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Detlef Lohse - One of the best experts on this subject based on the ideXlab platform.
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from zonal flow to Convection Rolls in rayleigh benard Convection with free slip plates
Journal of Fluid Mechanics, 2020Co-Authors: Qi Wang, Kai Leong Chong, Richard J A M Stevens, Roberto Verzicco, Detlef LohseAbstract:Rayleigh-Benard (RB) Convection with free-slip plates and horizontally periodic boundary conditions is investigated using direct numerical simulations. Two configurations are considered, one is two-dimensional (2-D) RB Convection and the other one three-dimensional (3-D) RB Convection with a rotating axis parallel to the plate, which for strong rotation mimics 2-D RB Convection. For the 2-D simulations, we explore the parameter range of Rayleigh numbers from to and Prandtl numbers from to. The effect of the width-to-height aspect ratio is investigated for. We show that zonal flow, which was observed, for example, by Goluskin et al. (J. Fluid. Mech., vol. 759, 2014, pp. 360-385) for, is only stable when is smaller than a critical value, which depends on and. The regime in which only zonal flow can exist is called the first regime in this study. With increasing, we find a second regime in which both zonal flow and different Convection Roll states can be statistically stable. For even larger, in a third regime, only Convection Roll states are statistically stable and zonal flow is not sustained. How many Convection Rolls form (or in other words, what the mean aspect ratio of an individual Roll is), depends on the initial conditions and on and. For instance, for and, the aspect ratio of an individual, statistically stable Convection Roll can vary in a large range between and. A Convection Roll with a large aspect ratio of, or more generally already with, can be seen as 'localized' zonal flow, and indeed carries over various properties of the global zonal flow. For the 3-D simulations, we fix and, and compare the flow for and. We first show that with increasing rotation rate both the flow structures and global quantities like the Nusselt number and the Reynolds number increasingly behave like in the 2-D case. We then demonstrate that with increasing aspect ratio, zonal flow, which was observed for small by von Hardenberg et al. (Phys. Rev. Lett., vol. 15, 2015, 134501), completely disappears for. For such large, only Convection Roll states are statistically stable. In-between, here for medium aspect ratio, the Convection Roll state and the zonal flow state are both statistically stable. What state is taken depends on the initial conditions, similarly as we found for the 2-D case.
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cafe latte spontaneous layer formation in laterally cooled double diffusive Convection
Journal of Fluid Mechanics, 2020Co-Authors: Kai Leong Chong, Qi Wang, Roberto Verzicco, Rui Yang, Detlef LohseAbstract:In the preparation of cafe latte, spectacular layer formation can occur between the espresso shot in a glass of milk and the milk itself. Xue et al. (Nat. Commun., vol. 8, 2017, pp. 1-6) showed that the injection velocity of espresso determines the depth of coffee-milk mixture. After a while, when a stable stratification forms in the mixture, the layering process can be modelled as a double diffusive Convection system with a stably stratified coffee-milk mixture cooled from the side. More specifically, we perform (two-dimensional) direct numerical simulations of laterally cooled double diffusive Convection for a wide parameter range, where the convective flow is driven by a lateral temperature gradient while stabilized by a vertical concentration gradient. Depending on the strength of stabilization as compared to the thermal driving, the system exhibits different flow regimes. When the thermal driving force dominates over the stabilizing force, the flow behaves like vertical Convection in which a large-scale circulation develops. However, with increasing strength of the stabilizing force, a meta-stable layered regime emerges. Initially, several vertically-stacked Convection Rolls develop, and these well-mixed layers are separated by sharp interfaces with large concentration gradients. The initial thickness of these emerging layers can be estimated by balancing the work exerted by thermal driving and the required potential energy to bring fluid out of its equilibrium position in the stably stratified fluid. In the layered regime, we further observe successive layer merging, and eventually only a single Convection Roll remains. We elucidate the following merging mechanism: as weakened circulation leads to accumulation of hot fluid adjacent to the hot sidewall, larger buoyancy forces associated with hotter fluid eventually break the layer interface. Then two layers merge into a larger layer, and circulation establishes again within the merged structure.
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sharp transitions in rotating turbulent Convection lagrangian acceleration statistics reveal a second critical rossby number
arXiv: Fluid Dynamics, 2019Co-Authors: Kim M J Alards, Federico Toschi, Richard J A M Stevens, Detlef Lohse, Rudie P J Kunnen, Herman ClercxAbstract:In RB Convection for fluids with Prandtl number $Pr\gtrsim 1$, rotation beyond a critical (small) rotation rate is known to cause a sudden enhancement of heat transfer which can be explained by a change in the character of the BL dynamics near the top and bottom plates of the Convection cell. Namely, with increasing rotation rate, the BL signature suddenly changes from Prandtl--Blasius type to Ekman type. The transition from a constant heat transfer to an almost linearly increasing heat transfer with increasing rotation rate is known to be sharp and the critical Rossby number $Ro_{c}$ occurs typically in the range $2.3\lesssim Ro_{c}\lesssim 2.9$ (for Rayleigh number $Ra=1.3\times 10^9$, $Pr=6.7$, and a Convection cell with aspect ratio $\Gamma=\frac{D}{H}=1$, with $D$ the diameter and $H$ the height of the cell). The explanation of the sharp transition in the heat transfer points to the change in the dominant flow structure. At $1/Ro\lesssim 1/Ro_c$ (slow rotation), the well-known LSC is found: a single domain-filling Convection Roll made up of many individual thermal plumes. At $1/Ro\gtrsim 1/Ro_c$ (rapid rotation), the LSC vanishes and is replaced with a collection of swirling plumes that align with the rotation axis. In this paper, by numerically studying Lagrangian acceleration statistics, related to the small-scale properties of the flow structures, we reveal that this transition between these different dominant flow structures happens at a second critical Rossby number, $Ro_{c_2}\approx 2.25$ (different from $Ro_{c_1}\approx 2.7$ for the sharp transition in the Nusselt number $Nu$; both values for the parameter settings of our present numerical study). When statistical data of Lagrangian tracers near the top plate are collected, it is found that the root-mean-square (rms) values and the kurtosis of the horizontal acceleration of these tracers show a sudden increase at $Ro_{c_2}$.
