Searcharxiv⌕ Search

arXiv subjects

Guenter Ahlers

Publications and source records attributed to Guenter Ahlers.

At least 19 recordsLinked to original sources
arXiv2019

Boundary Zonal Flow in Rotating Turbulent Rayleigh-Bénard Convection

For rapidly rotating turbulent Rayleigh--Bénard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like $Ra^{1/4}Ek^{2/3}$ where the Ekman number $Ek$ decreases with increasing rotation rate.

physics.flu-dyn↗
arXiv2016

Azimuthal diffusion of the large-scale-circulation plane, and absence of significant non-Boussinesq effects, in turbulent convection near the ultimate-state transition

We present measurements of the orientation $θ_0$ and temperature amplitude $δ$ of the large-scale circulation in a cylindrical sample of turbulent Rayleigh-Benard convection (RBC) with aspect ratio $Γ\equiv D/L = 1.00$ ($D$ and $L$ are the diameter and height respectively) and for the Prandtl number $Pr \simeq 0.8$. Results for $θ_0$ revealed a preferred orientation with upflow in the West, consistent with a broken azimuthal invariance due to Earth's Coriolis force [see \cite{BA06b}]. They yielded the azimuthal diffusivity $D_θ$ and a corresponding Reynolds number $Re_θ$ for Rayleigh numbers over the range $2\times 10^{12} < Ra < 1.5\times 10^{14}$. In the classical state ($Ra < 2\times 10^{13}$) the results were consistent with the measurements by \cite{BA06a} for $Ra < 10^{11}$ and $Pr = 4.38$ which gave $Re_θ \propto Ra^{0.28}$, and with the Prandtl-number dependence $Re_θ \propto Pr^{-1.2}$ as found previously also for the velocity-fluctuation Reynolds number $Re_V$ \cite[]{HGBA15b}. At larger $Ra$ the data for $Re_θ(Ra)$ revealed a transition to a new state, known as the "ultimate" state, which was first seen in the Nusselt number $Nu(Ra)$ and in $Re_V(Ra)$ at $Ra^*_1 \simeq 2\times 10^{13}$ and $Ra^*_2 \simeq 8\times 10^{13}$. In the ultimate state we found $Re_θ \propto Ra^{0.40\pm 0.03}$. Recently \cite{SU15} claimed that non-Oberbeck-Boussinesq effects on the Nusselt and Reynolds numbers of turbulent RBC may have been interpreted erroneously as a transition to a new state. We demonstrate that their reasoning is incorrect and that the transition observed in the Göttingen experiments and discussed in the present paper is indeed to a new state of RBC referred to as "ultimate".

physics.flu-dyn↗
arXiv2014

Logarithmic Spatial Variations and Universal $f^{-1}$ Power Spectra of Temperature Fluctuations in Turbulent Rayleigh-Bénard Convection

We report measurements of the temperature variance $σ^2(z,r)$ and frequency power spectrum $P(f,z,r)$ ($z$ is the distance from the sample bottom and $r$ the radial coordinate) in turbulent Rayleigh-Bénard convection (RBC) for Rayleigh numbers $\textrm{Ra} = 1.6\times10^{13}$ and $1.1\times10^{15}$ and for a Prandtl number $\textrm{Pr} \simeq 0.8$ for a sample with a height $L = 224$ cm and aspect ratio $D/L = 0.50$ ($D$ is the diameter). For $z/L$ less than or similar to $0.1$ $σ^2(z,r)$ was consistent with a logarithmic dependence on $z$, and there was a universal (independent of $\textrm{Ra}$, $r$, and $z$) normalized spectrum which, for $0.02$ less than or similar to $fτ_0$ less than or similar to $0.2$, had the form $P(fτ_0) = P_0 (fτ_0)^{-1}$ with $P_0 =0.208 \pm 0.008$ a universal constant. Here $τ_0 = \sqrt{2R}$ where $R$ is the radius of curvature of the temperature autocorrelation function $C(τ)$ at $τ= 0$. For $z/L \simeq 0.5$ the measurements yielded $P(fτ_0) \sim (fτ_0)^{-α}$ with $α$ in the range from 3/2 to 5/3. All the results are similar to those for velocity fluctuations in shear flows at sufficiently large Reynolds numbers, suggesting the possibility of an analogy between the flows that is yet to be determined in detail.

