scholarly journals The influence of far field stratification on shear-induced turbulent mixing

2021 ◽  
Vol 928 ◽  
Author(s):  
S.F. Lewin ◽  
C.P. Caulfield
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Richardson Number ◽  
Scaling Laws ◽  
Mixing Efficiency ◽  
Far Field ◽  
Mixing Rate ◽  
Gradient Richardson Number ◽  
Background Density ◽  
Secondary Instabilities

We compare the properties of the turbulence induced by the breakdown of Kelvin–Helmholtz instability (KHI) at high Reynolds number in two classes of stratified shear flows where the background density profile is given by either a linear function or a hyperbolic tangent function, at different values of the minimum initial gradient Richardson number ${{Ri}}_0$ . Considering global and local measures of mixing defined in terms of either the irreversible mixing rate $\mathscr {M}$ associated with the time evolution of the background potential energy, or an appropriately defined density variance dissipation rate $\chi$ , we find that the proliferation of secondary instabilities strongly affects the efficiency of mixing early in the flow evolution, and also that these secondary instabilities are highly sensitive to flow perturbations that are added at the point of maximal (two-dimensional) billow amplitude. Nevertheless, mixing efficiency does not appear to depend strongly on the far field density structure, a feature supported by the evolution of local horizontally averaged values of the buoyancy Reynolds number ${Re}_b$ and gradient Richardson number ${Ri}_g$ . We investigate the applicability of various proposed scaling laws for flux coefficients $\varGamma$ in terms of characteristic length scales, in particular discussing the relevance of the overturning ‘Thorpe scale’ in stratified turbulent flows. Finally, we compare a variety of empirical model parameterizations used to compute diapycnal diffusivity in an oceanographic context, arguing that for transient flows such as KHI-induced turbulence, simple models that relate the ‘age’ of a turbulent event to its mixing efficiency can produce reasonably robust mixing estimates.

scholarly journals Numerical Analysis of the Heterogeneity Effect on Electroosmotic Micromixers Based on the Standard Deviation of Concentration and Mixing Entropy Index

Micromachines ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 1055
Author(s):  
Alireza Farahinia ◽  
Jafar Jamaati ◽  
Hamid Niazmand ◽  
Wenjun Zhang
Keyword(s):  
Reynolds Number ◽  
Zeta Potential ◽  
Electroosmotic Flow ◽  
Molecular Diffusion ◽  
Slip Surface ◽  
Reynolds Numbers ◽  
Mixing Efficiency ◽  
Slip Coefficient ◽  
Mixing Rate ◽  
Heterogeneous Distribution

One approach to achieve a homogeneous mixture in microfluidic systems in the quickest time and shortest possible length is to employ electroosmotic flow characteristics with heterogeneous surface properties. Mixing using electroosmotic flow inside microchannels with homogeneous walls is done primarily under the influence of molecular diffusion, which is not strong enough to mix the fluids thoroughly. However, surface chemistry technology can help create desired patterns on microchannel walls to generate significant rotational currents and improve mixing efficiency remarkably. This study analyzes the function of a heterogeneous zeta-potential patch located on a microchannel wall in creating mixing inside a microchannel affected by electroosmotic flow and determines the optimal length to achieve the desired mixing rate. The approximate Helmholtz–Smoluchowski model is suggested to reduce computational costs and simplify the solving process. The results show that the heterogeneity length and location of the zeta-potential patch affect the final mixing proficiency. It was also observed that the slip coefficient on the wall has a more significant effect than the Reynolds number change on improving the mixing efficiency of electroosmotic micromixers, benefiting the heterogeneous distribution of zeta-potential. In addition, using a channel with a heterogeneous zeta-potential patch covered by a slip surface did not lead to an adequate mixing in low Reynolds numbers. Therefore, a homogeneous channel without any heterogeneity would be a priority in such a range of Reynolds numbers. However, increasing the Reynolds number and the presence of a slip coefficient on the heterogeneous channel wall enhances the mixing efficiency relative to the homogeneous one. It should be noted, though, that increasing the slip coefficient will make the mixing efficiency decrease sharply in any situation, especially in high Reynolds numbers.