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sharp transitions in rotating turbulent Convection lagrangian acceleration statistics reveal a second critical rossby number
Physical Review Fluids, 2019Co-Authors: Kim M J Alards, Federico Toschi, Richard J A M Stevens, Detlef Lohse, Rudie P J Kunnen, Herman ClercxAbstract:In Rayleigh–Benard Convection (RBC) for fluids with Prandtl number Pr≳1, rotation beyond a critical (small) rotation rate is known to cause a sudden enhancement of heat transfer, which can be explained by a change in the character of the boundary layer (BL) dynamics near the top and bottom plates of the Convection cell. Namely, with increasing rotation rate, the BL signature suddenly changes from Prandtl–Blasius type to Ekman type. The transition from a constant heat transfer to an almost linearly increasing heat transfer with increasing rotation rate is known to be sharp and the critical Rossby number Roc occurs typically in the range 2.3≲Roc≲2.9 (for Rayleigh number Ra=1.3×109, Pr=6.7, and a Convection cell with aspect ratio Γ=DH=1, with D the diameter and Hthe height of the cell). The explanation of the sharp transition in the heat transfer points to the change in the dominant flow structure. At 1/Ro≲1/Roc (slow rotation), the well-known large-scale circulation (LSC) is found: a single domain-filling Convection Roll made up of many individual thermal plumes. At 1/Ro≳1/Roc (rapid rotation), the LSC vanishes and is replaced with a collection of swirling plumes that align with the rotation axis. In this paper, by numerically studying Lagrangian acceleration statistics, related to the small-scale properties of the flow structures, we reveal that this transition between these different dominant flow structures happens at a second critical Rossby number, Roc2≈2.25(different from Roc1≈2.7 for the sharp transition in the Nusselt number Nu; both values for the parameter settings of our present numerical study). When statistical data of Lagrangian tracers near the top plate are collected, it is found that the root-mean-square values and the kurtosis of the horizontal acceleration of these tracers show a sudden increase at Roc2. To better understand the nature of this transition we compute joint statistics of the Lagrangian velocity and acceleration of fluid particles and vertical vorticity near the top plate. It is found that for Ro≳2.25 there is hardly any correlation between the vertical vorticity and extreme acceleration events of fluid particles. For Ro≲2.25, however, vortical regions are much more prominent and extreme horizontal acceleration events are now correlated to large values of positive (cyclonic) vorticity. This suggests that the observed sudden transition in the acceleration statistics is related to thermal plumes with cyclonic vorticity developing in the Ekman BL and subsequently becoming mature and entering the bulk of the flow for Ro≲2.25.
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flow organization in two dimensional non oberbeck boussinesq rayleigh benard Convection in water
Journal of Fluid Mechanics, 2009Co-Authors: Kazuyasu Sugiyama, Siegfried Grossmann, Enrico Calzavarini, Detlef LohseAbstract:Non-Oberbeck―Boussinesq (NOB) effects on the flow organization in two-dimensional Rayleigh―Benard turbulence are numerically analysed. The working fluid is water. We focus on the temperature profiles, the centre temperature, the Nusselt number and on the analysis of the velocity field. Several velocity amplitudes (or Reynolds numbers) and several kinetic profiles are introduced and studied; these together describe the various features of the rather complex flow organization. The results are presented both as functions of the Rayleigh number Ra (with Ra up to 10 8 ) for fixed temperature difference Δ between top and bottom plates and as functions of Δ ('non-Oberbeck―Boussinesqness') for fixed Ra with Δ up to 60 K. All results are consistent with the available experimental NOB data for the centre temperature T c and the Nusselt number ratio N UNOB /Nu OB (the label OB meaning that the Oberbeck―Boussinesq conditions are valid). For the temperature profiles we find ― due to plume emission from the boundary layers ― increasing deviations from the extended Prandtl―Blasius boundary layer theory presented in Ahlers et al. (J. Fluid Mech., vol. 569, 2006, p. 409) with increasing Ra, while the centre temperature itself is surprisingly well predicted by that theory. For given non-Oberbeck―Boussinesqness Δ, both the centre temperature T c and the Nusselt number ratio N UNOB /Nu OB only weakly depend on Ra in the Ra range considered here. Beyond Ra ≈ 10 6 the flow consists of a large diagonal centre Convection Roll and two smaller Rolls in the upper and lower corners, respectively ('corner flows'). Also in the NOB case the centre Convection Roll is still characterized by only one velocity scale. In contrast, the top and bottom corner flows are then of different strengths, the bottom one being a factor 1.3 faster (for Δ = 40 K) than the top one, due to the lower viscosity in the hotter bottom boundary layer. Under NOB conditions the enhanced lower corner flow as well as the enhanced centre Roll lead to an enhancement of the volume averaged energy based Reynolds number Re E = 〈1/ 2u 2 〉 1/2 L/v of about 4 % to 5 % for Δ = 60 K. Moreover, we find Re E NOB / Re E OB ≈ (β(T c )/β(T m )) 1/2 , with β the thermal expansion coefficient and T m the arithmetic mean temperature between top and bottom plate temperatures. This corresponds to the ratio of the free fall velocities at the respective temperatures. By artificially switching off the temperature dependence of β in the numerics, the NOB modifications of Re E is less than 1 % even at Δ = 60 K, revealing the temperature dependence of the thermal expansion coefficient as the main origin of the NOB effects on the global Reynolds number in water.
