Bibliography:
Bibliography:
2011
Water Vapor and Mechanical Work: A Comparison of Carnot and Steam Cycles
O. Pauluis
J Atmos Sci 68 91--102 (2011)
The impact of water vapor on the production of kinetic energy in the atmosphere is discussed here by comparing two idealized heat engines: the Carnot cycle and the steam cycle. A steam cycle transports water from a warm moist source to a colder dryer sink. It acts as a heat engine in which the energy source is the latent heat of evaporation. It is shown here that the amount of work produced by a steam cycle depends on relative humidity and is always less than that produced by the corresponding Carnot cycle.The Carnot and steam cycles can be combined into a mixed cycle that is forced by both sensible and latent heating at the warm source. The work performed depends on four parameters: the total energy transport; the temperature difference between the energy source and sink; the Bowen ratio, which measures the partitioning between the sensible and latent heat transports; and the relative humidity of the atmosphere. The role of relative humidity on the work produced by a steam cycle is discussed in terms of the Gibbs free energy and in terms of the internal entropy production.
M. Bister and N. Renno and O. Pauluis and K. Emanuel
P Roy Soc A-Math Phy 467 1--6 (2011)
Makarieva et al. (2010) assert that a dissipative heat engine is impossible and criticize earlier published work that they claim violates the laws of thermodynamics. Here we show that the earlier work does not violate fundamental physical laws and suggest that Makarieva et al. (2010) were misinterpreting expressions for wind speed as ones for work done on external objects. Moreover, we dispute their assertion that dissipative heating is necessarily compensated by a reduction of external heating.
2010
The Global Atmospheric Circulation in Moist Isentropic Coordinates
O. Pauluis and A. Czaja and R. Korty
J. Climate 23 3077--3093 (2010)
Differential heating of the earth's atmosphere drives a global circulation that transports energy from the tropical regions to higher latitudes. Because of the turbulent nature of the flow, any description of a "mean circulation'' or "mean parcel trajectories'' is tied to the specific averaging method and coordinate system. In this paper, the NCEP-NCAR reanalysis data spanning 1970-2004 are used to compare the mean circulation obtained by averaging the flow on surfaces of constant liquid water potential temperature, or dry isentropes, and on surfaces of constant equivalent potential temperature, or moist isentropes. While the two circulations are qualitatively similar, they differ in intensity. In the tropics, the total mass transport on dry isentropes is larger than the circulation on moist isentropes. In contrast, in midlatitudes, the total mass transport on moist isentropes is between 1.5 and 3 times larger than the mass transport on dry isentropes.It is shown here that the differences between the two circulations can be explained by the atmospheric transport of water vapor. In particular, the enhanced mass transport on moist isentropes corresponds to a poleward flow of warm moist air near the earth's surface in midlatitudes. This low-level poleward flow does not appear in the zonally averaged circulation on dry isentropes, as it is hidden by the presence of a larger equatorward flow of drier air at same potential temperature. However, as the equivalent potential temperature in this low-level poleward flow is close to the potential temperature of the air near the tropopause, it is included in the total circulation on moist isentropes. In the tropics, the situation is reversed: the Hadley circulation transports warm moist air toward the equator, and in the opposite direction to the flow at upper levels, and the circulation on dry isentropes is larger than that on moist isentropes.The relationship between circulation and entropy transport is also analyzed. Agross stratification is defined as the ratio of the entropy transport to the net transport on isentropic surfaces. It is found that in midlatitudes the gross stability for moist entropy is approximately the same as that for dry entropy. The gross stratification in the midlatitude circulation differs from what one would expect for either an overturning circulation or horizontal mixing; rather, it confirms that warm moist subtropical air ascends into the upper troposphere within the storm tracks.
