arXiv subjects

Ambrish Pandey

Publications and source records attributed to Ambrish Pandey.

30 records · Page 2Linked to original sources

arXiv2018

Turbulent superstructures in Rayleigh-Bénard convection

Turbulent Rayleigh-Bénard convection displays a large-scale order in the form of rolls and cells on lengths larger than the layer height once the fluctuations of temperature and velocity are removed. These turbulent superstructures are reminiscent of the patterns close to the onset of convection. They are analyzed by numerical simulations of turbulent convection in fluids at different Prandtl number ranging from 0.005 to 70 and for Rayleigh numbers up to $10^7$. For each case, we identify characteristic scales and times that separate the fast, small-scale turbulent fluctuations from the gradually changing large-scale superstructures. The characteristic scales of the large-scale patterns, which change with Prandtl and Rayleigh number, are also found to be correlated with the boundary layer dynamics, and in particular the clustering of thermal plumes at the top and bottom plates. Our analysis suggests a scale separation and thus the existence of a simplified description of the turbulent superstructures in geo- and astrophysical settings.

physics.flu-dyn↗

arXiv2017

On the Applicability of Low-Dimensional Models for Convective Flow Reversals at Extreme Prandtl Numbers

Constructing simpler models, either stochastic or deterministic, for exploring the phenomenon of flow reversals in fluid systems is in vogue across disciplines. Using direct numerical simulations and nonlinear time series analysis, we illustrate that the basic nature of flow reversals in convecting fluids can depend on the dimensionless parameters describing the system. Specifically, we find evidence of low-dimensional determinism in flow reversals occurring at zero Prandtl number, whereas we fail to find such signatures for reversals at infinite Prandtl number. Thus, even in a single system, as one varies the system parameters, one can encounter reversals that are fundamentally different in nature. Consequently, we conclude that a single general low-dimensional deterministic model cannot faithfully characterize flow reversals for every set of parameter values.

physics.flu-dyn↗

arXiv2016

Transitional boundary layers in low-Prandtl-number convection

The boundary layer structure of the velocity and temperature fields in turbulent Rayleigh-Benard flows in closed cylindrical cells of unit aspect ratio is revisited from a transitional and turbulent viscous boundary layer perspective. When the Rayleigh number is large enough, the dynamics at the bottom and top plates can be separated into an impact region of downwelling plumes, an ejection region of upwelling plumes and an interior region away from the side walls. The latter is dominated by the shear of the large-scale circulation (LSC) roll which fills the whole cell and continuously varies its orientation. The working fluid is liquid mercury or gallium at a Prandtl number Pr=0.021 for Rayleigh numbers between Ra=3e+5 and 4e+8. The generated turbulent momentum transfer corresponds to macroscopic flow Reynolds numbers with values between 1800 and 46000. It is shown that the viscous boundary layers for the largest Rayleigh numbers are highly transitional and obey properties that are directly comparable to transitional channel flows at friction Reynolds numbers Re_tau slightly below 100. The transitional character of the viscous boundary layer is also underlined by the strong enhancement of the fluctuations of the wall stress components with increasing Rayleigh number. An extrapolation of our analysis data suggests that the friction Reynolds number Re_tau in the velocity boundary layer can reach values of 200 for Ra beyond 1e+11. Thus the viscous boundary layer in a liquid metal flow would become turbulent at a much lower Rayleigh number than for turbulent convection in gases and gas mixtures.

