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

Law of the wall in an unstably stratified turbulent channel flow

We perform direct numerical simulations of an unstably stratified turbulent channel flow to address the effects of buoyancy on the boundary layer dynamics and mean field quantities. We systematically span a range of parameters in the space of friction Reynolds number ($Re_{\tau}$) and Rayleigh number ($Ra$). Our focus is on deviations from the logarithmic law of the wall due to buoyant motion. The effects of convection in the relevant ranges are discussed providing measurements of mean profiles of velocity, temperature and Reynolds stresses as well as of the friction coefficient. A phenomenological model is proposed and shown to capture the observed deviations of the velocity profile in the log-law region from the non-convective case

New subgrid-scale models for large-eddy simulation of Rayleigh-Bénard convection

Published under licence in Journal of Physics: Conference Series by IOP Publishing Ltd. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.At the crossroad between flow topology analysis and the theory of turbulence, a new eddy-viscosity model for Large-eddy simulation has been recently proposed by Trias et al.[PoF, 27, 065103 (2015)]. The S3PQR-model has the proper cubic near-wall behaviour and no intrinsic limitations for statistically inhomogeneous flows. In this work, the new model has been tested for an air turbulent Rayleigh-Benard convection in a rectangular cell of aspect ratio unity and n span-wise open-ended distance. To do so, direct numerical simulation has been carried out at two Rayleigh numbers Ra = 108 and 1010, to assess the model performance and investigate a priori the effect of the turbulent Prandtl number. Using an approximate formula based on the Taylor series expansion, the turbulent Prandtl number has been calculated and revealed a constant and Ra-independent value across the bulk region equals to 0.55. It is found that the turbulent components of eddy-viscosity and eddy-diffusivity are positively prevalent to maintain a turbulent wind essentially driven by the mean buoyant force at the sidewalls. On the other hand, the new eddy-viscosity model is preliminary tested for the case of Ra = 108 and showed overestimation of heat flux within the boundary layer but fairly good prediction of turbulent kinetics at this moderate turbulent flow.Peer ReviewedPostprint (published version

Large-scale instabilities in a non-rotating turbulent convection

Formation of large-scale coherent structures in a turbulent convection via excitation of large-scale instability is studied. The redistribution of the turbulent heat flux due to non-uniform large-scale motions plays a crucial role in the formation of the coherent large-scale structures in the turbulent convection. The modification of the turbulent heat flux results in strong reduction of the critical Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the excitation of the large-scale instability. The mean-field equations which describe the large-scale instability, are solved numerically. We determine the key parameters that affect formation of the large-scale coherent structures in the turbulent convection. In particular, the degree of thermal anisotropy and the lateral background heat flux strongly modify the growth rates of the large-scale instability, the frequencies of the generated convective-shear waves and change the thresholds required for the excitation of the large-scale instability. This study elucidates the origins of the large-scale circulations and rolls in the atmospheric convective boundary layers and the meso-granular structures in the solar convection.Comment: 13 pages, 13 figures, Physics of Fluids, in pres

Scaling laws for convection and jet speeds in the giant planets

Three-dimensional studies of convection in deep spherical shells have been used to test the hypothesis that the strong jet streams on Jupiter, Saturn, Uranus, and Neptune result from convection throughout the molecular envelopes. Due to computational limitations, these simulations must adopt viscosities and heat fluxes many orders of magnitude larger than the planetary values. Several numerical investigations have identified trends for how the mean jet speed varies with heat flux and viscosity, but no previous theories have been advanced to explain these trends. Here, we show using simple arguments that if convective release of potential energy pumps the jets and viscosity damps them, the mean jet speeds split into two regimes. When the convection is weakly nonlinear, the equilibrated jet speeds should scale approximately with F/nu, where F is the convective heat flux and nu is the viscosity. When the convection is strongly nonlinear, the jet speeds are faster and should scale approximately as (F/nu)^{1/2}. We demonstrate how this regime shift can naturally result from a shift in the behavior of the jet-pumping efficiency with heat flux and viscosity. Moreover, the simulations hint at a third regime where, at sufficiently small viscosities, the jet speed becomes independent of the viscosity. We show based on mixing-length estimates that if such a regime exists, mean jet speeds should scale as heat flux to the 1/4 power. Our scalings provide a good match to the mean jet speeds obtained in previous Boussinesq and anelastic, three-dimensional simulations of convection within giant planets over a broad range of parameters. When extrapolated to the real heat fluxes, these scalings suggest that the mass-weighted jet speeds in the molecular envelopes of the giant planets are much weaker--by an order of magnitude or more--than the speeds measured at cloud level.Comment: 23 pages, 10 figures, in press at Icaru

Nonlinear diffusion model for Rayleigh-Taylor mixing

The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusiviy models for the mean temperature profile. It is found that a non-linear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection.Comment: 4 pages, 4 figure, PRL in pres