IDEALIZED MOIST RAYLEIGH-BENARD CONVECTION WITH PIECEWISE LINEAR EQUATION OF STATE
O. Pauluis and J. Schumacher
Commun Math Sci 8 295--319 (2010)
An idealized framework to study the impacts of phase transitions on atmospheric dynamics is described. Condensation of water vapor releases a significant amount of latent heat, which directly affects the atmospheric temperature and density. Here, phase transitions are treated by assuming that air parcels are in local thermodynamic equilibrium, which implies that condensed water can only be present when the air parcel is saturated. This reduces the number of variables necessary to describe the thermodynamic state of moist air to three. It also introduces a discontinuity in the partial derivatives of the equation of state. A simplified version of the equation of state is obtained by a separate linearization for saturated and unsaturated parcels. When this equation of state is implemented in a Boussinesq system, the buoyancy can be expressed as a piecewise linear function of two prognostic thermodynamic variables, D and M, and height z. Numerical experiments on the nonlinear evolution of the convection and the impact of latent heat release on the buoyant flux are presented.
Impacts of Convective Lifetime on Moist Geostrophic Adjustment
J. Dias and O. Pauluis
J Atmos Sci 67 2960--2971 (2010)
This paper presents a theoretical study of the effects of moist convection on geostrophic adjustment in an infinite channel. The governing equations correspond to a linearized shallow water system of equations for the atmosphere first vertical baroclinic mode, which is coupled to a vertically averaged moisture equation. The coupling is through a parameterization that represents precipitation. The transient behavior and final state of the flow initially at rest with active precipitation limited to half of the channel is investigated, both numerically and analytically. It is shown that an initial imbalance resulting from precipitation induces a circulation that dries out the nonprecipitating region and further enhances precipitation. This interaction between precipitation and dynamics leads to a sharper temperature gradient and stronger jet in the final state, when compared to the dry adjustment. Unlike in the dry case, the moist geostrophic adjustment cannot be entirely determined from the initial unbalanced flow, since it depends on the time scale for convection. Analytic approximations are derived in limits of both fast and slow convective adjustment time.
Winter intensification of the moist branch of the circulation in simulations of 21st century climate
F. Laliberte and O. Pauluis
Geophys Res Lett 37 L20707 (2010)
In this paper, changes in isentropic circulations associated with global warming in the A1B model outputs for the 20th and 21st centuries are analyzed. The changes in the circulations on dry and moist isentropes are quantified through the use of three bulk measures of the circulations: mass transport, entropy transport and effective stratification. The circulation on dry isentropes is expected to weaken due to a reduction of the meridional heat transport and to an increase in stratification. In contrast, the moist branch of the circulation, measured in terms of the difference between the circulations on moist and dry isentropes, strengthens during the winter months. This intensification is characterized not only by an increase in the eddy latent heat transport but also by an increase in the mass transport. This indicate a larger poleward mass flow of warm moist subtropical air into the stormtracks leading to enhanced moist ascent within baroclinic eddies. Citation: Laliberte, F., and O. Pauluis (2010), Winter intensification of the moist branch of the circulation in simulations of 21st century climate, Geophys. Res. Lett., 37, L20707, doi:10.1029/2010GL045007.
Buoyancy statistics in moist turbulent Rayleigh-Benard convection
J. Schumacher and O. Pauluis
J. Fluid Mech. 648 509--519 (2010)
We study shallow moist Rayleigh-Benard convection in the Boussinesq approximation in three-dimensional direct numerical simulations. The thermodynamics of phase changes is approximated by a piecewise linear equation of state close to the phase boundary. The impact of phase changes on the turbulent fluctuations and the transfer of buoyancy through the layer is discussed as a function of the Rayleigh number and the ability to form liquid water. The enhanced buoyancy flux due to phase changes is compared with dry convection reference cases and related to the cloud cover in the convection layer. This study indicates that the moist Rayleigh-Benard problem offers a practical framework for the development and evaluation of parameterizations for atmospheric convection.
