Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell

Verzicco, Roberto; Camussi, Roberto

doi:10.1017/s0022112002003063

Cited by 282 publications

(380 citation statements)

References 28 publications

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“…1A. The statistical properties of the flow are consistent with those observed in previous works (19,20), particularly the Nusselt number (which measures the ratio of convective to conductive heat transfer) and the mean temperature and velocity field profiles (Fig. S1).…”

Section: Modelssupporting

confidence: 87%

Learning to soar in turbulent environments

Reddy

Celani

Sejnowski

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

150

115

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Birds and gliders exploit warm, rising atmospheric currents (thermals) to reach heights comparable to low-lying clouds with a reduced expenditure of energy. This strategy of flight (thermal soaring) is frequently used by migratory birds. Soaring provides a remarkable instance of complex decision making in biology and requires a longterm strategy to effectively use the ascending thermals. Furthermore, the problem is technologically relevant to extend the flying range of autonomous gliders. Thermal soaring is commonly observed in the atmospheric convective boundary layer on warm, sunny days. The formation of thermals unavoidably generates strong turbulent fluctuations, which constitute an essential element of soaring. Here, we approach soaring flight as a problem of learning to navigate complex, highly fluctuating turbulent environments. We simulate the atmospheric boundary layer by numerical models of turbulent convective flow and combine them with model-free, experience-based, reinforcement learning algorithms to train the gliders. For the learned policies in the regimes of moderate and strong turbulence levels, the glider adopts an increasingly conservative policy as turbulence levels increase, quantifying the degree of risk affordable in turbulent environments. Reinforcement learning uncovers those sensorimotor cues that permit effective control over soaring in turbulent environments.thermal soaring | turbulence | navigation | reinforcement learning M igrating birds and gliders use upward wind currents in the atmosphere to gain height while minimizing the energy cost of propulsion by the flapping of the wings or engines (1, 2). This mode of flight, called soaring, has been observed in a variety of birds. For instance, birds of prey use soaring to maintain an elevated vantage point in their search for food (3); migrating storks exploit soaring to cover large distances in their quest for greener pastures (4). Different forms of soaring have been observed. Of particular interest here is thermal soaring, where a bird gains height by using warm air currents (thermals) formed in the atmospheric boundary layer. For both birds and gliders, a crucial part of the thermal soaring is to identify a thermal and to find and maintain its core, where the lift is typically the largest. Once migratory birds have climbed up to the top of a thermal, they glide down to the next thermal and repeat the process, a migration strategy that strongly reduces energy costs (4). Soaring strategies are also important for technological applications, namely, the development of autonomous gliders that can fly large distances with minimal energy consumption (5).Thermals arise as ascending convective plumes driven by the temperature gradient created due to the heating of the earth's surface by the sun (6). Hydrodynamic instabilities and processes that lead to the formation of a thermal inevitably give rise to a turbulent environment characterized by strong, erratic fluctuations (7,8). Birds or gliders attempting to find and maintain a thermal face...

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Section: Modelssupporting

confidence: 87%

Learning to soar in turbulent environments

Reddy

Celani

Sejnowski

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

150

115

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“…This Ra dependence has two important implications. First, the volume average ratio h f r i V =h m r i V will decrease with increasing Ra, a trend which agrees with the recent numerical results [10] but is opposite to that given by the first scenario of the GL theory [2,5]. Second, the measurements clearly reveal two competing effects of turbulence.…”

supporting

confidence: 82%

Measured Thermal Dissipation Field in Turbulent Rayleigh-Bénard Convection

Tong

Xia

2007

Phys. Rev. Lett.