Guenter Ahlers - One of the best experts on this subject based on the ideXlab platform.
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reynolds numbers and the elliptic approximation near the ultimate state of turbulent rayleigh benard Convection
New Journal of Physics, 2015Co-Authors: Xiaozhou He, Dennis P M Van Gils, Eberhard Bodenschatz, Guenter AhlersAbstract:We report results of Reynolds-number measurements, based on multi-point temperature measurements and the elliptic approximation (EA) of He and Zhang (2006 Phys. Rev. E 73 055303), Zhao and He (2009 Phys. Rev. E 79 046316) for turbulent Rayleigh–Benard Convection (RBC) over the Rayleigh-number range and for a Prandtl number Pr 0.8. The sample was a right-circular cylinder with the diameter D and the height L both equal to 112 cm. The Reynolds numbers ReU and ReV were obtained from the mean-flow velocity U and the root-mean-square fluctuation velocity V, respectively. Both were measured approximately at the mid-height of the sample and near (but not too near) the side wall close to a maximum of ReU. A detailed examination, based on several experimental tests, of the applicability of the EA to turbulent RBC in our parameter range is provided. The main contribution to ReU came from a large-scale circulation in the form of a single Convection Roll with the preferred azimuthal orientation of its down flow nearly coinciding with the location of the measurement probes. First we measured time sequences of ReU(t) and ReV(t) from short (10 s) segments which moved along much longer sequences of many hours. The corresponding probability distributions of ReU(t) and ReV(t) had single peaks and thus did not reveal significant flow reversals. The two averaged Reynolds numbers determined from the entire data sequences were of comparable size. For both ReU and ReV could be described by a power-law dependence on Ra with an exponent ζ close to 0.44. This exponent is consistent with several other measurements for the classical RBC state at smaller Ra and larger Pr and with the Grossmann–Lohse (GL) prediction for ReU (Grossmann and Lohse 2000 J. Fluid. Mech. 407 27; Grossmann and Lohse 2001 86 3316; Grossmann and Lohse 2002 66 016305) but disagrees with the prediction by GL (Grossmann and Lohse 2004 Phys. Fluids 16 4462) for ReV. At the dependence of ReV on Ra changed, and for larger Ra , consistent with the prediction for ReU (Grossmann and Lohse 2000 J. Fluid. Mech. 407 27; Grossmann and Lohse Phys. Rev. Lett. 2001 86 3316; Grossmann and Lohse Phys. Rev. E 2002 66 016305; Grossmann and Lohse 2012 Phys. Fluids 24 125103) in the ultimate state of RBC.
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turbulent rayleigh benard Convection for a prandtl number of 0 67
Journal of Fluid Mechanics, 2009Co-Authors: Guenter Ahlers, Eberhard Bodenschatz, Denis Funfschilling, James HoggAbstract:For the Rayleigh-number range 10 7 ≲ Ra ≲ 10 11 we report measurements of the Nusselt number Nu and of properties of the large-scale circulation (LSC) for cylindrical samples of helium gas (Prandtl number Pr = 0.674) that have aspect ratio Γ ≡ D / L = 0.50 ( D and L are the diameter and the height respectively) and are heated from below. The results for Nu are consistent with recent direct numerical simulations. We measured the amplitude δ of the azimuthal temperature variation induced by the LSC at the sidewall, and the LSC circulation-plane orientation θ 0 , at three vertical positions. For the entire Ra range the LSC involves a Convection Roll that is coherent over the height of the system. However, this structure frequently collapses completely at irregular time intervals and then reorganizes from the incoherent flow. At small δ the probability distribution p (δ) increases linearly from zero; for Γ = 1 and Pr = 4.38 this increase is exponential. No evidence of a two-Roll structure, with one above the other, was observed. This differs from recent direct numerical simulations for Γ = 0.5 and Pr = 0.7, where a one-Roll LSC was found to exist only for Ra ≲ 10 9 to 10 10 , and from measurements for Γ = 0.5 and Pr ≃ 5, where one- and two-Roll structures were observed with transitions between them at random time intervals.
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heat transfer and large scale dynamics in turbulent rayleigh benard Convection
Reviews of Modern Physics, 2009Co-Authors: Guenter Ahlers, Siegfried Grossmann, Detlef LohseAbstract:The progress in our understanding of several aspects of turbulent Rayleigh-Benard Convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and on how the thicknesses of the thermal and the kinetic boundary layers scale with Ra and Pr. Non-Oberbeck-Boussinesq effects and the dynamics of the large scale Convection Roll are addressed as well. The review ends with a list of challenges for future research on the turbulent Rayleigh-Benard system.
Qi Wang - One of the best experts on this subject based on the ideXlab platform.