physics.flu-dyn↗

arXiv2016

Phenomenology of buoyancy-driven turbulence: recent results

In this paper, we review the recent developments in the field of buoyancy-driven turbulence. Scaling and numerical arguments show that the stably-stratified turbulence with moderate stratification has kinetic energy spectrum $E_u(k) \sim k^{-11/5}$ and the kinetic energy flux $Π_u(k) \sim k^{-4/5}$, which is called Bolgiano-Obukhov scaling. The energy flux for the Rayleigh-Bénard convection (RBC) however is approximately constant in the inertial range that results in Kolmorogorv's spectrum ($E_u(k) \sim k^{-5/3}$) for the kinetic energy. The phenomenology of RBC should apply to other flows where the buoyancy feeds the kinetic energy, e.g. bubbly turbulence and fully-developed Rayleigh Taylor instability. This paper also covers several models that predict the Reynolds and Nusselt numbers of RBC. Recent works show that the viscous dissipation rate of RBC scales as $\sim \mathrm{Ra}^{1.3}$, where $\mathrm{Ra}$ is the Rayleigh number.

physics.flu-dyn↗

arXiv2016

Scaling of large-scale quantities in Rayleigh-Bénard convection

We derive a formula for the Péclet number ($\mathrm{Pe}$) by estimating the relative strengths of various terms of the momentum equation. Using direct numerical simulations in three dimensions we show that in the turbulent regime, the fluid acceleration is dominated by the pressure gradient, with relatively small contributions arising from the buoyancy and the viscous term, in the viscous regime, acceleration is very small due to a balance between the buoyancy and the viscous term. Our formula for $\mathrm{Pe}$ describes the past experiments and numerical data quite well. We also show that the ratio of the nonlinear term and the viscous term is $\mathrm{Re} \mathrm{Ra}^{-0.14}$, where $\mathrm{Re}$ and $\mathrm{Ra}$ are Reynolds and Rayleigh numbers respectively, and that the viscous dissipation rate $ε_u = (U^3/d) \mathrm{Ra}^{-0.21}$, where $U$ is the root mean square velocity and $d$ is the distance between the two horizontal plates. The aforementioned decrease in nonlinearity compared to free turbulence arises due to the wall effects.

physics.flu-dyn↗

arXiv2016

Dynamics of large-scale quantities in Rayleigh-Bénard convection

In this paper we estimate the relative strengths of various terms of the Rayleigh-Bénard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity, $U$, or the Péclet number that is applicable for arbitrary Rayleigh number $\mathrm{Ra}$ and Prandtl number $\mathrm{Pr}$. Our formula fits reasonably well with the earlier simulation and experimental results. Our analysis also shows that the wall-bounded convection has enhanced viscous force compared to free turbulence. We also demonstrate how correlations deviate the Nusselt number scaling from the theoretical prediction of $\mathrm{Ra}^{1/2}$ to the experimentally observed scaling of nearly $\mathrm{Ra}^{0.3}$.

physics.flu-dyn↗

arXiv2016

Near isotropic behaviour of turbulent thermal convection

We investigate the anisotropy in turbulent convection in a 3D box using direct numerical simulation. We compute the anisotropic parameter $A = u_\perp^{2}/(2u_{\parallel}^{2})$, where $u_{\perp}$ and $u_{\parallel}$ are the components of velocity perpendicular and parallel to the buoyancy direction, the shell and ring spectra, and shell-to-shell energy transfers. We observe that the flow is nearly isotropic for the Prandtl number $\mathrm{Pr} \approx 1$, but the anisotropy increases with the Prandtl number. For $\mathrm{Pr}=\infty$, $A \approx 0.3$, thus anisotropy is not very significant even in extreme cases. We also observe that $u_{\parallel}$ feeds energy to $u_{\perp}$ via pressure. The computation of shell-to-shell energy transfers reveals that the energy transfer in turbulent convection is local and forward, similar to hydrodynamic turbulence. These results are consistent with the Kolmogorov's spectrum observed by Kumar et al.~[Phys. Rev. E {\bf 90}, 023016 (2014)] for turbulent convection.