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The time-averaged local thermal dissipation rate N r in turbulent convection is obtained from direct measurements of the temperature gradient vector in a cylindrical cell filled with water. It is found that N r contains two contributions. One is generated by thermal plumes, present mainly in the plumedominated bulk region, and decreases with increasing Rayleigh number Ra. The other contribution comes from the mean temperature gradient, being concentrated in the thermal boundary layers, and increases with Ra. The experiment thus provides a new physical picture about the thermal dissipation field in turbulent convection. DOI: 10.1103/PhysRevLett.98.144501 PACS numbers: 47.27.Tÿ, 44.25.+f Turbulent Rayleigh-Bénard convection in a fluid layer confined between two horizontal plates of separation H occurs when the Rayleigh number Ra becomes sufficiently large. Here Ra is defined as Ra g TH 3 = , where g is the gravitational acceleration, T is the temperature difference between the lower heated and upper cooled plates, and , , and are, respectively, the thermal expansion coefficient, the kinematic viscosity, and the thermal diffusivity of the convecting fluid. An important issue that has been under intensive experimental and theoretical scrutiny in recent years is to understand how heat is transported vertically through the convection cell [1,2]. A large number of heat transport measurements have been carried out in various convecting fluids with wide parameter range and great precision [3]. These measurements shed new light on the mechanism of heat transport and have stimulated considerable theoretical efforts, aimed at explaining the functional form of the measured Nusselt number Nu Ra; Pr (normalized heat flux) as a function of two experimental control parameters: Ra and the Prandtl number Pr= . An quantity that is closely connected to Nu Ra; Pr is the thermal dissipation field T r; t j rT r; t j 2 , where rT r; t is the temperature gradient field. The determination of T r; t involves simultaneous measurement of three components of rT r; t . Experimental studies of scalar dissipation fields have been carried out in turbulent flows [4], in which temperature (or concentration of a contaminant) is a passive scalar. In this case, T r; t measures a mixing rate, at which fluctuations of T (or T 2 ) are destroyed. For thermal convection, however, temperature is an active scalar which drives the convective flow. In this case, T r; t is directly linked to the local dynamics of the flow and one finds [2] N r is decomposed into the boundary-layer and bulk contributions, which have different scaling behavior with varying Ra and Pr. More recently, a second scenario was proposed [5] with N r being decomposed into two different contributions: thermal plumes (including the boundary layers) and turbulent background. While the two scenarios involve different physical pictures about the local dynamics of turbulent convection, the calculated Nu Ra; Pr using the two different models turns out to be of the same scaling form. This su...

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“…After all, the convective flow is driven by instabilities of the upper and lower thermal boundary layers. Recent experiment [8] and numerical simulations [9] showed that the ratio of the boundary contribution of T r to the corresponding bulk contribution is an increasing rather than a decreasing function of Ra, as was commonly believed. These studies suggest that the global heat transport measurements will always be ''contaminated'' by contributions from the boundaries.…”

mentioning

confidence: 83%

Scaling of the Local Convective Heat Flux in Turbulent Rayleigh-Bénard Convection

2008

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Local convective heat flux J r in turbulent thermal convection is obtained from simultaneous velocity and temperature measurements in a cylindrical cell filled with water. The measured J r in the bulk region shows a different scaling behavior with varying Rayleigh numbers compared with that measured in the plume-dominated regions near the sidewall and near the lower conducting plate. The local transport measurements thus allow us to disentangle boundary and bulk contributions to the total heat flux and directly check their respective scaling behavior against the theoretical predictions. DOI: 10.1103/PhysRevLett.100.244503 PACS numbers: 47.27.te, 44.25.+f Turbulent convection in a fluid layer confined between two horizontal plates of separation H and heated from below (Rayleigh-Bénard convection) has become an important platform to study a number of important phenomena of general interest in nonequilibrium physics [1,2]. These include the scaling of global heat transport, the dynamics of viscous and thermal boundary layers, and the interaction between a large-scale circulation (LSC) of the bulk fluid and small-scale fluctuations generated by thermal plumes. An important issue that has been under intensive experimental and theoretical scrutiny in recent years is to understand how the normalized total heat flux, which is called the Nusselt number Nu Ra; Pr , changes with two experimental control parameters: the Rayleigh number Ra and the Prandtl number Pr [3]. Recent heat transport measurements [4] have indicated that the functional form of the measured Nu Ra; Pr is perhaps more complicated than simple power laws of Ra and Pr, as was originally proposed [1,2].The theory of Grossmann and Lohse (GL) [2,5] explains this phenomenon by a decomposition of the thermal dissipation field T r and viscous dissipation field u r into two parts. In one scenario [2], T r and u r are decomposed into the boundary-layer and bulk contributions, which have different scaling behavior with varying Ra and Pr. As a result, the total heat flux measured across the entire cell contains both the boundary and bulk contributions, and thus Nu Ra; Pr is described by a sum of two different power laws.Early theories [1,2] assumed that when Ra becomes very large, the bulk contribution will become dominant over the boundary-layer contribution. In this case, Nu Ra; Pr can be described by a simple power law of Ra and Pr. For example, Kraichnan [6] predicted an asymptotic scaling law Nu RaPr 1=2 , which states that the convective heat flux is independent of and . The GL theory also gave the same scaling when both the thermal and viscous dissipations are bulk-dominated. While considerable experimental efforts have been made, this ultimate state of thermal convection still remains elusive [7]. This is caused partially by the fact that the boundaries are very important in this system, even when Ra becomes very large. After all, the convective flow is driven by instabilities of the upper and lower thermal boundary layers. Recent experiment [8] and num...

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Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell

Cited by 282 publications

References 28 publications

Learning to soar in turbulent environments

Learning to soar in turbulent environments

Measured Thermal Dissipation Field in Turbulent Rayleigh-Bénard Convection

Scaling of the Local Convective Heat Flux in Turbulent Rayleigh-Bénard Convection

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