Anomalous transport of a passive scalar at the transition to dynamical chaos in a barotropic shear layer

2019 ◽  
Vol 74 ◽  
pp. 211-218 ◽  
Author(s):  
V.P. Reutov ◽  
G.V. Rybushkina
Keyword(s):  
Shear Layer ◽  
Passive Scalar ◽  
Anomalous Transport ◽  
Dynamical Chaos

scholarly journals How the turbulent/non-turbulent interface is different from internal turbulence

2019 ◽  
Vol 866 ◽  
pp. 216-238 ◽  
Author(s):  
G. E. Elsinga ◽  
C. B. da Silva
Keyword(s):  
Shear Layer ◽  
Flow Pattern ◽  
Large Scale ◽  
Layer Structure ◽  
Compressive Strain ◽  
Turbulent Jets ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Flow Topology ◽  
Definition Of

The average patterns of the velocity and scalar fields near turbulent/non-turbulent interfaces (TNTI), obtained from direct numerical simulations (DNS) of planar turbulent jets and shear free turbulence, are assessed in the strain eigenframe. These flow patterns help to clarify many aspects of the flow dynamics, including a passive scalar, near a TNTI layer, that are otherwise not easily and clearly assessed. The averaged flow field near the TNTI layer exhibits a saddle-node flow topology associated with a vortex in one half of the interface, while the other half of the interface consists of a shear layer. This observed flow pattern is thus very different from the shear-layer structure consisting of two aligned vortical motions bounded by two large-scale regions of uniform flow, that typically characterizes the average strain field in the fully developed turbulent regions. Moreover, strain dominates over vorticity near the TNTI layer, in contrast to internal turbulence. Consequently, the most compressive principal straining direction is perpendicular to the TNTI layer, and the characteristic 45-degree angle displayed in internal shear layers is not observed at the TNTI layer. The particular flow pattern observed near the TNTI layer has important consequences for the dynamics of a passive scalar field, and explains why regions of particularly high scalar gradient (magnitude) are typically found at TNTIs separating fluid with different levels of scalar concentration. Finally, it is demonstrated that, within the fully developed internal turbulent region, the scalar gradient exhibits an angle with the most compressive straining direction with a peak probability at around 20$^{\text{o}}$. The scalar gradient and the most compressive strain are not preferentially aligned, as has been considered for many years. The misconception originated from an ambiguous definition of the positive directions of the strain eigenvectors.

scholarly journals Dynamical Chaos and Lateral Transport of a Passive Scalar in the Annular Reverse Jet Flow

2021 ◽  
Vol 17 (3) ◽  
pp. 263-274
Author(s):  
V. P. Reutov ◽  
◽  
G. V. Rybushkina ◽  
Keyword(s):  
Lyapunov Exponent ◽  
Cross Flow ◽  
Passive Scalar ◽  
Jet Flow ◽  
Wave Generation ◽  
Critical Parameters ◽  
Dynamical Chaos ◽  
Lateral Transport ◽  
Frequency Spectra ◽  
Flow Transport

The transition to dynamical chaos and the related lateral (cross-flow) transport of a passive scalar in the reverse annular jet flow generating two chains of wave-vortex structures are studied. The quasi-geostrophic equations for the barotropic (quasi-two-dimensional) flow written in polar coordinates with allowance for the beta-effect and external friction are solved numerically using a pseudospectral method. The critical parameters of the equilibrium flow with a complex “two-hump” azimuth velocity profile facilitating a faster transition to the complex dynamics are determined. Two regular multiharmonic regimes of wave generation are revealed with increasing flow supercriticality before the onset of Eulerian chaos. The occurrence of the complex flow dynamics is confirmed by a direct calculation of the largest Lyapunov exponent. The evolution of streamline images is analyzed by making video, thereby chains with single and composite structures are distinguished. The wavenumber-frequency spectra confirming the possibility of chaotic transport of the passive scalar are drawn for the basic regimes of wave generation. The power law exponents for the azimuth particle displacement and their variance, which proved the occurrence of the anomalous azimuth transport of the passive scalar, are determined. Lagrangian chaos is studied by computing the finite-time Lyapunov exponent and its distribution function. The internal chain (with respect to the annulus center) is found to be totally subject to Lagrangian chaos, while only the external chain boundary is chaotic. It is revealed that the cross-flow transport occurs only in the regime of Eulerian dynamical chaos, since there exists a barrier to it in the multiharmonic regimes. The images of fluid particles confirming the presence of lateral transport are obtained and their quantitative characteristics are determined.

