This paper provides a detailed study of scale-by-scale budgets in turbulent Rayleigh-Bénard convection and aims at testing the applicability of Kolmogorov (1941) and Bolgiano (1959) theories for this flow. Particular emphasis is laid on anisotropic and inhomogeneous effects: the SO(3) decomposition of structure functions (Arad et al 1999) and a method of description of inhomogeneities proposed by Danaila et al (2001) are used to derive inhomogeneous and anisotropic generalizations of Kolmogorov and Yaglom equations applying to RB convection. The various terms in these equations are computed using data from a DNS of turbulent Boussinesq convection at $\rayleigh=10^6$ and $\prandtl=1$ with aspect ratio A=5. The analysis of the isotropic component demonstrates that the shape of the third-order velocity structure function is significantly influenced by buoyancy forcing and large-scale inhomogeneities, while the mixed third-order structure function appearing in Yaglom equation exhibits a clear scaling exponent 1 in a small range of scales. The magnitudes of the various low $\ell$ degree anisotropic components of the equations are also estimated and are shown to be comparable to their isotropic counterparts at moderate to large scales. Finally, a qualitative analysis shows that the influence of buoyancy forcing at scales smaller than the Bolgiano scale is likely to remain important up to $\rayleigh=10^9$, thus preventing Kolmogorov scalings from showing up in convective flows at lower Rayleigh numbers.
We present the first detailed thermal and velocity field characterization of convection in a rotating cylindrical tank of liquid gallium, which has thermophysical properties similar to those of planetary core fluids. Our laboratory experiments, and a closely associated direct numerical simulation, are all carried out in the regime prior to the onset of steady convective modes. This allows us to study the oscillatory convective modes, sidewall modes and broadband turbulent flow that develop in liquid metals before the advent of steady columnar modes. Our thermo-velocimetric measurements show th…
Gravito-inertial waves can be excited at the interface of convective and radiative regions and by the Reynolds stresses in the bulk of the convection zone. The magnitude of their energy flux will therefore vary with the properties of the convection. To assess how convection changes with rotation, a simplified local monomodal model for rotating convection is presented that provides the magnitude of the rms velocity, degree of superadiabaticity, and characteristic length scale as a function of the convective Rossby number as well as with thermal and viscous diffusivities. In the context of this …
Gravito-inertial waves are excited at the interface of convective and radiative regions and by the Reynolds stresses in the bulk of the convection zones of rotating stars and planets. Such waves have notable asteroseismic signatures in the frequency spectra of rotating stars, particularly among rapidly rotating early-type stars, which provides a means of probing their internal structure and dynamics. They can also transport angular momentum, chemical species, and energy from the excitation region to where they dissipate in radiative regions. To estimate the excitation and convective parameter …
The observation of global acoustic waves (p modes) in the Sun has been key to unveiling its internal structure and dynamics. A different kind of wave, known as sectoral Rossby modes, have been observed and identified, which potentially opens the door to probing internal processes that are inaccessible through p mode helioseismology. Yet another set of waves, appearing as retrograde-propagating, equatorially antisymmetric vorticity waves, have also been observed but their identification remained elusive. Here, through a numerical model implemented as an eigenvalue problem, we provide evidence s…
In this paper, we analyze the scaling of velocity structure functions of turbulent thermal convection. Using high-resolution numerical simulations, we show that the structure functions scale similar to those of hydrodynamic turbulence, with the scaling exponents in agreement with She and Leveque's predictions [Phys. Rev. Lett. 72, 336-339 (1994)]. The probability distribution functions of velocity increments are non-Gaussian with wide tails in the dissipative scales and become close to Gaussian in the inertial range. The tails of the probability distribution follow a stretched exponential. We …
We report for the first time on triadic resonances in a rotating convection system. Using direct numerical simulations, we find that convective modes in a rotating spherical fluid can excite a pair of inertial modes whose frequencies and wavenumbers match the triadic resonance conditions. Depending on the structures of the convective modes, triadic resonances can lead to the growth of either a pair of modes with lower frequencies and wavenumbers, or a pair of modes with higher frequencies and wavenumbers, providing a possible mechanism for the bi-directional energy cascade. Increased thermal f…
The settling behaviour of small inertial particles in turbulent convection is a fundamental problem across several disciplines, from geophysics to metallurgy. In a geophysical context, the settling of dense crystals controls the mode of solidification of magma chambers and planetary-scale magma oceans, while rising of light bubbles of volatiles drives volcanic outgassing and the formation of primordial atmospheres. Motivated by these geophysical systems, we perform a systematic numerical study on the settling rate of particles in a rectangular two-dimensional Rayleigh-Benard system with Raylei…
The dynamic behavior of crystals in convecting fluids determines how magma bodies solidify. In particular, it is often important to estimate how long crystals stay in suspension in the host liquid before being deposited at its bottom (or top, for light particles). We perform a systematic 3D numerical study of particle-laden Rayleigh-Benard convection, and derive a robust model for the particle residence time. For Rayleigh numbers higher than 10^7, inertial particles' trajectories exhibit a monotonic transition from fluid tracer-like to free-fall dynamics, the control parameter being the ratio …
Multiple chaotic and turbulent regimes in Rayleigh-Bénard convection have been studied and classified from the onset of deterministic chaos to the fully developed turbulence using the distributed chaos approach supported by results of laboratory experiments and numerical simulations. It is shown that the regimes can replace each other depending on value of the Rayleigh number and location in the convection cell (in the bulk of the flow or in the boundary layers). The inertial-buoyancy and helicity based invariants play crucial role in the formation of the regimes. Transition from the classical…
Turbulent thermal convection is characterized by the formation of large-scale structures and strong spatial inhomogeneity. This work addresses the relative heat transport contributions of the large-scale plume ejecting versus plume impacting zones in turbulent Rayleigh-Bénard convection. Based on direct numerical simulations of the two dimensional (2-D) problem, we show the existence of a crossover in the wall heat transport from initially impacting dominated to ultimately ejecting dominated at a Rayleigh number of $Ra\approx 3 \times 10^{11}$. This is consistent with the trends observed in 3-…
The onset of convection in the form of magneto-inertial waves in a rotating fluid sphere permeated by a constant axial electric current is studied through a perturbation analysis. Explicit expressions for the dependence of the Rayleigh number on the azimuthal wavenumber are derived in the limit of high thermal diffusivity. Results for the case of thermally infinitely conducting boundaries and for the case of nearly thermally insulating boundaries are obtained.
