Dissipative heat engine is thermodynamically inconsistent

A heat engine operating on the basis of the Carnot cycle is considered, where the mechanical work performed is dissipated within the engine at the temperature of the warmer isotherm and the resulting heat is added to the engine together with an external heat input. The resulting work performed by the engine per cycle is increased at the expense of dissipated work produced in the previous cycle. It is shown that such a dissipative heat engine is thermodynamically inconsistent violating the first and second laws of thermodynamics. The existing physical models employing the dissipative heat engine concept, in particular, the heat engine model of hurricane development, are physically invalid.Comment: 9 pages, 2 figure

The key physical parameters governing frictional dissipation in a precipitating atmosphere

Precipitation generates small-scale turbulent air flows the energy of which ultimately dissipates to heat. The power of this process has previously been estimated to be around 2-4 W m-2 in the tropics: a value comparable in magnitude to the dynamic power of the global circulation. Here we suggest that this previous power estimate is approximately double the true figure. Our result reflects a revised evaluation of the mean precipitation path length Hp. We investigate the dependence of Hp on surface temperature,relative humidity,temperature lapse rate and degree of condensation in the ascending air. We find that the degree of condensation,defined as the relative change of the saturated water vapor mixing ratio in the region of condensation, is a major factor determining Hp. We estimate from theory that the mean large-scale rate of frictional dissipation associated with total precipitation in the tropics lies between 1 and 2 W m-2 and show that our estimate is supported by empirical evidence. We show that under terrestrial conditions frictional dissipation constitutes a minor fraction of the dynamic power of condensation-induced atmospheric circulation,which is estimated to be at least 2.5 times larger. However,because Hp increases with surface temperature Ts, the rate of frictional dissipation would exceed that of condensation-induced dynamics, and thus block major circulation, at Ts >~320 K in a moist adiabatic atmosphere.Comment: 12 pp, 2 figure

Condensation of water vapor in the gravitational field

Physical peculiarities of water vapor condensation under conditions of hydrostatic equilibrium are considered. The power of stationary dynamic air fluxes and the vertical temperature distribution caused by condensation on large horizontal scales are estimated.Comment: 10 p

Greenhouse effect dependence on atmospheric concentrations of greenhouse substances and the nature of climate stability on Earth

International audienceDue to the exponential positive feedback between sea surface temperature and saturated water vapour concentration, dependence of the planetary greenhouse effect on atmospheric water content is critical for stability of a climate with extensive liquid hydrosphere. In this paper on the basis of the law of energy conservation we develop a simple physically transparent approach to description of radiative transfer in an atmosphere containing greenhouse substances. It is shown that the analytical solution of the equation thus derived coincides with the exact solution of the well-known radiative transfer equation to the accuracy of 20% for all values of atmospheric optical depth. The derived equation makes it possible to easily take into account the non-radiative thermal fluxes (convection and latent heat) and obtain an analytical dependence of the greenhouse effect on atmospheric concentrations of a set of greenhouse substances with arbitrary absorption intervals. The established dependence is used to analyse stability of the modern climate of Earth. It is shown that the modern value of global mean surface temperature, which corresponds to the liquid state of the terrestrial hydrosphere, is physically unstable. The observed stability of modern climate over geological timescales is therefore likely to be due to dynamic singularities in the physical temperature-dependent behaviour of the greenhouse effect. We hypothesise that such singularities may appear due to controlling functioning of the natural global biota and discuss major arguments in support of this conclusion

Biotic pump of atmospheric moisture as driver of the hydrological cycle on land

In this paper the basic geophysical and ecological principles are jointly analyzed that allow the landmasses of Earth to remain moistened sufficiently for terrestrial life to be possible. 1. Under gravity, land inevitably loses water to the ocean. To keep land moistened, the gravitational water runoff must be continuously compensated by the atmospheric ocean-to-land moisture transport. Using data for five terrestrial transects of the International Geosphere Biosphere Program we show that the mean distance to which air fluxes can transport moisture over non-forested areas, does not exceed several hundred kilometers; precipitation decreases exponentially with distance from the ocean. 2. In contrast, precipitation over extensive natural forests does not depend on the distance from the ocean along several thousand kilometers, as illustrated for the Amazon and Yenisey river basins and Equatorial Africa. This points to the existence of an active biotic pump transporting atmospheric moisture inland from the ocean. 3. Physical principles of the biotic moisture pump are investigated based on the previously unstudied properties of atmospheric water vapor, which can be either in or out of aerostatic equilibrium depending on the lapse rate of air temperature. A novel physical principle is formulated according to which the low-level air moves from areas with weak evaporation to areas with more intensive evaporation. Due to the high leaf area index, natural forests maintain high evaporation fluxes, which support the ascending air motion over the forest and "suck in" moist air from the ocean, which is the essence of the biotic pump of atmospheric moisture. In the result, the gravitational runoff water losses from the optimally moistened forest soil can be fully compensated by the biotically enhanced precipitation at any distance from the ocean. 4. It is discussed how a continent-scale biotic water pump mechanism could be produced by natural selection acting on individual trees. 5. Replacement of the natural forest cover by a low leaf index vegetation leads to an up to tenfold reduction in the mean continental precipitation and runoff, in contrast to the previously available estimates made without accounting for the biotic moisture pump. The analyzed body of evidence testifies that the long-term stability of an intense terrestrial water cycle is unachievable without the recovery of natural, self-sustaining forests on continent-wide areas

