Lagrangian tracer dynamics in a closed cylindrical turbulent convection cell

Turbulent Rayleigh-Benard convection in a closed cylindrical cell is studied in the Lagrangian frame of reference with the help of three-dimensional direct numerical simulations. The aspect ratio of the cell Gamma is varied between 1 and 12, and the Rayleigh number Ra between 10^7 and 10^9. The Prandtl number Pr is fixed at 0.7. It is found that both the pair dispersion of the Lagrangian tracer particles and the statistics of the acceleration components measured along the particle trajectories depend on the aspect ratio for a fixed Rayleigh number for the parameter range covered in our studies. This suggests that large-scale circulations present in the convection cell affect the Lagrangian dynamics. Our findings are in qualitative agreement with existing Lagrangian laboratory experiments on turbulent convection.Comment: 10 pages, 11 Postscript figure

Small-scale statistics in turbulent Rayleigh-Benard convection

Zusammenfassung:Anhand direkter numerischer Simulationen (DNS) werden detaillierte Untersuchungen in turbulenter Rayleigh-Bénard Konvektion in einer zylindrischen Zelle mit isothermen oberen und unteren Platten und adiabatischen Seitenwänden durchgeführt. Die Schwerpunkte der Untersuchungen sind die Statistiken der Temperatur T, ihrer Fluktuationen θ, und ihrer Gradienten; die Statistik der thermischen Dissipationsrate εT und ihre Skalierung mit der Rayleigh-Zahl Ra; die Abhängigkeit des Wärmetransports vom Seitenverhältnis der Zelle Γ und damit zusammenhängende Änderungen in der großskaligen Zirkulation (GSZ) sowie die Lagrangesche Teilchendynamik in Konvektion. Die Simulationsparameter sind Ra = 107 − 109, Γ = 0.5 − 12 und die Prandtl-Zahl Pr = 0.7. Die Wahrscheinlichkeitsdichtefunktionen (WDF) von T und θ weichen in allen Regionen der Zelle vom Gaußschen Fall ab. Anhand der Schiefe von ∂zθ konnte die Rückkehr der kleinskaligen Turbulenz zur lokalen Isotropie mit zunehmender Ra im Innern der Zelle festgestellt werden. Ähnlich wie beim skalaren Mischen, weicht die WDF der thermischen Dissipationsrate der Temperaturfluktuationen, εθ, von der Log-Normalform ab. Die WDFs sind stets gestreckte exponentielle Verteilungen, deren Schweife mit wachsender Ra auf Grund zunehmender kleinskaliger Intermittenz weiter werden. Der Grad der Intermittenz ist stärker sowohl in der thermischen Grenzschicht (TGS) als auch im Volumen. Er ist stets stärker im Seitenwandbereich als im Innern der Zelle. Darüber hinaus liefert εθ nicht nur im Volumen den dominanten Beitrag zur Gesamtdissipation, sondern trägt auch in der TGS signifikant bei. Das Potenzgesetz 〈εT〉 ~ Raζ ergibt immer einen negativen Exponenten ζ, sowohl im Volumen als auch in von Plumes beherrschten Gebieten und im turbulenten Hintergrund. Das steht im Gegensatz zur Skalentheorie des Wärmetransports, stimmt aber gut mit Experimenten überein. Die Nusselt-Zahl, Nu, folgt dem Gesetz Nu = A(Γ)×Raβ(Γ), mit einer Potenzgesetz-Abhängigkeit der Parameter A und β. Das Minimum der Kurve Nu(Γ) liegt genau dort wo die GSZ einen Übergang von einer großen Rolle zu zwei hat. Nu(Γ) variiert zwischen 3%–11% und wird geometrieunabhängig für Γ ≥≈ 8. Die Muster im vollen turbulenten Regime haben Ähnlichkeit mit Strukturen im schwach nichtlinearen Regime. Fünfeckige bzw. sechseckige im Rollen werden beobachtet, wenn Γ ≥ 8. Die Lagrangesche Teilchendispersion in Konvektion zeigt einen Übergang vom ballistischen Regime zum Richardson-Regime, jedoch kein Taylor-Regime auf Grund die Endlichkeit der Konvektionszelle. Die Existenz des Richardsonregimes hängt sensitiv vom Anfangsabstand der Teilchen im Paar ab, ähnlich wie in homogen isotroper Turbulenz. Unser Interpolationsschema gibt die Nusseltzahlen im Lagrangeschen Bezugssystem richtig wieder. Die Statisitik der Komponenten des Beschleunigungsvektors ist sehr intermittent ähnlich zu isotroper Turbulenz. Alle drei Verteilungen fallen im Gegensatz zur Konvektion in einer unendlich ausgedehnten Strömgungsschicht zusammen