Thermal convection of fluid is a more efficient way than diffusion to carry heat from hot sources to cold places. Here, we experimentally study the Rayleigh-Bénard convection of aqueous glycerol solution in a cubic cell with suspensions of rod-like particles made of polydimethylsiloxane (PDMS). The particles are inertial due to their large thermal expansion coefficient and finite sizes. The thermal expansion coefficient of the particles is three times larger than that of the background fluid. This contrast makes the suspended particles lighter than the local fluid in hot regions and heavier in…
Effects of quasi-point vortices on the inertial range of scales in homogeneous two-dimensional turbulence (classic and quantum) have been studied using the notion of distributed chaos. Results of direct numerical simulations of decaying turbulence, turbulence with small-scale forcing, and turbulent thermal convection on a sphere as well as results of the Global Atmospheric Sampling Program (GASP) measurements in the tropospheric and stratospheric turbulence over mountainous terrain (the small-scale forcing) have been used for this purpose. The superfluid and Bose-Einstein two-dimensional turbu…
We analyze the Prandtl number (Pr) dependence of spectra and fluxes of kinetic energy, as well as the energy injection rates and dissipation rates, of turbulent thermal convection using numerical data. As expected, for a flow with $ \mathrm{Pr} \lessapprox 1 $, the inertial-range kinetic energy flux is constant, and the kinetic energy spectrum is Kolmogorov-like ($ k^{-5/3} $). More importantly, we show that the amplitudes of the kinetic energy fluxes and spectra and those of structure functions increase with the decrease of Pr, thus exhibiting stronger nonlinearity for flows with small Prandt…
We discuss two aspects of turbulent Rayleigh-Bénard convection (RBC) on the basis of high-resolution direct numerical simulations in a unique setting; a closed cylindrical cell of aspect ratio of one. First, we present a comprehensive comparison of statistical quantities such as energy dissipation rates and boundary layer thickness scales. Data are used from three simulation run series at Prandtl numbers $Pr$ that cover two orders of magnitude. In contrast to most previous studies in RBC the focus of the present work is on convective turbulence at very low Prandtl numbers including $Pr=0.021$ …
Fully developed forced convective flow in a channel filled with porous material bounded by two impermeable walls subject to constant heat flux is considered. We consider Brinkman-Forchhimer equation to govern the flow inside the porous medium which accounts for the presence of inertial term. We assume that the porous medium is anisotropic in nature and permeability is varying along all the directions, correspondingly, permeability will be a matrix which appear as a positive semi-definite matrix in the momentum equation. The anisotropic nature of the porous medium is characterized by anisotropi…
The dynamics of inertial particles in Rayleigh-Bénard convection, where both particles and fluid exhibit thermal expansion, is studied using direct numerical simulations (DNS). We consider the effect of particles with a thermal expansion coefficient larger than that of the fluid, causing particles to become lighter than the fluid near the hot bottom plate and heavier than the fluid near the cold top plate. Because of the opposite directions of the net Archimedes' force on particles and fluid, particles deposited at the plate now experience a relative force towards the bulk. The characteristic …
The radial gradient of the rotation rate in the near-surface shear layer (NSSL) of the Sun is independent of latitude and radius. Theoretical mean-field models have been successful in explaining this property of the solar NSSL, while global direct convection models have been unsuccessful. We investigate reason for this discrepancy by measuring the mean flows, Reynolds stress, and turbulent transport coefficients under NSSL conditions. Simulations have minimal ingredients. These ingredients are inhomogeneity due to boundaries, anisotropic turbulence, and rotation. Parameters of the simulations …