physics.flu-dyn↗

arXiv2015

Flow reversals in turbulent convection with free-slip walls

We perform numerical simulations of turbulent convection for infinite Prandtl number with free-slip walls, and study the dynamics of flow reversals. We show interesting correlations between the flow reversals and the nonlinear interactions among the large-scale flow structures represented by the modes $(1,1), (2,1), (3,1)$ and some others. After a flow reversal, the odd modes, e.g. $(1,1), (3,1)$, switch sign, but the even modes, e.g. $(2,2)$, retain their sign. The mixed modes $(1,2)$ and $(2,1)$ fluctuate around zero. Using the properties of the modes and their interactions, we show that they form a Klein four-group $Z_2 \times Z_2$. We also show that for the free-slip boundary condition, the corner rolls and vortex reconnection are absent during a flow reversal, in contrast to active role played by them in flow reversals for the no-slip boundary condition. We argue that the flow reversals with the no-slip and free-slip boundary conditions are different because they are induced by nonlinearities $ ({\bf u} \cdot \nabla) {\bf u}$ and $({\bf u} \cdot \nabla) θ$ respectively.

physics.flu-dyn↗

arXiv2014

Similarities between 2D and 3D convection for large Prandtl number

Using direct numerical simulations of Rayleigh-Bénard convection (RBC), we perform a comparative study of the spectra and fluxes of energy and entropy, and the scaling of large-scale quantities for large and infinite Prandtl numbers in two (2D) and three (3D) dimensions. We observe close similarities between the 2D and 3D RBC, in particular the kinetic energy spectrum $E_u(k) \sim k^{-13/3}$, and the entropy spectrum exhibits a dual branch with a dominant $k^{-2}$ spectrum. We showed that the dominant Fourier modes in the 2D and 3D flows are very close. Consequently, the 3D RBC is quasi two-dimensional, which is the reason for the similarities between the 2D and 3D RBC for large- and infinite Prandtl numbers.

physics.flu-dyn↗

arXiv2014

Scaling of heat flux and energy spectrum for "very large" Prandtl number convection

Under the limit of infinite Prandtl number, we derive analytical expressions for the large-scale quantities, e.g., Péclet number Pe, Nusselt number Nu, and rms value of the temperature fluctuations $θ_\mathrm{rms}$. We complement the analytical work with direct numerical simulations, and show that $\mathrm{Nu} \sim \mathrm{Ra}^γ$ with $γ\approx (0.30-0.32)$, $\mathrm{Pe} \sim \mathrm{Ra}^η$ with $η\approx (0.57-0.61)$, and $θ_\mathrm{rms} \sim \mathrm{const}$. The Nusselt number is observed to be an intricate function of $\mathrm{Pe}$, $θ_\mathrm{rms}$, and a correlation function between the vertical velocity and temperature. Using the scaling of large-scale fields, we show that the energy spectrum $E_u(k)\sim k^{-13/3}$, which is in a very good agreement with our numerical results. The entropy spectrum $E_θ(k)$ however exhibits dual branches consisting of $k^{-2}$ and $k^0$ spectra; the $k^{-2}$ branch corresponds to the Fourier modes $\hatθ(0,0,2n)$, which are approximately $-1/(2n π)$. The scaling relations for Prandtl number beyond $10^2$ match with those for infinite Prandtl number.

physics.flu-dyn↗

arXiv2013

Role of Bulk flow in Turbulent Convection

In this paper we present scaling of large-scale quantities like Peclét and Nusselt numbers, and the dissipation rates of kinetic energy and entropy. Our arguments are based on the scaling of bulk quantities and earlier experimental and simulation results. We also present the inertial-range properties of spectra and fluxes of kinetic energy and entropy.

physics.flu-dyn↗

arXiv2012

Field correlations and the ultimate regime of turbulent convection

Using direct numerical simulations of Rayleigh-Bénard convection (RBC) under free-slip boundary condition, we show that the normalized correlation function between the vertical velocity field and the temperature field, as well as the normalized viscous dissipation rate, scales as $Ra^{-0.22}$ for moderately large Rayleigh number $Ra$. This scaling accounts for the Nusselt number ($Nu$) exponent to be around 0.3 observed in experiments. Numerical simulations also reveal that the above normalized correlation functions are constants for the convection simulation under periodic boundary conditions.

physics.flu-dyn↗