Revisiting the Turbulent Prandtl Number in an Idealized Atmospheric Surface Layer

2015 ◽  
Vol 72 (6) ◽  
pp. 2394-2410 ◽  
Author(s):  
Dan Li ◽  
Gabriel G. Katul ◽  
Sergej S. Zilitinkevich
Keyword(s):  
Surface Layer ◽  
Prandtl Number ◽  
Turbulent Flows ◽  
Richardson Number ◽  
Atmospheric Surface Layer ◽  
Scaling Laws ◽  
Atmospheric Stability ◽  
Turbulent Prandtl Number ◽  
Energy Distributions ◽  
Turbulent Eddies

Abstract Cospectral budgets are used to link the kinetic and potential energy distributions of turbulent eddies, as measured by their spectra, to macroscopic relations between the turbulent Prandtl number (Prt) and atmospheric stability measures such as the stability parameter ζ, the gradient Richardson number Rg, or the flux Richardson number Rf in the atmospheric surface layer. The dependence of Prt on ζ, Rg, or Rf is shown to be primarily controlled by the ratio of Kolmogorov and Kolmogorov–Obukhov–Corrsin phenomenological constants and a constant associated with isotropization of turbulent flux production that can be independently determined using rapid distortion theory in homogeneous turbulence. Changes in scaling laws of the vertical velocity and air temperature spectra are also shown to affect the Prt–ζ (or Prt–Rg or Prt–Rf) relation. Results suggest that departure of Prt from unity under neutral conditions is induced by dissimilarity between momentum and heat in terms of Rotta constants, isotropization constants, and constants in the flux transfer terms. A maximum flux Richardson number Rfm predicted from the cospectral budgets method (=0.25) is in good agreement with values in the literature, suggesting that Rfm may be tied to the collapse of Kolmogorov spectra instead of laminarization of turbulent flows under stable stratification. The linkages between microscale energy distributions of turbulent eddies and macroscopic relations that are principally determined by dimensional considerations or similarity theories suggest that when these scalewise energy distributions of eddies experience a “transition” to other distributions (e.g., when Rf is increased over Rfm), dimensional considerations or similarity theories may fail to predict bulk flow properties.

scholarly journals Turbulent mixing due to the Holmboe wave instability at high Reynolds number

2016 ◽  
Vol 803 ◽  
pp. 591-621 ◽  
Author(s):  
Hesam Salehipour ◽  
C. P. Caulfield ◽  
W. R. Peltier
Keyword(s):  
Reynolds Number ◽  
Richardson Number ◽  
Initial Density ◽  
Finite Amplitude ◽  
Transition To Turbulence ◽  
Wave Instability ◽  
Length Scales ◽  
Density Interface ◽  
Gradient Richardson Number ◽  
High Reynolds