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from zonal flow to Convection Rolls in rayleigh benard Convection with free slip plates
Journal of Fluid Mechanics, 2020Co-Authors: Qi Wang, Kai Leong Chong, Richard J A M Stevens, Roberto Verzicco, Detlef LohseAbstract:Rayleigh-Benard (RB) Convection with free-slip plates and horizontally periodic boundary conditions is investigated using direct numerical simulations. Two configurations are considered, one is two-dimensional (2-D) RB Convection and the other one three-dimensional (3-D) RB Convection with a rotating axis parallel to the plate, which for strong rotation mimics 2-D RB Convection. For the 2-D simulations, we explore the parameter range of Rayleigh numbers from to and Prandtl numbers from to. The effect of the width-to-height aspect ratio is investigated for. We show that zonal flow, which was observed, for example, by Goluskin et al. (J. Fluid. Mech., vol. 759, 2014, pp. 360-385) for, is only stable when is smaller than a critical value, which depends on and. The regime in which only zonal flow can exist is called the first regime in this study. With increasing, we find a second regime in which both zonal flow and different Convection Roll states can be statistically stable. For even larger, in a third regime, only Convection Roll states are statistically stable and zonal flow is not sustained. How many Convection Rolls form (or in other words, what the mean aspect ratio of an individual Roll is), depends on the initial conditions and on and. For instance, for and, the aspect ratio of an individual, statistically stable Convection Roll can vary in a large range between and. A Convection Roll with a large aspect ratio of, or more generally already with, can be seen as 'localized' zonal flow, and indeed carries over various properties of the global zonal flow. For the 3-D simulations, we fix and, and compare the flow for and. We first show that with increasing rotation rate both the flow structures and global quantities like the Nusselt number and the Reynolds number increasingly behave like in the 2-D case. We then demonstrate that with increasing aspect ratio, zonal flow, which was observed for small by von Hardenberg et al. (Phys. Rev. Lett., vol. 15, 2015, 134501), completely disappears for. For such large, only Convection Roll states are statistically stable. In-between, here for medium aspect ratio, the Convection Roll state and the zonal flow state are both statistically stable. What state is taken depends on the initial conditions, similarly as we found for the 2-D case.
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cafe latte spontaneous layer formation in laterally cooled double diffusive Convection
Journal of Fluid Mechanics, 2020Co-Authors: Kai Leong Chong, Qi Wang, Roberto Verzicco, Rui Yang, Detlef LohseAbstract:In the preparation of cafe latte, spectacular layer formation can occur between the espresso shot in a glass of milk and the milk itself. Xue et al. (Nat. Commun., vol. 8, 2017, pp. 1-6) showed that the injection velocity of espresso determines the depth of coffee-milk mixture. After a while, when a stable stratification forms in the mixture, the layering process can be modelled as a double diffusive Convection system with a stably stratified coffee-milk mixture cooled from the side. More specifically, we perform (two-dimensional) direct numerical simulations of laterally cooled double diffusive Convection for a wide parameter range, where the convective flow is driven by a lateral temperature gradient while stabilized by a vertical concentration gradient. Depending on the strength of stabilization as compared to the thermal driving, the system exhibits different flow regimes. When the thermal driving force dominates over the stabilizing force, the flow behaves like vertical Convection in which a large-scale circulation develops. However, with increasing strength of the stabilizing force, a meta-stable layered regime emerges. Initially, several vertically-stacked Convection Rolls develop, and these well-mixed layers are separated by sharp interfaces with large concentration gradients. The initial thickness of these emerging layers can be estimated by balancing the work exerted by thermal driving and the required potential energy to bring fluid out of its equilibrium position in the stably stratified fluid. In the layered regime, we further observe successive layer merging, and eventually only a single Convection Roll remains. We elucidate the following merging mechanism: as weakened circulation leads to accumulation of hot fluid adjacent to the hot sidewall, larger buoyancy forces associated with hotter fluid eventually break the layer interface. Then two layers merge into a larger layer, and circulation establishes again within the merged structure.
