scholarly journals Vegetated mixing layer around a finite-size patch of submerged plants: Part 2. Turbulence statistics and structures

2012 ◽  
Vol 48 (12) ◽  
Author(s):  
Alexander N. Sukhodolov ◽  
Tatiana A. Sukhodolova
Keyword(s):  
Mixing Layer ◽  
Finite Size ◽  
Submerged Plants ◽  
Turbulence Statistics

Dynamics of buoyancy-driven flows at moderately high Atwood numbers

2016 ◽  
Vol 795 ◽  
pp. 313-355 ◽  
Author(s):  
Bhanesh Akula ◽  
Devesh Ranjan
Keyword(s):  
Volume Fraction ◽  
Mixing Layer ◽  
Mie Scattering ◽  
Splitter Plate ◽  
Total Probability ◽  
Reynolds Stresses ◽  
Turbulence Statistics ◽  
Velocity Statistics ◽  
Anisotropy Tensor ◽  
Atwood Number

Simultaneous density and velocity turbulence statistics for Rayleigh–Taylor-driven flows at a moderately high Atwood number ($A_{t}$) of $0.73\pm 0.02$ are obtained using a new convective type or statistically steady gas tunnel facility. Air and air–helium mixture are used as working fluids to create a density difference in this facility, with a thin splitter plate separating the two streams flowing parallel to each other at the same velocity ($U=3~\text{m}~\text{s}^{-1}$). At the end of the splitter plate, the two miscible fluids are allowed to mix and the instability develops. Visualization and Mie-scattering techniques are used to obtain structure shape, volume fraction profile and mixing height growth information. Particle image velocimetry (PIV) and hot-wire techniques are used to measure planar and point-wise velocity statistics in the developing mixing layer. Asymmetry is evident in the flow field from the Mie-scattering images, with the spike side showing a more gradual decline in volume fraction than the bubble side. The spike side of the mixing layer grows 50 % faster than the bubble side. PIV is implemented for the first time in these moderately high-Atwood-number experiments ($A_{t}>0.1$) to obtain root-mean-square velocities, anisotropy tensor components and Reynolds stresses across the mixing layer. Overall, the turbulence statistics measured have shown different scaling compared to small-Atwood-number experiments. However, the total probability density functions for the velocities and turbulent mass fluxes exhibit behaviour similar to small-Atwood-number experiments. Conditional statistics reveal different values for turbulence statistics for spikes and bubbles, unlike small-Atwood-number experiments.

The mixing layer and its coherence examined from the point of view of two-dimensional turbulence

1988 ◽  
Vol 192 ◽  
pp. 511-534 ◽  
Author(s):  
Marcel Lesieur ◽  
Chantal Staquet ◽  
Pascal Le Roy ◽  
Pierre Comte
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
White Noise ◽  
Mixing Layer ◽  
Finite Size ◽  
Spanwise Direction ◽  
Computational Domain ◽  
Two Dimensional ◽  
Infinite Domain ◽  
Kinetic Energy Spectrum

A two-dimensional numerical large-eddy simulation of a temporal mixing layer submitted to a white-noise perturbation is performed. It is shown that the first pairing of vortices having the same sign is responsible for the formation of a continuous spatial longitudinal energy spectrum of slope between k−4 and k−3. After two successive pairings this spectral range extends to more than 1 decade. The vorticity thickness, averaged over several calculations differing by the initial white-noise realization, is shown to grow linearly, and eventually saturates. This saturation is associated with the finite size of the computational domain.We then examine the predictability of the mixing layer, considering the growth of decorrelation between pairs of flows differing slightly at the first roll-up. The inverse cascade of error through the kinetic energy spectrum is displayed. The error rate is shown to grow exponentially, and saturates together with the levelling-off of the vorticity thickness growth. Extrapolation of these results leads to the conclusion that, in an infinite domain, the two fields would become completely decorrelated. It turns out that the two-dimensional mixing layer is an example of flow that is unpredictable and possesses a broadband kinetic energy spectrum, though composed mainly of spatially coherent structures.It is finally shown how this two-dimensional predictability analysis can be associated with the growth of a particular spanwise perturbation developing on a Kelvin-Helmholtz billow: this is done in the framework of a one-mode spectral truncation in the spanwise direction. Within this analogy, the loss of two-dimensional predictability would correspond to a return to three-dimensionality and a loss of coherence. We indicate also how a new coherent structure could then be recreated, using an eddy-viscosity assumption and the linear instability of the mean inflexional shear.

scholarly journals Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics

2014 ◽  
Vol 748 ◽  
pp. 113-142 ◽  
Author(s):  
M. Lombardini ◽  
D. I. Pullin ◽  
D. I. Meiron
Keyword(s):  
Turbulent Mixing ◽  
Spherical Surface ◽  
Density Ratio ◽  
Mixing Layer ◽  
Inertial Subrange ◽  
Planar Geometry ◽  
Late Time ◽  
Mean Flow ◽  
Turbulence Statistics ◽  
Decaying Turbulence