We consider numerically the transition to turbulence and associated mixing in stratified shear flows with initial velocity distribution $\overline{U}(z,0)\,\boldsymbol{e}_{x}=U_{0}\,\boldsymbol{e}_{x}\tanh (z/d)$ and initial density distribution $\overline{\unicode[STIX]{x1D70C}}(z,0)=\unicode[STIX]{x1D70C}_{0}[1-\tanh (z/\unicode[STIX]{x1D6FF})]$ away from a hydrostatic reference state $\unicode[STIX]{x1D70C}_{r}\gg \unicode[STIX]{x1D70C}_{0}$. When the ratio $R=d/\unicode[STIX]{x1D6FF}$ of the characteristic length scales over which the velocity and density vary is equal to one, this flow is primarily susceptible to the classic well-known Kelvin–Helmholtz instability (KHI). This instability, which typically manifests at finite amplitude as an array of elliptical vortices, strongly ‘overturns’ the density interface of strong initial gradient, which nevertheless is the location of minimum initial gradient Richardson number $Ri_{g}(0)=Ri_{b}=g\unicode[STIX]{x1D70C}_{0}d/\unicode[STIX]{x1D70C}_{r}U_{0}^{2}$, where $Ri_{g}(z)=-([g/\unicode[STIX]{x1D70C}_{r}]\,\text{d}\overline{\unicode[STIX]{x1D70C}}/\text{d}z)/(\text{d}\overline{U}/\text{d}z)^{2}$ and $Ri_{b}$ is a bulk Richardson number. As is well known, at sufficiently high Reynolds numbers ($Re$), the primary KHI induces a vigorous but inherently transient burst of turbulence and associated irreversible mixing localised in the vicinity of the density interface, leading to a relatively well-mixed region bounded by stronger density gradients above and below. We explore the qualitatively different behaviour that arises when $R\gg 1$, and so the density interface is sharp, with $Ri_{g}(z)$ now being maximum at the density interface $Ri_{g}(0)=RRi_{b}$. This flow is primarily susceptible to Holmboe wave instability (HWI) (Holmboe, Geophys. Publ., vol. 24, 1962, pp. 67–113), which manifests at finite amplitude in this symmetric flow as counter-propagating trains of elliptical vortices above and below the density interface, thus perturbing the interface so as to exhibit characteristically cusped interfacial waves which thereby ‘scour’ the density interface. Unlike previous lower-$Re$ experimental and numerical studies, when $Re$ is sufficiently high the primary HWI becomes increasingly more three-dimensional due to the emergence of shear-aligned secondary convective instabilities. As $Re$ increases, (i) the growth rate of secondary instabilities appears to saturate and (ii) the perturbation kinetic energy exhibits a $k^{-5/3}$ spectrum for sufficiently large length scales that are influenced by anisotropic buoyancy effects. Therefore, at sufficiently high $Re$, vigorous turbulence is triggered that also significantly ‘scours’ the primary density interface, leading to substantial irreversible mixing and vertical transport of mass above and below the (robust) primary density interface. Furthermore, HWI produces a markedly more long-lived turbulence event compared to KHI at a similarly high $Re$. Despite their vastly different mechanics (i.e. ‘overturning’ versus ‘scouring’) and localisation, the mixing induced by KHI and HWI is comparable in both absolute terms and relative efficiency. Our results establish that, provided the flow Reynolds number is sufficiently high, shear layers with sharp density interfaces and associated locally high values of the gradient Richardson number may still be sites of substantial and efficient irreversible mixing.

Flux Richardson number measurements in stable atmospheric shear flows

2002 ◽  
Vol 459 ◽  
pp. 307-316 ◽  
Author(s):  
E. R. PARDYJAK ◽  
P. MONTI ◽  
H. J. S. FERNANDO
Keyword(s):  
Boundary Layer ◽  
Richardson Number ◽  
Salt Lake ◽  
National Laboratory ◽  
Salt Lake City ◽  
Field Studies ◽  
Large Reynolds Number ◽  
Mixing Efficiency ◽  
Data Set ◽  
Gradient Richardson Number

The flux Richardson number Rf (also known as the mixing efficiency) for the stably stratified atmospheric boundary layer is investigated as a function of the gradient Richardson number Rig using data taken during two field studies: the Vertical Transport and Mixing Experiment (VTMX) in Salt Lake City, Utah (October 2000), and a long-term rural field data set from Technical Area 6 (TA-6) at Los Alamos National Laboratory, New Mexico. The results show the existence of a maximum Rf (0.4–0.5) at a gradient Richardson number of approximately unity. These large-Reynolds-number results agree well with recent laboratory stratified shear layer measurements, but are at odds with some commonly used Rf parameterizations, particularly under high-Rig conditions. The observed variations in buoyancy flux and turbulent kinetic energy production are consistent with the concept of global intermittency of the atmospheric stable boundary layer.

Streamwise Curvature Effect on the Incompressible Turbulent Mean Velocity Over Curved Surfaces

2000 ◽  
Vol 122 (3) ◽  
pp. 547-551 ◽  
Author(s):  
N. Kim ◽  
D. L. Rhode
Keyword(s):  
Turbulent Flows ◽  
Richardson Number ◽  
Solution Technique ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Streamline Curvature ◽  
Curvature Effects ◽  
Gradient Richardson Number ◽  
The Mean ◽  
Strong Curvature