physics.flu-dyn↗
arXiv2014

Logarithmic temperature profiles of turbulent Rayleigh-Bénard convection in the classical and ultimate state for a Prandtl number of 0.8

We report on experimental determinations of the temperature field in the interior (bulk) of turbulent Rayleigh-Benard convection for a cylindrical sample with aspect ratio (diameter over height) of 0.50, both in the classical and in the ultimate state. The Prandtl number was close to 0.8. We find a "logarithmic layer" in which the temperature varies as A*ln(z/L) + B with the distance z from the bottom plate of the sample. The amplitude A varies with radial position r. In the classical state these results are in good agreement with direct numerical simulations (DNS); in the ultimate state there are as yet no DNS. A close analogy between the temperature field in the classical state and the "Law of the Wall" for the time-averaged down-stream velocity in shear flow is discussed.

physics.flu-dyn↗
arXiv2012

Effect of tilting on turbulent convection: Cylindrical samples with aspect ratio $Γ=0.50$

We report measurements of properties of turbulent thermal convection of a fluid with a Prandtl number $\Pra=4.38$ in a cylindrical cell with an aspect ratio $Γ=0.50$. The rotational symmetry was broken by a small tilt of the sample axis relative to gravity. Measurements of the heat transport (as expressed by the Nusselt number \Nu), as well as of large-scale-circulation (LSC) properties by means of temperature measurements along the sidewall, are presented. In contradistinction to similar experiments using containers of aspect ratio $Γ=1.00$ \cite[]{ABN06} and $Γ=0.50$ \cite[]{CRCC04,SXX05,RGKS10}, we see a very small increase of the heat transport for tilt angles up to about 0.1 rad. Based on measurements of properties of the LSC we explain this increase by a stabilization of the single-roll state (SRS) of the LSC and a de-stabilization of the double-roll state (DRS) (it is known from previous work that the SRS has a slightly larger heat transport than the DRS). Further, we present quantitative measurements of the strength of the LSC, its orientation, and its torsional oscillation as a function of the tilt angle.

physics.flu-dyn↗
arXiv2012

Heat transport by turbulent Rayleigh-Bénard convection for $\Pra\ \simeq 0.8$ and $4\times 10^{11} \alt \Ra\ \alt 2\times10^{14}$: Ultimate-state transition for aspect ratio $Γ= 1.00$

We report experimental results for heat-transport measurements by turbulent Rayleigh-Bénard convection in a cylindrical sample of aspect ratio $Γ\equiv D/L = 1.00$ ($D = 1.12$ m is the diameter and $L = 1.12$ m the height). They are for the Rayleigh-number range $4\times10^{11} \alt \Ra \alt 2\times10^{14}$ and for Prandtl numbers \Pra\ between 0.79 and 0.86. For $\Ra < \Ra^*_1 \simeq 2\times 10^{13}$ we find $\Nu = N_0 \Ra^{γ_{eff}}$ with $γ_{eff} = 0.321 \pm 0.002$ and $N_0 = 0.0776$, consistent with classical turbulent Rayleigh-Bénard convection in a system with laminar boundary layers below the top and above the bottom plate and with the prediction of Grossmann and Lohse. For $\Ra > \Ra_1^*$ the data rise above the classical-state power-law and show greater scatter. In analogy to similar behavior observed for $Γ= 0.50$, we interpret this observation as the onset of the transition to the ultimate state. Within our resolution this onset occurs at nearly the same value of $\Ra_1^*$ as it does for $Γ= 0.50$. This differs from an earlier estimate by Roche {\it et al.} which yielded a transition at $\Ra_U \simeq 1.3\times 10^{11} Γ^{-2.5\pm 0.5}$. A $Γ$-independent $\Ra^*_1$ would suggest that the boundary-layer shear transition is induced by fluctuations on a scale less than the sample dimensions rather than by a global $Γ$-dependent flow mode. Within the resolution of the measurements the heat transport above $\Ra_1^*$ is equal for the two $Γ$ values, suggesting a universal aspect of the ultimate-state transition and properties. The enhanced scatter of \Nu\ in the transition region, which exceeds the experimental resolution, indicates an intrinsic irreproducibility of the state of the system.