Passive scalar mixing in Mc <1 planar shear layer flows

2015 ◽  
Vol 123 ◽  
pp. 32-43 ◽  
Author(s):  
Bing Wang ◽  
Wei Wei ◽  
Yunlong Zhang ◽  
Huiqiang Zhang ◽  
Shuyan Xue
Keyword(s):  
Shear Layer ◽  
Passive Scalar ◽  
Scalar Mixing ◽  
Planar Shear

Mechanisms of transition and heat transfer in a separation bubble

2000 ◽  
Vol 403 ◽  
pp. 329-349 ◽  
Author(s):  
PHILIPPE R. SPALART ◽  
MICHAEL KH. STRELETS
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shear Layer ◽  
Skin Friction ◽  
Separation Bubble ◽  
Passive Scalar ◽  
Reynolds Analogy ◽  
Transition Mechanism ◽  
Displacement Thickness ◽  
Uniform Wall

The laminar boundary layer on a flat surface is made to separate by way of aspiration through an opposite boundary, causing approximately a 25% deceleration. The detached shear layer transitions to turbulence, reattaches, and evolves towards a normal turbulent boundary layer. We performed the direct numerical simulation (DNS) of this flow, and believe that a precise experimental repeat is possible. The pressure distribution and the Reynolds number based on bubble length are close to those on airfoils; numerous features are in agreement with Gaster's and other experiments and correlations. At transition a large negative surge in skin friction is seen, following weak negative values and a brief contact with zero; this could be described as a turbulent re-separation. Temperature is treated as a passive scalar, first with uniform wall temperature and then with uniform wall heat flux. The transition mechanism involves the wavering of the shear layer and then Kelvin–Helmholtz vortices, which instantly become three-dimensional without pairing, but not primary Görtler vortices. The possible dependence of the DNS solution on the residual incoming disturbances, which we keep well below 0.1%, and on the presence of a ‘hard’ opposite boundary, are discussed. We argue that this flow, unlike the many transitional flows which hinge on a convective instability, is fully specified by just three parameters: the amount of aspiration, and the streamwise and the depth Reynolds numbers (heat transfer adds the Prandtl number). This makes comparisons meaningful, and relevant to separation bubbles on airfoils in low-disturbance environments. We obtained Reynolds-averaged Navier–Stokes (RANS) results with simple turbulence models and spontaneous transition. The agreement on skin friction, displacement thickness, and pressure is rather good, which we attribute to the simple nature of ‘transition by contact’ due to flow reversal. In contrast, a surge of the heat-transfer coefficient violates the Reynolds analogy, and is greatly under-predicted by the models.

scholarly journals Unsteady chains of wave structures and anomalous transport of а passive scalar in a barotropic jet flow

2019 ◽  
Vol 55 (6) ◽  
pp. 201-210
Author(s):  
V. P. Reutov ◽  
G. V. Rybushkina
Keyword(s):  
Complex Dynamics ◽  
Tracer Particle ◽  
Pseudospectral Method ◽  
Passive Scalar ◽  
Jet Flow ◽  
Anomalous Transport ◽  
Zonal Flows ◽  
Beta Effect ◽  
Two Dimensional Flow ◽  
And Diffusion

The onset of anomalous transport of a passive scalar at the excitation of unsteady chains of wave structures with closed streamlines in a barotropic jet flow modeling zonal flows in the Earths atmosphere and ocean and in laboratory experiments is investigated. The analysis is performed within a dynamical model describing saturation of the barotropic instability in a plane-parallel channel flow with allowance for the beta-effect and external friction. The equations of a quasi-two-dimensional flow are solved numerically with the aid of a pseudospectral method. It is found that the generation of high modes in a jet with a two-hump velocity profile leads to accelerated transition to the complex dynamics, at which an increase in supercriticality first gives rise to а multiharmonic regime with a discrete spectrum. The exponents of the power dependence on the time of the averaged (over the ensemble) tracer particle displacement and its variance are computed for the basic generation regimes, which confirms the occurrence of anomalous diffusion of the scalar. A self-similar probability density function of tracer displacements is obtained and the dependence of the transition to complex dynamics on the number of vortices in the chain and on the strength of the beta-effect is elucidated. Numerical estimates are presented, which confirm the possibility of generation of unsteady vortex chains and the related anomalous transport of the scalar.barotropic flow; chains of wave structures; dynamical chaos; anomalous advection and diffusion

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