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From zonal flow to Convection Rolls in Rayleigh-B\'enard Convection with free-slip plates
2020Co-Authors: Qi Wang, Chong, Kai Leong, Stevens, Richard J. A. M., Verzicco Roberto, Lohse DetlefAbstract:Rayleigh-B\'enard (RB) Convection with free-slip plates and horizontally periodic boundary conditions is investigated using direct numerical simulations. Two configurations are considered, one is two-dimension (2D) RB Convection and the other one three-dimension (3D) RB Convection with a rotating axis parallel to the plate. We explore the parameter range of Rayleigh numbers Ra from $10^7 to $10^9$ and Prandtl numbers $Pr$ from $1$ to $100$. We show that zonal flow, which was observed, for example, by Goluskin \emph{et al}. \emph{J. Fluid. Mech.} 759, 360-385 (2014) for $\Gamma=2$, is only stable when $\Gamma$ is smaller than a critical value, which depends on $Ra$ and $Pr$. With increasing $\Gamma$, we find a second regime in which both zonal flow and different Convection Roll states can be statistically stable. For even larger $\Gamma$, in a third regime, only Convection Roll states are statistically stable and zonal flow is not sustained. For the 3D simulations, we fix $Ra=10^7$ and $Pr=0.71$, and compare the flow for $\Gamma=8$ and $\Gamma = 16$. We demonstrate that with increasing aspect ratio $\Gamma$, zonal flow, which was observed for small $\Gamma=2\pi$ by von Hardenberg \emph{et al}. \emph{Phys. Rev. Lett.} 15, 134501 (2015), completely disappears for $\Gamma=16$. For such large $\Gamma$ only Convection Roll states are statistically stable. In between, here for medium aspect ratio $\Gamma = 8$, the Convection Roll state and the zonal flow state are both statistically stable. What state is taken depends on the initial conditions, similarly as we found for the 2D case.Comment: 26 pages, 12 figure
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From zonal flow to Convection Rolls in Rayleigh-Bénard Convection with free-slip plates
'Cambridge University Press (CUP)', 2020Co-Authors: Qi Wang, Chong, Kai Leong, Verzicco Roberto, Stevens, Richard J.a.m., Lohse DetlefAbstract:Rayleigh-Bénard (RB) Convection with free-slip plates and horizontally periodic boundary conditions is investigated using direct numerical simulations. Two configurations are considered, one is two-dimensional (2-D) RB Convection and the other one three-dimensional (3-D) RB Convection with a rotating axis parallel to the plate, which for strong rotation mimics 2-D RB Convection. For the 2-D simulations, we explore the parameter range of Rayleigh numbers from to and Prandtl numbers from to. The effect of the width-to-height aspect ratio is investigated for. We show that zonal flow, which was observed, for example, by Goluskin et al. (J. Fluid. Mech., vol. 759, 2014, pp. 360-385) for, is only stable when is smaller than a critical value, which depends on and. The regime in which only zonal flow can exist is called the first regime in this study. With increasing, we find a second regime in which both zonal flow and different Convection Roll states can be statistically stable. For even larger, in a third regime, only Convection Roll states are statistically stable and zonal flow is not sustained. How many Convection Rolls form (or in other words, what the mean aspect ratio of an individual Roll is), depends on the initial conditions and on and. For instance, for and, the aspect ratio of an individual, statistically stable Convection Roll can vary in a large range between and. A Convection Roll with a large aspect ratio of, or more generally already with, can be seen as 'localized' zonal flow, and indeed carries over various properties of the global zonal flow. For the 3-D simulations, we fix and, and compare the flow for and. We first show that with increasing rotation rate both the flow structures and global quantities like the Nusselt number and the Reynolds number increasingly behave like in the 2-D case. We then demonstrate that with increasing aspect ratio, zonal flow, which was observed for small by von Hardenberg et al. (Phys. Rev. Lett., vol. 15, 2015, 134501), completely disappears for. For such large, only Convection Roll states are statistically stable. In-between, here for medium aspect ratio, the Convection Roll state and the zonal flow state are both statistically stable. What state is taken depends on the initial conditions, similarly as we found for the 2-D case
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Café latte: Spontaneous layer formation in laterally cooled double diffusive Convection
'Cambridge University Press (CUP)', 2020Co-Authors: Chong, Kai Leong, Qi Wang, Verzicco Roberto, Yang Rui, Lohse DetlefAbstract:In the preparation of café latte, spectacular layer formation can occur between the espresso shot in a glass of milk and the milk itself. Xue et al. (Nat. Commun., vol. 8, 2017, pp. 1-6) showed that the injection velocity of espresso determines the depth of coffee-milk mixture. After a while, when a stable stratification forms in the mixture, the layering process can be modelled as a double diffusive Convection system with a stably stratified coffee-milk mixture cooled from the side. More specifically, we perform (two-dimensional) direct numerical simulations of laterally cooled double diffusive Convection for a wide parameter range, where the convective flow is driven by a lateral temperature gradient while stabilized by a vertical concentration gradient. Depending on the strength of stabilization as compared to the thermal driving, the system exhibits different flow regimes. When the thermal driving force dominates over the stabilizing force, the flow behaves like vertical Convection in which a large-scale circulation develops. However, with increasing strength of the stabilizing force, a meta-stable layered regime emerges. Initially, several vertically-stacked Convection Rolls develop, and these well-mixed layers are separated by sharp interfaces with large concentration gradients. The initial thickness of these emerging layers can be estimated by balancing the work exerted by thermal driving and the required potential energy to bring fluid out of its equilibrium position in the stably stratified fluid. In the layered regime, we further observe successive layer merging, and eventually only a single Convection Roll remains. We elucidate the following merging mechanism: as weakened circulation leads to accumulation of hot fluid adjacent to the hot sidewall, larger buoyancy forces associated with hotter fluid eventually break the layer interface. Then two layers merge into a larger layer, and circulation establishes again within the merged structure
Lohse Detlef - One of the best experts on this subject based on the ideXlab platform.