physics.flu-dyn↗
arXiv2012

Heat transport by turbulent Rayleigh-Bénard convection for $\Pra\ \simeq 0.8$ and $3\times 10^{12} \alt \Ra\ \alt 10^{15}$: Aspect ratio $Γ= 0.50$

We report experimental results for heat-transport measurements, in the form of the Nusselt number \Nu, by turbulent Rayleigh-Bénard convection in a cylindrical sample of aspect ratio $Γ\equiv D/L = 0.50$ ($D = 1.12$ m is the diameter and $L = 2.24$ m the height). The measurements were made using sulfur hexafluoride at pressures up to 19 bars as the fluid. They are for the Rayleigh-number range $3\times 10^{12} \alt \Ra \alt 10^{15}$ and for Prandtl numbers \Pra\ between 0.79 and 0.86. For $\Ra < \Ra^*_1 \simeq 1.4\times 10^{13}$ we find $\Nu = N_0 \Ra^{γ_{eff}}$ with $γ_{eff} = 0.312 \pm 0.002$, consistent with classical turbulent Rayleigh-Bénard convection in a system with laminar boundary layers below the top and above the bottom plate. For $\Ra^*_1 < \Ra < \Ra^*_2$ (with $\Ra^*_2 \simeq 5\times 10^{14}$) $γ_{eff}$ gradually increases up to $0.37\pm 0.01$. We argue that above $\Ra^*_2$ the system is in the ultimate state of convection where the boundary layers, both thermal and kinetic, are also turbulent. Several previous measurements for $Γ= 0.50$ are re-examined and compared with the present results.

physics.flu-dyn↗
arXiv2012

Logarithmic temperature profiles in turbulent Rayleigh-Bénard convection

We report results for the temperature profiles of turbulent Rayleigh-Bénard convection (RBC) in the interior of a cylindrical sample of aspect ratio $Γ\equiv D/L = 0.50$ ($D$ and $L$ are the diameter and height respectively). Results from experiment over the Rayleigh number range $4\times 10^{12} \alt Ra \alt 10^{15}$ for a Prandtl number $\Pra \simeq 0.8$ and from direct numerical simulation (DNS) at $Ra = 2 \times 10^{12}$ for $\Pra = 0.7$ are presented. We find that the temperature varies as $A*ln(z/L) + B$ where $z$ is the distance from the bottom or top plate. This is the case in the classical as well as in the ultimate state of RBC. From DNS we find that $A$ in the classical state decreases in the radial direction as the distance from the side wall increases and becomes small near the sample center.

physics.flu-dyn↗
arXiv2011

Finite-size effects lead to supercritical bifurcations in turbulent rotating Rayleigh-Bénard convection

In turbulent thermal convection in cylindrical samples of aspect ratio Γ= D/L (D is the diameter and L the height) the Nusselt number Nu is enhanced when the sample is rotated about its vertical axis, because of the formation of Ekman vortices that extract additional fluid out of thermal boundary layers at the top and bottom. We show from experiments and direct numerical simulations that the enhancement occurs only above a bifurcation point at a critical inverse Rossby number $1/\Ro_c$, with $1/\Ro_c \propto 1/Γ$. We present a Ginzburg-Landau like model that explains the existence of a bifurcation at finite $1/\Ro_c$ as a finite-size effect. The model yields the proportionality between $1/\Ro_c$ and $1/Γ$ and is consistent with several other measured or computed system properties.

