed of Two Frequency Components

2015 ◽  
Author(s):  
Kotaro Takamure ◽  
Shigehira Ozono
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Random Phase ◽  
Homogeneous Turbulence ◽  
Single Frequency ◽  
Tunnel Length ◽  
Driving Mode ◽  
Spectral Peaks ◽  
Frequency Components ◽  
High Reynolds

We attempted to determine the number of frequency components required for efficient turbulence generation using a multi-fan type wind tunnel where 99 fans were driven to generate turbulence. In a previous study, a random-phase mode was applied, where an input signal composed of forty frequency components was fed to each fan with quasi-random phases. Using this driving mode, we achieved high-Reynolds-number homogeneous turbulence of Reλ ∼ 750 in a relatively short distance. In the present study, in order to understand the elementary process of the evolution, one single frequency or two frequencies were used, instead of forty. When using the single frequency, initial dominant spectral peaks remain at lower frequencies over the tunnel length. In the case of two frequencies, f1 and f2 (f1 = n1f0 and f2 = n2f0; n1 < n2), where n1 and n2 are integers, and f0 is defined as the reciprocal of a basic input data period, the turbulence characteristics depend on the relation between n1 and n2. When n1 and n2 are not coprime (i.e., n2 can be divided by n1), dominant spectral peaks remain over the tunnel length as in the case of using a single frequency, but when coprime (i.e., n2 cannot be divided by n1), the spectral shape becomes relatively smooth with the initial dominant peaks disappearing. However, it was found that the development of turbulence is much slower for the two-frequency case than for the forty-frequency case.

scholarly journals Self-similar decay of high Reynolds number Taylor-Couette turbulence

2016 ◽  
Vol 1 (6) ◽  
Author(s):  
Ruben A. Verschoof ◽  
Sander G. Huisman ◽  
Roeland C. A. van der Veen ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Self Similar ◽  
Taylor Couette ◽  
High Reynolds
Sign in / Sign up

Export Citation Format

Share Document