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Flow organisation in laterally unconfined Rayleigh–Bénard turbulence
'Cambridge University Press (CUP)', 2021Co-Authors: Blass Alexander, Stevens, Richard J. A. M., Verzicco Roberto, Lohse Detlef, Krug DominikAbstract:We investigate the large-scale circulation (LSC) of turbulent Rayleigh–Bénard Convection in a large box of aspect ratio Γ=32Γ=32 for Rayleigh numbers up to Ra=109Ra=109 and at a fixed Prandtl number Pr=1Pr=1 . A conditional averaging technique allows us to extract statistics of the LSC even though the number and the orientation of the structures vary throughout the domain. We find that various properties of the LSC obtained here, such as the wall-shear stress distribution, the boundary layer thicknesses and the wind Reynolds number, do not differ significantly from results in confined domains ( Γ≈1Γ≈1 ). This is remarkable given that the size of the structures (as measured by the width of a single Convection Roll) more than doubles at the highest RaRa as the confinement is removed. An extrapolation towards the critical shear Reynolds number of Recrits≈420Rescrit≈420 , at which the boundary layer (BL) typically becomes turbulent, predicts that the transition to the ultimate regime is expected at Racrit≈O(1015)Racrit≈O(1015) in unconfined geometries. This result is in line with the Göttingen experimental observations (He et al., Phys. Rev. Lett., vol. 108, 2012, 024502; New J. Phys., vol. 17, 2015, 063028). Furthermore, we confirm that the local heat transport close to the wall is highest in the plume impacting region, where the thermal BL is thinnest, and lowest in the plume emitting region, where the thermal BL is thickest. This trend, however, weakens with increasing RaRa
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From zonal flow to Convection Rolls in Rayleigh-B\'enard Convection with free-slip plates
2020Co-Authors: Qi Wang, Chong, Kai Leong, Stevens, Richard J. A. M., Verzicco Roberto, Lohse DetlefAbstract:Rayleigh-B\'enard (RB) Convection with free-slip plates and horizontally periodic boundary conditions is investigated using direct numerical simulations. Two configurations are considered, one is two-dimension (2D) RB Convection and the other one three-dimension (3D) RB Convection with a rotating axis parallel to the plate. We explore the parameter range of Rayleigh numbers Ra from $10^7 to $10^9$ and Prandtl numbers $Pr$ from $1$ to $100$. We show that zonal flow, which was observed, for example, by Goluskin \emph{et al}. \emph{J. Fluid. Mech.} 759, 360-385 (2014) for $\Gamma=2$, is only stable when $\Gamma$ is smaller than a critical value, which depends on $Ra$ and $Pr$. With increasing $\Gamma$, we find a second regime in which both zonal flow and different Convection Roll states can be statistically stable. For even larger $\Gamma$, in a third regime, only Convection Roll states are statistically stable and zonal flow is not sustained. For the 3D simulations, we fix $Ra=10^7$ and $Pr=0.71$, and compare the flow for $\Gamma=8$ and $\Gamma = 16$. We demonstrate that with increasing aspect ratio $\Gamma$, zonal flow, which was observed for small $\Gamma=2\pi$ by von Hardenberg \emph{et al}. \emph{Phys. Rev. Lett.} 15, 134501 (2015), completely disappears for $\Gamma=16$. For such large $\Gamma$ only Convection Roll states are statistically stable. In between, here for medium aspect ratio $\Gamma = 8$, the Convection Roll state and the zonal flow state are both statistically stable. What state is taken depends on the initial conditions, similarly as we found for the 2D case.Comment: 26 pages, 12 figure
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From zonal flow to Convection Rolls in Rayleigh-Bénard Convection with free-slip plates
'Cambridge University Press (CUP)', 2020Co-Authors: Qi Wang, Chong, Kai Leong, Verzicco Roberto, Stevens, Richard J.a.m., Lohse DetlefAbstract:Rayleigh-Bénard (RB) Convection with free-slip plates and horizontally periodic boundary conditions is investigated using direct numerical simulations. Two configurations are considered, one is two-dimensional (2-D) RB Convection and the other one three-dimensional (3-D) RB Convection with a rotating axis parallel to the plate, which for strong rotation mimics 2-D RB Convection. For the 2-D simulations, we explore the parameter range of Rayleigh numbers from to and Prandtl numbers from to. The effect of the width-to-height aspect ratio is investigated for. We show that zonal flow, which was observed, for example, by Goluskin et al. (J. Fluid. Mech., vol. 759, 2014, pp. 360-385) for, is only stable when is smaller than a critical value, which depends on and. The regime in which only zonal flow can exist is called the first regime in this study. With increasing, we find a second regime in which both zonal flow and different Convection Roll states can be statistically stable. For even larger, in a third regime, only Convection Roll states are statistically stable and zonal flow is not sustained. How many Convection Rolls form (or in other words, what the mean aspect ratio of an individual Roll is), depends on the initial conditions and on and. For instance, for and, the aspect ratio of an individual, statistically stable Convection Roll can vary in a large range between and. A Convection Roll with a large aspect ratio of, or more generally already with, can be seen as 'localized' zonal flow, and indeed carries over various properties of the global zonal flow. For the 3-D simulations, we fix and, and compare the flow for and. We first show that with increasing rotation rate both the flow structures and global quantities like the Nusselt number and the Reynolds number increasingly behave like in the 2-D case. We then demonstrate that with increasing aspect ratio, zonal flow, which was observed for small by von Hardenberg et al. (Phys. Rev. Lett., vol. 15, 2015, 134501), completely disappears for. For such large, only Convection Roll states are statistically stable. In-between, here for medium aspect ratio, the Convection Roll state and the zonal flow state are both statistically stable. What state is taken depends on the initial conditions, similarly as we found for the 2-D case
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Flow organization in laterally unconfined Rayleigh-B\'enard turbulence