physics.flu-dyn↗
arXiv2011

Mutual Friction in Superfluid He^4 Near the λ-line

We present experimental results for the thermal resistivity ρ of superfluid He^4 along several isobars between saturated vapor pressure and the melting pressure. The measurements are for the temperature range 1 - T_c(q)/T_λ < t < 2{\times}10^{-5} and the heat-flux range 3 < q < 70 μW/cm^2. Here t {\equiv} 1-T/T_λ, T_λ is the transition temperature in the limit of zero q, and T_c is the transition temperature at finite q. The data suggest that the resistivity has an incipient singularity at T_λ which can be described by the power law ρ = (t/t0)^{-(mν+α)} where t0 = (q/q0)^x. However, the singularity is supplanted by the transition to a more highly dissipative phase at T_c(q) < T_λ. The results suggest a mild dependence of mν + α on P, but can be described quite well by mν + α = 2.76, x = 0.89, and q_0 = q_{0,0} - q_{0,1}P with q_{0,0} = 401 W/cm^2 and q_{0,1} = -5.0 W /{cm^2-bar}. The results imply that the Gorter-Mellink mutual friction exponent m has a value close to 3.46 and is distinctly larger than the classical value m = 3. We suggest that the reason for this may be found in the nature of the counterflow close to T_λ, which is expected to involve turbulent normalfluid flow.

cond-mat.other↗
arXiv2009

Effect of a polymer additive on heat transport in turbulent Rayleigh-Bénard convection

Measurements of heat transport, as expressed by the Nusselt number $Nu$, are reported for turbulent Rayleigh-Bénard convection of water containing up to 120 ppm by weight of poly-[ethylene oxide] with a molecular weight of $4\times10^6$ g/mole. Over the Rayleigh number range $ 5\times 10^9 \alt Ra \alt 7 \times 10^{10}$ $Nu$ is smaller than it is for pure water by up to 10%.

physics.flu-dyn↗
arXiv2009

Search for the "ultimate state" in turbulent Rayleigh-Bénard convection

Measurements of the Nusselt number $Nu$ and of temperature variations $ΔT_b$ in the bulk fluid are reported for turbulent Rayleigh-Bénard convection of a cylindrical sample. They cover the Rayleigh-number range $10^{9} \alt Ra \alt 3\times 10^{14}$ using He (Prandtl number $Pr = 0.67$), N$_2$ ($Pr = 0.72$) and SF$_6$ ($Pr = 0.79$ to 0.84) at pressures up to 15 bars and near-ambient temperatures. The sample had a height $L=2.24$m and diameter $D = 1.12$m and was located in a new High-Pressure Convection Facility (HPCF) at the Max Planck Institute for Dynamics and Self-Organization in Göttingen, Germany. The data do not show the transition to an "ultimate regime" reported by Chavanne et al. and are consistent with the measurements of Niemela et al.

physics.flu-dyn↗
arXiv2009

Azimuthal asymmetries of the large-scale circulation in turbulent Rayleigh-Benard convection

Previously we published a dynamical model (E. Brown and G. Ahlers, Phys. Fluids, 20, 075101 (2008)) for the large-scale-circulation (LSC) dynamics of Rayleigh-Benard convection in cylindrical containers. The model consists of a pair of stochastic ordinary differential equations, motivated by the Navier-Stokes equations, one each for the strength delta and the orientation theta_0 of the LSC. Here we extend it to cases where the rotational invariance of the system is broken by one of several physically relevant perturbations. As an example we present experimental measurements of the LSC dynamics for a container tilted relative to gravity. In that case the model predicts that the buoyancy of the thermal boundary layers encourages fluid to travel along the steepest slope, that it locks the LSC in this direction, and that it strengthens the flow, as seen in experiments. The increase in LSC strength is shown to be responsible for the observed suppression of cessations and azimuthal fluctuations. We predict and observe that for large enough tilt angles, the restoring force that aligns the flow with the slope is strong enough to cause oscillations of the LSC around this orientation. This planar oscillation mode is different from coherent torsional oscillations that have been observed previously. The model was applied also to containers with elliptical cross-sections and predicts that the pressure due to the side walls forces the flow into a preferred orientation in the direction of the longest diameter. When the ellipticity is large enough, then oscillations around this orientation are predicted.