AbstractWe present large-eddy simulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial shock Mach number $\approx $1.2, the density ratio (precisely $|A_0|\approx 0.67$) and the perturbation shape (dominant spherical wavenumber $\ell _0=40$ and amplitude-to-initial radius of 3 %): the incident shock travels from the lighter fluid to the heavy one, or inversely, from the heavy to the light fluid. In Part 1 (Lombardini, M., Pullin, D. I. & Meiron, D. I., J. Fluid Mech., vol. 748, 2014, pp. 85–112), we described the computational problem and presented results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. In particular, it was shown that both configurations reach similar convergence ratios $\approx $2. Here, turbulent mixing is studied through various turbulence statistics. The mixing activity is first measured through two mixing parameters, the mixing fraction parameter $\varTheta $ and the effective Atwood ratio $A_e$, which reach similar late time values in both light–heavy and heavy–light configurations. The Taylor-scale Reynolds numbers attained at late times are estimated at approximately 2000 in the light–heavy case and 1000 in the heavy–light case. An analysis of the density self-correlation $b$, a fundamental quantity in the study of variable-density turbulence, shows asymmetries in the mixing layer and non-Boussinesq effects generally observed in high-Reynolds-number Rayleigh–Taylor (RT) turbulence. These traits are more pronounced in the light–heavy mixing layer, as a result of its flow history, in particular because of RT-unstable phases (see Part 1). Another measure distinguishing light–heavy from heavy–light mixing is the velocity-to-scalar Taylor microscales ratio. In particular, at late times, larger values of this ratio are reported in the heavy–light case. The late-time mixing displays the traits some of the traits of the decaying turbulence observed in planar Richtmyer–Meshkov (RM) flows. Only partial isotropization of the flow (in the sense of turbulent kinetic energy (TKE) and dissipation) is observed at late times, the Reynolds normal stresses (and, thus, the directional Taylor microscales) being anisotropic while the directional Kolmogorov microscales approach isotropy. A spectral analysis is developed for the general study of statistically isotropic turbulent fields on a spherical surface, and applied to the present flow. The resulting angular power spectra show the development of an inertial subrange approaching a Kolmogorov-like $-5/3$ power law at high wavenumbers, similarly to the scaling obtained in planar geometry. It confirms the findings of Thomas & Kares (Phys. Rev. Lett., vol. 109, 2012, 075004) at higher convergence ratios and indicates that the turbulent scales do not seem to feel the effect of the spherical mixing-layer curvature.

A numerical investigation of the coherent vortices in turbulence behind a backward-facing step

1993 ◽  
Vol 256 ◽  
pp. 1-25 ◽  
Author(s):  
Aristeu Silveira Neto ◽  
Dominique Grand ◽  
Olivier Métais ◽  
Marcel Lesieur
Keyword(s):  
Mixing Layer ◽  
Large Eddy Simulations ◽  
Three Dimensions ◽  
Scale Model ◽  
Backward Facing Step ◽  
Turbulence Statistics ◽  
Longitudinal Vortices ◽  
Large Eddy ◽  
Coherent Vortices ◽  
Subgrid Scale Model

This paper presents a statistical and topological study of a complex turbulent flow over a backward-facing step by means of direct and large-eddy simulations. Direct simulations are first performed for an isothermal two-dimensional case. In this case, shedding of coherent vortices in the mixing layer is demonstrated. Both direct and large-eddy simulations are then carried out in three dimensions. The subgrid-scale model used is the structure-function model proposed by Métais & Lesieur (1992). Lowstep computations corresponding to the geometry of Eaton & Johnston's (1980) laboratory experiment give turbulence statistics in better agreement with the experimental data than both Smagorinsky's method and K-ε modelling. Furthermore, calculations for a high step show that the eddy structure of the flow presents striking analogies with forced plane mixing layers: large billows are shed behind the step with intense longitudinal vortices strained between them.

The partial realization theory of finite size two-dimensional arrays

1981 ◽  
Vol 64 (10) ◽  
pp. 1-8
Author(s):  
Tsuyoshi Matsuo ◽  
Yasumichi Hasegawa ◽  
Yoshikuni Okada
Keyword(s):  
Finite Size ◽  
Two Dimensional ◽  
Realization Theory

Ignition of a reactive mixing layer

1999 ◽  
Vol 96 (6) ◽  
pp. 1016-1021 ◽  
Author(s):  
C. Nicoli ◽  
P. Haldenwang ◽  
B. Denet
Keyword(s):  
Mixing Layer ◽  
Reactive Mixing
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