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

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

Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection

The heat transport and corresponding changes in the large-scale circulation (LSC) in turbulent Rayleigh-B\'{e}nard convection are studied by means of three-dimensional direct numerical simulations as a function of the aspect ratio $\Gamma$ of a closed cylindrical cell and the Rayleigh number $Ra$. For small and moderate aspect ratios, the global heat transfer law $Nu=A\times Ra^{\beta}$ shows a power law dependence of both fit coefficients $A$ and $\beta$ on the aspect ratio. A minimum Nusselt number coincides with the point where the LSC undergoes a transition from a single-roll to a double-roll pattern. With increasing aspect ratio, we detect complex multi-roll LSC configurations. The aspect ratio dependence of the turbulent heat transfer for small and moderate $\Gamma$ is in line with a varying amount of energy contained in the LSC, as quantified by the Proper Orthogonal Decomposition analysis. For $\Gamma\gtrsim 8$ the heat transfer becomes independent of the aspect ratio.Comment: 17 pages, 11 Postscript figures (in parts downscaled), accepted for J. Fluid Mec

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

Numerical Solution of Nonlinear Fractional Volterra Integro-Differential Equations via Bernoulli Polynomials

This paper presents a computational approach for solving a class of nonlinear Volterra integro-differential equations of fractional order which is based on the Bernoulli polynomials approximation. Our method consists of reducing the main problems to the solution of algebraic equations systems by expanding the required approximate solutions as the linear combination of the Bernoulli polynomials. Several examples are given and the numerical results are shown to demonstrate the efficiency of the proposed method

Differential diagnosis of decreased bone density in an infant without fractures and genetic tests. An autopsy report

Decreased bone density is classically associated with the osteogenesis imperfecta (OI) group of disorders, rickets, and malabsorption. The morphological evaluation, especially without genetic testing and detailed previous medical documentation, is difficult. Hematoxylin and eosin, and special stains give details on the changes in the bone matrix and the severity of dysmorphological bone formation. Herein we present a case report of a diseased infant with surgically corrected ileal atresia and impaired bone formation, without any other morphological changes in the internal organs. Interpretation of the changes, on the background of the lacking medical documentation and genetic tests, was based on the pathophysiological mechanisms of malabsorption and non-specific changes observed and reported in the OI spectrum of disorders

Understanding the mechanisms of dietary restriction to extend healthy lifespan in Drosophila melanogaster.

Dietary restriction (DR), defined as a moderate reduction in food intake short of malnutrition, has been shown to extend healthy lifespan in a diverse range of organisms, from yeast to primates. In this work we aim to uncover the mechanism by which DR extends lifespan. The prevailing theory of somatic maintenance by resource reallocation proposes that the balance of nutrient allocation is weighted either towards reproduction, when environmental nutrients are abundant, or towards maintenance of the soma when food is limited, thereby aiding organismal survival during food shortages. This theory has found support in reports that dietary restricted Drosophila melanogaster (fruit fly) benefit from increased lifespan but have compromised reproduction, and that the inverse is true of fully fed flies. It has recently been found that addition of the ten essential amino acids (EAA) to a DR diet is sufficient to decrease lifespan and increase fecundity to the same degree as full feeding, implicating EAAs as the dietary mediators of the responses of lifespan and fecundity to DR. In this thesis I characterise the physiological and metabolic parameters that define DR flies, fully fed flies and EAA-supplemented DR flies, with the aim of identifying candidate factors that consistently correlate with lifespan for the three treatments in order to identify the causes of longer life in response to DR. We also use genetic tools to explore the role of nutrient signalling pathways in mediating the relationship between nutrition and ageing, with special focus on the amino acid sensitive target of rapamycin (TOR) pathway, the insulin/insulin-like growth factor signalling (IIS) pathway, and the general amino acid control (GAAC) pathway. These studies find a role for TOR signalling in mediating the effects of DR on lifespan and this effect appears to be different from those caused by altered IIS and GAAC pathways. These data also implicate accumulation of fat as consistently correlated with, and so possibly causal for, longer life. Finally, I investigated the potential roles that these nutrient sensing/signalling pathways might play in modifying feeding behaviour in response to changes in dietary nutrient quality. Here, the GAAC pathway proved to play an important and specific role in the way single amino acid deficient foods are detected to alter feeding behavior. These data are somewhat consistent with mammalian studies on nutrient-specific feeding alterations and establish the groundwork for detailed studies into the molecular processes involved. As a combined body of work, this thesis outlines important data on the mechanisms of DR to extend life as well as new information about the nutrients and molecular signals involved in shaping feeding choices