Resolving the fine-scale structure in turbulent Rayleigh-Benard convection

We present high-resolution direct numerical simulation studies of turbulent Rayleigh-Benard convection in a closed cylindrical cell with an aspect ratio of one. The focus of our analysis is on the finest scales of convective turbulence, in particular the statistics of the kinetic energy and thermal dissipation rates in the bulk and the whole cell. The fluctuations of the energy dissipation field can directly be translated into a fluctuating local dissipation scale which is found to develop ever finer fluctuations with increasing Rayleigh number. The range of these scales as well as the probability of high-amplitude dissipation events decreases with increasing Prandtl number. In addition, we examine the joint statistics of the two dissipation fields and the consequences of high-amplitude events. We also have investigated the convergence properties of our spectral element method and have found that both dissipation fields are very sensitive to insufficient resolution. We demonstrate that global transport properties, such as the Nusselt number, and the energy balances are partly insensitive to insufficient resolution and yield correct results even when the dissipation fields are under-resolved. Our present numerical framework is also compared with high-resolution simulations which use a finite difference method. For most of the compared quantities the agreement is found to be satisfactory.Comment: 33 pages, 24 figure

Scaling relations in large-Prandtl-number natural thermal convection

In this study we follow Grossmann and Lohse, Phys. Rev. Lett. 86 (2001), who derived various scalings regimes for the dependence of the Nusselt number $Nu$ and the Reynolds number $Re$ on the Rayleigh number $Ra$ and the Prandtl number $Pr$. We focus on theoretical arguments as well as on numerical simulations for the case of large-$Pr$ natural thermal convection. Based on an analysis of self-similarity of the boundary layer equations, we derive that in this case the limiting large-$Pr$ boundary-layer dominated regime is I$_\infty^<$, introduced and defined in [1], with the scaling relations $Nu\sim Pr^0\,Ra^{1/3}$ and $Re\sim Pr^{-1}\,Ra^{2/3}$. Our direct numerical simulations for $Ra$ from $10^4$ to $10^9$ and $Pr$ from 0.1 to 200 show that the regime I$_\infty^<$ is almost indistinguishable from the regime III$_\infty$, where the kinetic dissipation is bulk-dominated. With increasing $Ra$, the scaling relations undergo a transition to those in IV$_u$ of reference [1], where the thermal dissipation is determined by its bulk contribution

Mean Temperature Profiles in Turbulent Thermal Convection

To predict the mean temperature profiles in turbulent thermal convection, the thermal boundary layer (BL) equation including the effects of fluctuations has to be solved. In Shishkina et al., Phys. Rev. Lett. 114 (2015), the thermal BL equation with the fluctuations taken into account as an eddy thermal diffusivity has been solved for large Prandtl-number fluids for which the eddy thermal diffusivity and the velocity field can be approximated respectively as a cubic and a linear function of the distance from the plate. In the present work we make use of the idea of Prandtl's mixing length model and relate the eddy thermal diffusivity to the stream function. With this proposed relation, we can solve the thermal BL equation and obtain a closed-form expression for the dimensionless mean temperature profile in terms of two independent parameters for fluids with a general Prandtl number. With a proper choice of the parameters, our predictions of the temperature profiles are in excellent agreement with the results of our direct numerical simulations for a wide range of Prandtl numbers from 0.01 to 2547.9 and Rayleigh numbers from 10^7 to 10^9.Comment: 8 pages, 4 figure

User interaction with online information resources: an informetrics approach

This research strived to investigate and provide answer to these questions: how researchers interact with online information resources when they search for information to meet their information needs. The research also intended to address the issues and problems involved in information retrieval to provide an appropriate solution to their challenges. We have conducted a qualitative approach to the investigation. We carried out interview to collect data. In this way, we chose and interviewed the 15 most informed scholars who normally interact with information and resources. Results indicated that the use of web-based information resources is dominants among researchers. Researchers were more likely to get the resources they needed from social networks. Consulting the databases and scientific social networks such as Google Scholar was common. Among the online information resources, the use of academic journals, specialized and public libraries website and online resources and personal repositories has been among highly commended resources. Among the challenges that researchers have had in using information sources was that some of resource titles did not reveal information within them. Researchers were to search for hours and days to find the information seekers and users. Lack of standarized format for searching information in search engines for databases lead researchers to misinformation, and most of interviewees complained about this matter. Results also showed that researchers categorize the retrieved information into four components: 1. Explicit useful information 2. Hidden useful information 3. Explicit inappropriate information 4. Explicit Disturbing information Findings advice information systems policy makers to adjust their propositions on the information behavior of the new generation researchers and online residents and revise their indexing and collection development guidelines