Thermodynamics of fluid turbulence: A unified approach to the maximum transport properties

Ozawa, Hisashi; Shimokawa, Shinya; Sakuma, Hirofumi

doi:10.1103/physreve.64.026303

Cited by 78 publications

(98 citation statements)

References 32 publications

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“…This limit results fundamentally from the laws of thermodynamics, as shown in the brief derivation in the Appendix A1, and surface exchange fluxes are subjected to this limit. This limit relates very closely to a range of previous applications of thermodynamic limits to similar systems, for example, to turbulent phenomena (Ozawa et al, 2001), planetary heat transport (Lorenz et al, 2001), to the atmospheric circulation (Kleidon et al, 2003(Kleidon et al, , 2006, and to hydrology (Kleidon and Schymanski, 2008;Zehe et al, 2010Zehe et al, , 2013Kleidon et al, 2013). While the existence of this thermodynamic limit should hence not be a concern, the question is rather whether land surface fluxes indeed operate at this limit, and whether the assumption of the steady state is justified.…”

Section: Limitationsmentioning

confidence: 99%

Estimates of the climatological land surface energy and water balance derived from maximum convective power

Kleidon

Renner

Porada

2014

Hydrol. Earth Syst. Sci.

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Abstract. The land surface energy and water balances are tightly coupled by the partitioning of absorbed solar radiation into terrestrial radiation and the turbulent fluxes of sensible and latent heat, as well as the partitioning of precipitation into evaporation and runoff. Evaporation forms the critical link between these two balances. Its rate is strongly affected by turbulent exchange as it provides the means to efficiently exchange moisture between the heated, moist surface and the cooled, dry atmosphere. Here, we use the constraint that this mass exchange operates at the thermodynamic limit of maximum power to derive analytical expressions for the partitioning of the surface energy and water balances on land. We use satellite-derived forcing of absorbed solar radiation, surface temperature and precipitation to derive simple spatial estimates for the annual mean fluxes of sensible and latent heat and evaluate these estimates with the ERA-Interim reanalysis data set and observations of the discharge of large river basins. Given the extremely simple approach, we find that our estimates explain the climatic mean variations in net radiation, evaporation, and river discharge reasonably well. We conclude that our analytical, minimum approach provides adequate first order estimates of the surface energy and water balance on land and that the thermodynamic limit of maximum power provides a useful closure assumption to constrain the energy partitioning at the land surface.

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Section: Limitationsmentioning

confidence: 99%

Estimates of the climatological land surface energy and water balance derived from maximum convective power

Kleidon

Renner

Porada

2014

Hydrol. Earth Syst. Sci.

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“…Under this fixed boundary condition, MEP translates into the maximization of the flux, so that Malkus' maximum flux hypothesis is consistent with MEP for fixed boundary conditions. Ozawa et al (2001) related the maximum flux hypothesis to MEP in more detail (see also Schneider and Kay 1994). They argued that the maximization is achieved by the fluid system by creating steep gradients near the system boundary with critical stability numbers (e.g., Reynolds number, Nuesselt number, etc.)…”

Section: Demonstration Of Mep States: Potential Mechanismmentioning

confidence: 99%

Nonequilibrium thermodynamics and maximum entropy production in the Earth system

Kleidon

2009

Naturwissenschaften

149

123

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The Earth system is maintained in a unique state far from thermodynamic equilibrium, as, for instance, reflected in the high concentration of reactive oxygen in the atmosphere. The myriad of processes that transform energy, that result in the motion of mass in the atmosphere, in oceans, and on land, processes that drive the global water, carbon, and other biogeochemical cycles, all have in common that they are irreversible in their nature. Entropy production is a general consequence of these processes and measures their degree of irreversibility. The proposed principle of maximum entropy production (MEP) states that systems are driven to steady states in which they produce entropy at the maximum possible rate given the prevailing constraints. In this review, the basics of nonequilibrium thermodynamics are described, as well as how these apply to Earth system processes. Applications of the MEP principle are discussed, ranging from the strength of the atmospheric circulation, the hydrological cycle, and biogeochemical cycles to the role that life plays in these processes. Nonequilibrium thermodynamics and the MEP principle have potentially wide-ranging implications for our understanding of Earth system functioning, how it has evolved in the past, and why it is habitable. Entropy production allows us to quantify an objective direction of Earth system change (closer to vs further away from thermodynamic equilibrium, or, equivalently, towards a state of MEP). When a maximum in entropy production is reached, MEP implies A. Kleidon (B) Max-Planck-Institut für Biogeochemie, Postfach 10 01 64, 07701 Jena, Germany e-mail: akleidon@bgc-jena.mpg.de that the Earth system reacts to perturbations primarily with negative feedbacks. In conclusion, this nonequilibrium thermodynamic view of the Earth system shows great promise to establish a holistic description of the Earth as one system. This perspective is likely to allow us to better understand and predict its function as one entity, how it has evolved in the past, and how it is modified by human activities in the future.

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“…If the potential gradient at the boundary is fixed, but the flux is allowed to vary, a flux-force trade-off can form within the system. MEP then results in a maximization of the flux [e.g., Ozawa et al, 2001]. An example is Bernard convection, which is driven by fixed temperatures at the boundaries of a convection cell.…”

Section: Role Of Boundary Conditionsmentioning

confidence: 99%

Thermodynamics and optimality of the water budget on land: A review

Kleidon¹,

Schymanski²

2008

Geophysical Research Letters

111

131

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[1] The water balance on land plays a critical role in connecting key hydrological processes with climate and ecology. Over the last few years, several advances have been made in applying thermodynamic and optimality approaches to better describe Earth system processes in general, and the water balance on land in particular. Both concepts relate to the proposed principle of Maximum Entropy Production (MEP), which states that complex systems far from thermodynamic equilibrium organize in a way such that the rate of entropy production-a measure of irreversibility-is maximized in steady state. MEP provides a foundation to understand optimality in hydrology at a fundamental, thermodynamic level that is applicable across a wide range of Earth systems beyond hydrology. This review describes the foundation of the water balance far from thermodynamic equilibrium and potential applications of MEP. Some of the objections to optimality and thermodynamics are discussed as well as its potential implications. Citation: Kleidon, A., and S. Schymanski (2008), Thermodynamics and optimality of the water budget on land: A review, Geophys. Res. Lett., 35, L20404,

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Thermodynamics of fluid turbulence: A unified approach to the maximum transport properties

Cited by 78 publications

References 32 publications

Estimates of the climatological land surface energy and water balance derived from maximum convective power

Estimates of the climatological land surface energy and water balance derived from maximum convective power

Nonequilibrium thermodynamics and maximum entropy production in the Earth system

Thermodynamics and optimality of the water budget on land: A review

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