Prandtl number effects in convective turbulence

Verzicco, Roberto; Camussi, Roberto

doi:10.1017/s0022112098003619

Cited by 179 publications

(212 citation statements)

References 20 publications

Supporting

Mentioning

161

Contrasting

Unclassified

Order By: Relevance

“…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: 88%

Learning to soar in turbulent environments

Reddy

Celani

Sejnowski

et al. 2016

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

150

115

View full text Add to dashboard Cite

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...

show abstract

Section: Modelssupporting

confidence: 88%

Learning to soar in turbulent environments

Reddy

Celani

Sejnowski

et al. 2016

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

150

115

View full text Add to dashboard Cite

show abstract

“…This trend was also reported from simulations of nonrotating convection. 24,25 The model does not reproduce this dependence of Nu on . Given that for Ͼ 1 viscosity is larger than thermal diffusivity, it is plausible that the vortical state is less prominent, and the current model is thus not relevant at higher .…”

Section: Phys Fluids 20 066602 ͑2008͒mentioning

confidence: 93%

A model for vortical plumes in rotating convection

et al. 2008

View full text Add to dashboard Cite

In turbulent rotating convection a typical flow structuring in columnar vortices is observed. In the internal structure of these vortices several symmetries are approximately satisfied. A model for these columnar vortices is derived by prescribing these symmetries. The symmetry constraints are applied to the Navier-Stokes equations with rotation in the Boussinesq approximation. It is found that the application of the symmetries results in a set of linearized equations. An investigation of the linearized equations leads to a model for the columnar vortices and a prediction for the heat flux ͑Nusselt number͒ that is very appropriate compared to the results from direct numerical simulations of the full governing equations.

show abstract

“…[20][21][22]. All else being equal, nonrotating convection experiments and simulations find that low Pr fluids produce more vigorous convection, yet lower Nu values than moderate Pr fluids (23,24). Just as varying Pr affects the dynamics of turbulent convection, so too does the influence of rotation.…”

mentioning

confidence: 99%

Turbulent convection in liquid metal with and without rotation

King

Aurnou

2013

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

View full text Add to dashboard Cite

The magnetic fields of Earth and other planets are generated by turbulent, rotating convection in liquid metal. Liquid metals are peculiar in that they diffuse heat more readily than momentum, quantified by their small Prandtl numbers, Pr = 1. Most analog models of planetary dynamos, however, use moderate Pr fluids, and the systematic influence of reducing Pr is not well understood. We perform rotating Rayleigh-Bénard convection experiments in the liquid metal gallium (Pr = 0:025) over a range of nondimensional buoyancy forcing (Ra) and rotation periods (E). Our primary diagnostic is the efficiency of convective heat transfer (Nu). In general, we find that the convective behavior of liquid metal differs substantially from that of moderate Pr fluids, such as water. In particular, a transition between rotationally constrained and weakly rotating turbulent states is identified, and this transition differs substantially from that observed in moderate Pr fluids. This difference, we hypothesize, may explain the different classes of magnetic fields observed on the Gas and Ice Giant planets, whose dynamo regions consist of Pr < 1 and Pr > 1 fluids, respectively.T he interiors of Earth and other terrestrial bodies, as well as the Gas Giant planets, contain vast oceans of flowing metals. Mixed by turbulent convection as these planets cool, the flowing conductors produce electric currents that maintain planetary magnetic fields. These bodies also rotate, and it is expected that the resulting Coriolis forces strongly influence convective dynamo processes. Beyond linear theory (1), however, not much is known about the dynamics of rotating convection in liquid metal that underlie planetary magnetic field generation.Theory and experiments often focus on a simplified analog of geophysical and astrophysical systems, Rayleigh-Bénard convection (RBC). The RBC system consists of a fluid layer contained between flat, horizontal plates separated by distance h, the bottom of which is warmer than the top by ΔT, and with downward pointing gravity, g. Near the bottom boundary, the fluid warms and expands by a volumetric factor α (per degree kelvin) and similarly cools and contracts near the top boundary, such that the fluid is unstably stratified.Rotating convection is explored by spinning the RBC system about a vertical axis at an angular rate Ω, which is adopted as the reference frame for the model. The fluid dynamics of the system are characterized by three dimensionless parameters. The Prandtl number, Pr ≡ ν=κ, defines the diffusive transport properties of the fluid, where ν and κ are its viscous and thermal diffusivities. The Rayleigh number, Ra ≡ αgΔTh 3 =ðνκÞ, prescribes the magnitude of the buoyancy force. Finally, the rotation period is specified by the Ekman number, E ≡ ν=ð2Ωh 2 Þ. The primary diagnostic used in many convection studies, including this one, is the Nusselt number, which characterizes the efficiency of heat transport by convection as Nu ≡ qh=ðkΔTÞ, where q is total heat flux and k is the fluid's thermal conductivi...

show abstract

Prandtl number effects in convective turbulence

Cited by 179 publications

References 20 publications

Learning to soar in turbulent environments

Learning to soar in turbulent environments

A model for vortical plumes in rotating convection

Turbulent convection in liquid metal with and without rotation

Contact Info

Product

Resources

About