A critical analysis of the assumptions underlying the formulation of maximum potential intensity for tropical cyclones

Emanuel's concept of maximum potential intensity (E-PI) estimates the maximum velocity of tropical cyclones from environmental parameters assuming thermal wind (gradient-wind and hydrostatic balances) and slantwise neutrality in the free troposphere. E-PI's key equation relates proportionally the radial gradients of saturated moist entropy and angular momentum. Here the E-PI derivation is reconsidered to show that the thermal wind and slantwise neutrality imply zero radial gradients of saturation entropy and angular momentum at an altitude where, for a given radius, the tangential wind has a maximum. It is further shown that, while E-PI's key equation requires that, at the point of maximum tangential wind, the air temperature must increase towards the storm center, the thermal wind equation dictates the opposite. From the analysis of the equations of motion at the altitude of maximum tangential wind in the free troposphere, it is concluded that here the air flow must be supergradient. This implies that the supergradiency factor (a measure of the gradient-wind imbalance) must change in the free troposphere as the air flow tends to restore the balance. It is shown that such a change modifies the derivative of saturation entropy over angular momentum, which cannot therefore remain constant in the free troposphere as E-PI requires. The implications of these findings for the internal coherence of E-PI, including its boundary layer closure, are discussed.Comment: Revised for JAS. Reply to three reviewers can be found in appendix C. 25 pages, 1 figur

Where do winds come from? A new theory on how water vapor condensation influences atmospheric pressure and dynamics

Phase transitions of atmospheric water play a ubiquitous role in the Earth's climate system, but their direct impact on atmospheric dynamics has escaped wide attention. Here we examine and advance a theory as to how condensation influences atmospheric pressure through the mass removal of water from the gas phase with a simultaneous account of the latent heat release. Building from the fundamental physical principles we show that condensation is associated with a decline in air pressure in the lower atmosphere. This decline occurs up to a certain height, which ranges from 3 to 4 km for surface temperatures from 10 to 30 deg C. We then estimate the horizontal pressure differences associated with water vapor condensation and find that these are comparable in magnitude with the pressure differences driving observed circulation patterns. The water vapor delivered to the atmosphere via evaporation represents a store of potential energy available to accelerate air and thus drive winds. Our estimates suggest that the global mean power at which this potential energy is released by condensation is around one per cent of the global solar power -- this is similar to the known stationary dissipative power of general atmospheric circulation. We conclude that condensation and evaporation merit attention as major, if previously overlooked, factors in driving atmospheric dynamics

Comment on "The Tropospheric Land-Sea Warming Contrast as the Driver of Tropical Sea Level Pressure Changes" by Bayr and Dommenget

T Bayr and D Dommenget [J. Climate 26 (2013) 1387] proposed a model of temperature-driven air redistribution to quantify the ratio between changes of sea level pressure $p_s$ and mean tropospheric temperature $T_a$ in the tropics. This model assumes that the height of the tropical troposphere is isobaric. Here problems with this model are identified. A revised relationship between $p_s$ and $T_a$ is derived governed by two parameters -- the isobaric and isothermal heights -- rather than just one. Further insight is provided by the model of R S Lindzen and S Nigam [J. Atmos. Sci. 44 (1987) 2418], which was the first to use the concept of isobaric height to relate tropical $p_s$ to air temperature, and did this by assuming that isobaric height is always around 3 km and isothermal height is likewise near constant. Observational data, presented here, show that neither of these heights is spatially universal nor do their mean values match previous assumptions. Analyses show that the ratio of the long-term changes in $p_s$ and $T_a$ associated with land-sea temperature contrasts in a warming climate -- the focus of Bayr and Dommenget [2013] -- is in fact determined by the corresponding ratio of spatial differences in the annual mean $p_s$ and $T_a$. The latter ratio, reflecting lower pressure at higher temperature in the tropics, is dominated by meridional pressure and temperature differences rather than by land-sea contrasts. Considerations of isobaric heights are shown to be unable to predict either spatial or temporal variation in $p_s$. As noted by Bayr and Dommenget [2013], the role of moisture dynamics in generating sea level pressure variation remains in need of further theoretical investigations.Comment: 26 pages, 11 figures. arXiv admin note: text overlap with arXiv:1404.101