Simulation of shear orientation effects on stably stratified homogeneous turbulence with RANS second-order modelling

2009 ◽  
Vol 10 ◽  
pp. N43
Author(s):  
J. C.F. Pereira ◽  
J. M.P Rocha
Keyword(s):  
Second Order ◽  
Homogeneous Turbulence ◽  
Orientation Effects ◽  
Shear Orientation

scholarly journals A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors

2015 ◽  
Vol 788 ◽  
pp. 147-182 ◽  
Author(s):  
Vincent Mons ◽  
Claude Cambon ◽  
Pierre Sagaut
Keyword(s):  
Turbulent Flows ◽  
Computational Cost ◽  
Second Order ◽  
Homogeneous Turbulence ◽  
Spectral Model ◽  
Polarization Anisotropy ◽  
Mean Flow ◽  
Correlation Tensor ◽  
Directional Anisotropy ◽  
Flow Gradients

A nonlinear spectral model in terms of spherically averaged descriptors is derived for the prediction of homogeneous turbulence dynamics in the presence of arbitrary mean-velocity gradients. The governing equations for the tensor $\hat{\unicode[STIX]{x1D619}}_{ij}(\boldsymbol{k},t)$, the Fourier transform of the two-point second-order correlation tensor, are first closed by an anisotropic eddy-damped quasinormal Markovian procedure. This closure is restricted to turbulent flows where linear effects induced by mean-flow gradients have no essential qualitative effects on the dynamics of triple correlations compared with the induced production effects in the equations for second-order correlations. Truncation at the first relevant order of spectral angular dependence allows us to derive from these equations in vector $\boldsymbol{k}$ our final model equations in terms of the wavenumber modulus $k$ only. Analytical spherical integration results in a significant decrease in computational cost. Besides, the model remains consistent with the decomposition in terms of directional anisotropy and polarization anisotropy, with a spherically averaged anisotropic spectral tensor for each contribution. Restriction of anisotropy to spherically averaged descriptors, however, entails a loss of information, and realizability conditions are considered to quantify the upper boundary of anisotropy that can be investigated with the proposed model. Several flow configurations are considered to assess the validity of the present model. Satisfactory agreement with experiments on grid-generated turbulence subjected to successive plane strains is observed, which confirms the capability of the model to account for production of anisotropy by mean-flow gradients. The nonlinear transfer terms of the model are further tested by considering the return to isotropy (RTI) of different turbulent flows. Different RTI rates for directional anisotropy and polarization anisotropy allow us to correctly predict the apparent delayed RTI shown after axisymmetric expansion. The last test case deals with homogeneous turbulence subjected to a constant pure plane shear. The interplay between linear and nonlinear effects is reproduced, yielding the eventual exponential growth of the turbulent kinetic energy.

scholarly journals Statistical State Dynamics of Weak Jets in Barotropic Beta-Plane Turbulence

2019 ◽  
Vol 76 (3) ◽  
pp. 919-945 ◽  
Author(s):  
Nikolaos A. Bakas ◽  
Navid C. Constantinou ◽  
Petros J. Ioannou
Keyword(s):  
Second Order ◽  
Homogeneous Turbulence ◽  
Nonlinear Flow ◽  
Flow Forming ◽  
Ginzburg Landau ◽  
Linear Flow ◽  
Weakly Nonlinear ◽  
Zonal Jets ◽  
Statistical State ◽  
Wide Range

Abstract Zonal jets in a barotropic setup emerge out of homogeneous turbulence through a flow-forming instability of the homogeneous turbulent state (zonostrophic instability), which occurs as the turbulence intensity increases. This has been demonstrated using the statistical state dynamics (SSD) framework with a closure at second order. Furthermore, it was shown that for small supercriticality the flow-forming instability follows Ginzburg–Landau (G–L) dynamics. Here, the SSD framework is used to study the equilibration of this flow-forming instability for small supercriticality. First, we compare the predictions of the weakly nonlinear G–L dynamics to the fully nonlinear SSD dynamics closed at second order for a wide range of parameters. A new branch of jet equilibria is revealed that is not contiguously connected with the G–L branch. This new branch at weak supercriticalities involves jets with larger amplitude compared to the ones of the G–L branch. Furthermore, this new branch continues even for subcritical values with respect to the linear flow-forming instability. Thus, a new nonlinear flow-forming instability out of homogeneous turbulence is revealed. Second, we investigate how both the linear flow-forming instability and the novel nonlinear flow-forming instability are equilibrated. We identify the physical processes underlying the jet equilibration as well as the types of eddies that contribute in each process. Third, we propose a modification of the diffusion coefficient of the G–L dynamics that is able to capture the evolution of weak jets at scales other than the marginal scale (side-band instabilities) for the linear flow-forming instability.

scholarly journals Thermo-molecular orientation effects in fluids of dipolar dumbbells

2014 ◽  
Vol 16 (40) ◽  
pp. 22097-22106 ◽  
Author(s):  
Christopher D. Daub ◽  
Per-Olof Åstrand ◽  
Fernando Bresme
Keyword(s):  
Molecular Orientation ◽  
Second Order ◽  
First Order ◽  
Orientation Effects

Plots of first-order (left) and novel second-order (right) thermomolecular orientation effects in fluids of dipolar dumbbells.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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