2020Co-Authors: Blass Alexander, Stevens, Richard J. A. M., Verzicco Roberto, Lohse Detlef, Krug DominikAbstract:We investigate the large-scale circulation (LSC) of turbulent Rayleigh-B\'enard Convection in a large box of aspect ratio $\Gamma =32$ for Rayleigh numbers up to $Ra=10^9$ and at a fixed Prandtl number $Pr=1$. A conditional averaging technique allows us to extract statistics of the LSC even though the number and the orientation of the structures vary throughout the domain. We find that various properties of the LSC obtained here, such as the wall-shear stress distribution, the boundary layer thicknesses and the wind Reynolds number, do not differ significantly from results in confined domains ($\Gamma \approx 1$). This is remarkable given that the size of the structures (as measured by the width of a single Convection Roll) more than doubles at the highest $Ra$ as the confinement is removed. An extrapolation towards the critical shear Reynolds number of $Re_s^{\textrm{crit}} \approx 420$, at which the boundary layer (BL) typically becomes turbulent, predicts that the transition to the ultimate regime is expected at $Ra_{\textrm{crit}} \approx \mathcal{O}(10^{15})$ in unconfined geometries. This result is in line with the G\"ottingen experimental observations. Furthermore, we confirm that the local heat transport close to the wall is highest in the plume impacting region, where the thermal BL is thinnest, and lowest in the plume emitting region, where the thermal BL is thickest. This trend, however, weakens with increasing $Ra$
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Café latte: Spontaneous layer formation in laterally cooled double diffusive Convection
'Cambridge University Press (CUP)', 2020Co-Authors: Chong, Kai Leong, Qi Wang, Verzicco Roberto, Yang Rui, Lohse DetlefAbstract:In the preparation of café latte, spectacular layer formation can occur between the espresso shot in a glass of milk and the milk itself. Xue et al. (Nat. Commun., vol. 8, 2017, pp. 1-6) showed that the injection velocity of espresso determines the depth of coffee-milk mixture. After a while, when a stable stratification forms in the mixture, the layering process can be modelled as a double diffusive Convection system with a stably stratified coffee-milk mixture cooled from the side. More specifically, we perform (two-dimensional) direct numerical simulations of laterally cooled double diffusive Convection for a wide parameter range, where the convective flow is driven by a lateral temperature gradient while stabilized by a vertical concentration gradient. Depending on the strength of stabilization as compared to the thermal driving, the system exhibits different flow regimes. When the thermal driving force dominates over the stabilizing force, the flow behaves like vertical Convection in which a large-scale circulation develops. However, with increasing strength of the stabilizing force, a meta-stable layered regime emerges. Initially, several vertically-stacked Convection Rolls develop, and these well-mixed layers are separated by sharp interfaces with large concentration gradients. The initial thickness of these emerging layers can be estimated by balancing the work exerted by thermal driving and the required potential energy to bring fluid out of its equilibrium position in the stably stratified fluid. In the layered regime, we further observe successive layer merging, and eventually only a single Convection Roll remains. We elucidate the following merging mechanism: as weakened circulation leads to accumulation of hot fluid adjacent to the hot sidewall, larger buoyancy forces associated with hotter fluid eventually break the layer interface. Then two layers merge into a larger layer, and circulation establishes again within the merged structure
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flow reversals in thermally driven turbulence
Physical Review Letters, 2010Co-Authors: Shengqi Zhou, Chao Sun, Richard J A M Stevens, Siegfried Grossmann, Kazuyasu Sugiyama, Tak Shing Chan, Keqing XiaAbstract:We analyze the reversals of the large-scale flow in Rayleigh-Benard Convection both through particle image velocimetry flow visualization and direct numerical simulations of the underlying Boussinesq equations in a (quasi-) two-dimensional, rectangular geometry of aspect ratio 1. For medium Prandtl number there is a diagonal large-scale Convection Roll and two smaller secondary Rolls in the two remaining corners diagonally opposing each other. These corner-flow Rolls play a crucial role for the large-scale wind reversal: They grow in kinetic energy and thus also in size thanks to plume detachments from the boundary layers up to the time that they take over the main, large-scale diagonal flow, thus leading to reversal. The Rayleigh vs Prandtl number space is mapped out. The occurrence of reversals sensitively depends on these parameters
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flow organization in two dimensional non oberbeck boussinesq rayleigh benard Convection in water
Journal of Fluid Mechanics, 2009Co-Authors: Kazuyasu Sugiyama, Siegfried Grossmann, Enrico Calzavarini, Detlef LohseAbstract:Non-Oberbeck―Boussinesq (NOB) effects on the flow organization in two-dimensional Rayleigh―Benard turbulence are numerically analysed. The working fluid is water. We focus on the temperature profiles, the centre temperature, the Nusselt number and on the analysis of the velocity field. Several velocity amplitudes (or Reynolds numbers) and several kinetic profiles are introduced and studied; these together describe the various features of the rather complex flow organization. The results are presented both as functions of the Rayleigh number Ra (with Ra up to 10 8 ) for fixed temperature difference Δ between top and bottom plates and as functions of Δ ('non-Oberbeck―Boussinesqness') for fixed Ra with Δ up to 60 K. All results are consistent with the available experimental NOB data for the centre temperature T c and the Nusselt number ratio N UNOB /Nu OB (the label OB meaning that the Oberbeck―Boussinesq conditions are valid). For the temperature profiles we find ― due to plume emission from the boundary layers ― increasing deviations from the extended Prandtl―Blasius boundary layer theory presented in Ahlers et al. (J. Fluid Mech., vol. 569, 2006, p. 409) with increasing Ra, while the centre temperature itself is surprisingly well predicted by that theory. For given non-Oberbeck―Boussinesqness Δ, both the centre temperature T c and the Nusselt number ratio N UNOB /Nu OB only weakly depend on Ra in the Ra range considered here. Beyond Ra ≈ 10 6 the flow consists of a large diagonal centre Convection Roll and two smaller Rolls in the upper and lower corners, respectively ('corner flows'). Also in the NOB case the centre Convection Roll is still characterized by only one velocity scale. In contrast, the top and bottom corner flows are then of different strengths, the bottom one being a factor 1.3 faster (for Δ = 40 K) than the top one, due to the lower viscosity in the hotter bottom boundary layer. Under NOB conditions the enhanced lower corner flow as well as the enhanced centre Roll lead to an enhancement of the volume averaged energy based Reynolds number Re E = 〈1/ 2u 2 〉 1/2 L/v of about 4 % to 5 % for Δ = 60 K. Moreover, we find Re E NOB / Re E OB ≈ (β(T c )/β(T m )) 1/2 , with β the thermal expansion coefficient and T m the arithmetic mean temperature between top and bottom plate temperatures. This corresponds to the ratio of the free fall velocities at the respective temperatures. By artificially switching off the temperature dependence of β in the numerics, the NOB modifications of Re E is less than 1 % even at Δ = 60 K, revealing the temperature dependence of the thermal expansion coefficient as the main origin of the NOB effects on the global Reynolds number in water.