A curvature law of the wall, which determines the mean velocity profile, is analytically derived for near-wall turbulent flows to include strong curved-channel wall curvature effects through a perturbation analysis. The new law allows improved analysis of such flows, and it provides the basis for improved wall function boundary conditions for their computation (CFD), even for strong curvature cases. The improved law is based on the algebraic eddy viscosity and curvature-corrected mixing length concepts, the latter of which is a linear function of the gradient Richardson number. To include the complete Richardson number effects, the local streamline curvature effects in the gradient Richardson number are kept. To overcome the mathematical difficulty of keeping all of these local streamline curvature terms, an innovative nonconstant-parameter perturbation solution technique is successfully applied. [S0098-2202(00)00903-2]

Experimental Study of Mixing and Entrainment in a Horizontal Turbulent Stratified Jet

2014 ◽  
Author(s):  
Duo Xu ◽  
Jun Chen
Keyword(s):  
Experimental Data ◽  
Experimental Study ◽  
High Resolution ◽  
Richardson Number ◽  
Mixing Efficiency ◽  
Statistical Relationship ◽  
Gradient Richardson Number ◽  
Theoretical Predictions

The mixing efficiency, flux Richardson number Rif, is investigated in a horizontally injected turbulent stratified jet with a co-existence of stable and unstable stratifications. The high resolution experimental data from a developed laser-based technique show the statistical relationship between Rif and the gradient Richardson number Rig. In addition, the data are used to study the development of entrainment by two approaches, and compared with theoretical predictions.

scholarly journals Scaling analysis and simulation of strongly stratified turbulent flows

2007 ◽  
Vol 585 ◽  
pp. 343-368 ◽  
Author(s):  
G. BRETHOUWER ◽  
P. BILLANT ◽  
E. LINDBORG ◽  
J.-M. CHOMAZ
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Turbulent Flows ◽  
Scaling Laws ◽  
Three Dimensional ◽  
Direct Numerical Simulations ◽  
Small Scale ◽  
Scaling Analysis ◽  
Length Scale ◽  
Stratified Turbulence

Direct numerical simulations of stably and strongly stratified turbulent flows with Reynolds number Re ≫ 1 and horizontal Froude number Fh ≪ 1 are presented. The results are interpreted on the basis of a scaling analysis of the governing equations. The analysis suggests that there are two different strongly stratified regimes according to the parameter $\mathcal{R} \,{=}\, \hbox{\it Re} F^2_h$. When $\mathcal{R} \,{\gg}\, 1$, viscous forces are unimportant and lv scales as lv ∼ U/N (U is a characteristic horizontal velocity and N is the Brunt–Väisälä frequency) so that the dynamics of the flow is inherently three-dimensional but strongly anisotropic. When $\mathcal{R} \,{\ll}\, 1$, vertical viscous shearing is important so that $l_v \,{\sim}\, l_h/\hbox{\it Re}^{1/2}$ (lh is a characteristic horizontal length scale). The parameter $\cal R$ is further shown to be related to the buoyancy Reynolds number and proportional to (lO/η)4/3, where lO is the Ozmidov length scale and η the Kolmogorov length scale. This implies that there are simultaneously two distinct ranges in strongly stratified turbulence when $\mathcal{R} \,{\gg}\, 1$: the scales larger than lO are strongly influenced by the stratification while those between lO and η are weakly affected by stratification. The direct numerical simulations with forced large-scale horizontal two-dimensional motions and uniform stratification cover a wide Re and Fh range and support the main parameter controlling strongly stratified turbulence being $\cal R$. The numerical results are in good agreement with the scaling laws for the vertical length scale. Thin horizontal layers are observed independently of the value of $\cal R$ but they tend to be smooth for $\cal R$< 1, while for $\cal R$ > 1 small-scale three-dimensional turbulent disturbances are increasingly superimposed. The dissipation of kinetic energy is mostly due to vertical shearing for $\cal R$ < 1 but tends to isotropy as $\cal R$ increases above unity. When $\mathcal{R}$ < 1, the horizontal and vertical energy spectra are very steep while, when $\cal R$ > 1, the horizontal spectra of kinetic and potential energy exhibit an approximate k−5/3h-power-law range and a clear forward energy cascade is observed.