physics.flu-dyn↗
arXiv2009

The cause of oscillations of the large-scale circulation of turbulent Rayleigh-B{é}nard convection

In agreement with a recent experimental discovery by Xia et. al. (2009), we also find a sloshing mode in experiments on the large-scale circulation (LSC) of turbulent Rayleigh-Benard convection in a cylindrical sample of aspect ratio one. The sloshing mode has the same frequency as the torsional oscillation discovered by Funfschilling and Ahlers (2004). We show that both modes can be described by an extension of a model developed previously [Brown and Ahlers (2008)] which consists of permitting a lateral displacement of the LSC circulation plane away from the vertical center line of the sample as well as a variation in displacements with height (such displacements had been excluded in the original model). Pressure gradients produced by the side wall of the container on average center the plane of the LSC so that it prefers to reach its longest diameter. If the LSC is displaced away from this diameter, the walls provide a restoring force. Turbulent fluctuations drive the LSC away from the central alignment, and combined with the restoring force they lead to oscillations. These oscillations are advected along with the LSC. This model predicts the correct wavenumber and phase of the oscillations, as well as estimates of the frequency, amplitude, and probability distributions of the displacements.

physics.flu-dyn↗
arXiv2009

Transitions between turbulent states in rotating Rayleigh-Benard convection

Weakly-rotating turbulent Rayleigh-Benard convection was studied experimentally and numerically. With increasing rotation and large enough Rayleigh number an abrupt transition from a turbulent state with nearly rotation-independent heat transport to another turbulent state with enhanced heat transfer is observed at a critical inverse Rossby number $1/Ro_c \simeq 0.4$. Whereas for $1/Ro < 1/Ro_c$ the strength of the large-scale convection-roll is either enhanced or essentially unmodified depending on parameters, its strength is increasingly diminished beyond $1/Ro_c$ where it competes with Ekman vortices that cause vertical fluid transport and thus heat-transfer enhancement.

physics.flu-dyn↗
arXiv2008

Enhanced heat transport by turbulent two-phase Rayleigh-Bénard convection

We report measurements of turbulent heat-transport in samples of ethane (C$_2$H$_6$) heated from below while the applied temperature difference $ΔT$ straddled the liquid-vapor co-existance curve $T_ϕ(P)$. When the sample top temperature $T_t$ decreased below $T_ϕ$, droplet condensation occurred and the latent heat of vaporization $H$ provided an additional heat-transport mechanism.The effective conductivity $λ_{eff}$ increased linearly with decreasing $T_t$, and reached a maximum value $λ_{eff}^*$ that was an order of magnitude larger than the single-phase $λ_{eff}$. As $P$ approached the critical pressure, $λ_{eff}^*$ increased dramatically even though $H$ vanished. We attribute this phenomenon to an enhanced droplet-nucleation rate as the critical point is approached.

physics.flu-dyn↗
arXiv2008

Prandtl-, Rayleigh-, and Rossby-number dependence of heat transport in turbulent rotating Rayleigh-Benard convection

Experimental and numerical data for the heat transfer as a function of the Rayleigh-, Prandtl-, and Rossby numbers in turbulent rotating Rayleigh-Benard convection are presented. For relatively small $Ra ~ 10^8$ and large Pr modest rotation can enhance the heat transfer by up to 30%. At larger Ra there is less heat-transfer enhancement, and at small Pr = 0.7. there is no heat-transfer enhancement at all. We suggest that the small-Pr behavior is due to the breakdown of the heat-transfer-enhancing Ekman pumping because of larger thermal diffusion.

physics.flu-dyn↗