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heat transfer and large scale dynamics in turbulent rayleigh benard Convection
Reviews of Modern Physics, 2009Co-Authors: Guenter Ahlers, Siegfried Grossmann, Detlef LohseAbstract:The progress in our understanding of several aspects of turbulent Rayleigh-Benard Convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and on how the thicknesses of the thermal and the kinetic boundary layers scale with Ra and Pr. Non-Oberbeck-Boussinesq effects and the dynamics of the large scale Convection Roll are addressed as well. The review ends with a list of challenges for future research on the turbulent Rayleigh-Benard system.
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scaling in thermal Convection a unifying theory
Journal of Fluid Mechanics, 2000Co-Authors: Siegfried Grossmann, Detlef LohseAbstract:A systematic theory for the scaling of the Nusselt number Nu and of the A systematic theory for the scaling of the Nusselt number Nu and of the Reynolds number Re in strong Rayleigh–Benard Convection is suggested and shown to be compatible with recent experiments. It assumes a coherent large-scale Convection Roll (‘wind of turbulence’) and is based on the dynamical equations both in the bulk and in the boundary layers. Several regimes are identified in the Rayleigh number Ra versus Prandtl number Pr phase space, defined by whether the boundary layer or the bulk dominates the global kinetic and thermal dissipation, respectively, and by whether the thermal or the kinetic boundary layer is thicker. The crossover between the regimes is calculated. In the regime which has most frequently been studied in experiment (Ra [less, similar] 1011) the leading terms are Nu [similar] Ra1/4Pr1/8, Re [similar] Ra1/2Pr[minus sign]3/4 for Pr [less, similar] 1 and Nu [similar] Ra1/4Pr[minus sign]1/12, Re [similar] Ra1/2Pr[minus sign]5/6 for Pr [greater, similar] 1. In most measurements these laws are modified by additive corrections from the neighbouring regimes so that the impression of a slightly larger (effective) Nu vs. Ra scaling exponent can arise. The most important of the neighbouring regimes towards large Ra are a regime with scaling Nu [similar] Ra1/2Pr1/2, Re [similar] Ra1/2Pr[minus sign]1/2 for medium Pr (‘Kraichnan regime’), a regime with scaling Nu [similar] Ra1/5Pr1/5, Re [similar] Ra2/5Pr[minus sign]3/5 for small Pr, a regime with Nu [similar] Ra1/3, Re [similar] Ra4/9Pr[minus sign]2/3 for larger Pr, and a regime with scaling Nu [similar] Ra3/7Pr[minus sign]1/7, Re [similar] Ra4/7Pr[minus sign]6/7 for even larger Pr. In particular, a linear combination of the ¼ and the 1/3 power laws for Nu with Ra, Nu = 0.27Ra1/4 + 0.038Ra1/3 (the prefactors follow from experiment), mimics a 2/7 power-law exponent in a regime as large as ten decades. For very large Ra the laminar shear boundary layer is speculated to break down through the non-normal-nonlinear transition to turbulence and another regime emerges.
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scaling in thermal Convection a unifying theory
arXiv: Chaotic Dynamics, 1999Co-Authors: Siegfried Grossmann, Detlef LohseAbstract:A systematic theory for the scaling of the Nusselt number $Nu$ and of the Reynolds number $Re$ in strong Rayleigh-Benard Convection is suggested and shown to be compatible with recent experiments. It assumes a coherent large scale Convection Roll (``wind of turbulence'') and is based on the dynamical equations both in the bulk and in the boundary layers. Several regimes are identified in the Rayleigh number versus Prandtl number phase space, defined by whether the boundary layer or the bulk dominates the global kinetic and thermal dissipation, respectively. The crossover between the regimes is calculated. In the regime which has most frequently been studied in experiment (Ra smaller than 10^{11}) the leading terms are $Nu\sim Ra^{1/4}Pr^{1/8}$, $Re \sim Ra^{1/2} Pr^{-3/4}$ for $Pr 1$. In most measurements these laws are modified by additive corrections from the neighboring regimes so that the impression of a slightly larger (effective) Nu vs Ra scaling exponent can arise. -- The presented theory is best summarized in the phase diagram figure 1.