On drag reduction scaling and sustainability bounds of superhydrophobic surfaces in high Reynolds number turbulent flows

2019 ◽  
Vol 864 ◽  
pp. 327-347 ◽  
Author(s):  
Amirreza Rastegari ◽  
Rayhaneh Akhavan
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Scaling Laws ◽  
Base Flow ◽  
Geometrical Parameters ◽  
Pressure Stability ◽  
High Reynolds

The drag reduction characteristics and sustainability bounds of superhydrophobic (SH) surfaces in high Reynolds number turbulent flows are investigated using results from direct numerical simulation (DNS) and scaling-law analysis. The DNS studies were performed, using lattice Boltzmann methods, in turbulent channel flows at bulk Reynolds numbers of $Re_{b}=3600$ ($Re_{\unicode[STIX]{x1D70F}_{0}}\approx 222$) and $Re_{b}=7860$ ($Re_{\unicode[STIX]{x1D70F}_{0}}\approx 442$) with SH longitudinal microgrooves or SH aligned microposts on the walls. Surface microtexture geometrical parameters corresponding to microgroove widths or micropost spacings of $4\lesssim g^{+0}\lesssim 128$ in base flow wall units and solid fractions of $1/64\leqslant \unicode[STIX]{x1D719}_{s}\leqslant 1/2$ were investigated at interface protrusion angles of $\unicode[STIX]{x1D703}_{p}=0^{\circ }$ and $\unicode[STIX]{x1D703}_{p}=-30^{\circ }$. Analysis of the governing equations and DNS results shows that the magnitude of drag reduction is not only a function of the geometry and size of the surface microtexture in wall units, but also the Reynolds number of the base flow. A Reynolds number independent measure of drag reduction can be constructed by parameterizing the magnitude of drag reduction in terms of the friction coefficient of the base flow and the shift, $(B-B_{0})$, in the intercept of a logarithmic law representation of the mean velocity profile in the flow with SH walls compared to the base flow, where $(B-B_{0})$ is Reynolds number independent. The scaling laws for $(B-B_{0})$, in terms of the geometrical parameters of the surface microtexture in wall units, are presented for SH longitudinal microgrooves and aligned microposts. The same scaling laws are found to also apply to liquid-infused (LI) surfaces as long as the viscosity ratios are large, $N\equiv \unicode[STIX]{x1D707}_{o}/\unicode[STIX]{x1D707}_{i}\gtrsim 10$. These scaling laws, in conjunction with the parametrization of drag reduction in terms of $(B-B_{0})$, allow for a priori prediction of the magnitude of drag reduction with SH or LI surfaces in turbulent flow at any Reynolds number. For the most stable of these SH surface microtextures, namely, longitudinal microgrooves, the pressure stability bounds of the SH surface under the pressure loads of turbulent flow are investigated. It is shown that the pressure stability bounds of SH surfaces are also significantly curtailed with increasing Reynolds number of the flow. Using these scaling laws, the narrow range of SH surface geometrical parameters which can yield large drag reduction as well as sustainability in high Reynolds number turbulent flows is identified.

Simulating flow separation from continuous surfaces: routes to overcoming the Reynolds number barrier

2009 ◽  
Vol 367 (1899) ◽  
pp. 2885-2903 ◽  
Author(s):  
Michael Leschziner ◽  
Ning Li ◽  
Fabrizio Tessicini
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Major Elements ◽  
Wall Layer ◽  
Navier Stokes ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Rans Models ◽  
High Reynolds ◽  
Near Wall

This paper provides a discussion of several aspects of the construction of approaches that combine statistical (Reynolds-averaged Navier–Stokes, RANS) models with large eddy simulation (LES), with the objective of making LES an economically viable method for predicting complex, high Reynolds number turbulent flows. The first part provides a review of alternative approaches, highlighting their rationale and major elements. Next, two particular methods are introduced in greater detail: one based on coupling near-wall RANS models to the outer LES domain on a single contiguous mesh, and the other involving the application of the RANS and LES procedures on separate zones, the former confined to a thin near-wall layer. Examples for their performance are included for channel flow and, in the case of the zonal strategy, for three separated flows. Finally, a discussion of prospects is given, as viewed from the writer's perspective.

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