It is not the entropy you produce, rather, how you produce it
T. Volk and O. Pauluis
Philos T R Soc B 365 1317--1322 (2010)
The principle of maximum entropy production (MEP) seeks to better understand a large variety of the Earth's environmental and ecological systems by postulating that processes far from thermodynamic equilibrium will 'adapt to steady states at which they dissipate energy and produce entropy at the maximum possible rate'. Our aim in this 'outside view', invited by Axel Kleidon, is to focus on what we think is an outstanding challenge for MEP and for irreversible thermodynamics in general: making specific predictions about the relative contribution of individual processes to entropy production. Using studies that compared entropy production in the atmosphere of a dry versus humid Earth, we show that two systems might have the same entropy production rate but very different internal dynamics of dissipation. Using the results of several of the papers in this special issue and a thought experiment, we show that components of life-containing systems can evolve to either lower or raise the entropy production rate. Our analysis makes explicit fundamental questions for MEP that should be brought into focus: can MEP predict not just the overall state of entropy production of a system but also the details of the sub-systems of dissipaters within the system? Which fluxes of the system are those that are most likely to be maximized? How it is possible for MEP theory to be so domain-neutral that it can claim to apply equally to both purely physical-chemical systems and also systems governed by the 'laws' of biological evolution? We conclude that the principle of MEP needs to take on the issue of exactly how entropy is produced.
Cloud patterns and mixing properties in shallow moist Rayleigh-Benard convection
T. Weidauer and O. Pauluis and J. Schumacher
New J Phys 12 105002 (2010)
Three-dimensional direct numerical simulations of idealized moist turbulent Rayleigh-Benard convection are presented. The thermodynamics of moist air is linearized close to the phase boundary between water vapor and liquid water. This formulation allows for a simplified saturation condition for the cloud formation, but omits supersaturation and rain. The sensitivity of this problem to changes of the Rayleigh number, the aspect ratio of the convection layer and the water vapor concentration is studied. The Rayleigh number is found to impact the behavior of the system in multiple ways. First, the relaxation time toward a well-mixed turbulent state increases with the Rayleigh number. Similarly, the flow exhibits a higher spatial and temporal intermittency at higher Rayleigh number. This is in line with an enhanced intermittency of the upward buoyancy flux, which we quantify by a multifractal analysis. In addition, phase transition introduces an asymmetry in the distribution of the thermodynamic properties of the well-mixed state. This asymmetry is most pronounced in layers where clouds are partially present. Furthermore, the geometrical properties of the cloud formations averaged with respect to the height of the layer are studied. Similar to isocontours in scalar mixing, the boundaries of isolated clouds show no strict (mono-)fractal behavior. The results of the perimeter-area analysis of the largest isolated clouds agree well with those of large eddy simulations of cumulus convection. This perimeter-area scaling is also similar to that of percolation processes in a plane.
2009
Convectively Coupled Waves Propagating along an Equatorial ITCZ
J. Dias and O. Pauluis
J Atmos Sci 66 2237--2255 (2009)
The dynamics of convectively coupled gravity waves traveling over a precipitating region are analyzed in an idealized model for the large-scale atmospheric circulation. The model is composed of a shallow water system coupled to an advection equation for moisture through the convection term, utilizing a quasi-equilibrium relaxation to moisture closure. Here the authors investigate the model in the strict quasi-equilibrium (SQE) of infinitely short relaxation time. This framework is applied to study the behavior of a disturbance propagating along a narrow precipitation band, similar to the intertropical convergence zone (ITCZ). For an ITCZ width on the order of the equatorial Rossby radius, Kelvin waves propagate at the moist gravity wave speed (about 15 m s(-1)), whereas for a narrow ITCZ, the propagation speed is comparable to the dry gravity wave (about 50 m s(-1)). It is also shown that a Kelvin wave propagating along a narrow precipitation region exhibits a meridional circulation that modulates the precipitation rate and affects the propagation speed of the wave.
2008
The global atmospheric circulation on moist isentropes
O. Pauluis and A. Czaja and R. Korty
Science 321 1075--1078 (2008)
The global atmospheric circulation transports energy from the equatorial regions to higher latitudes through a poleward flow of high- energy and - entropy parcels and an equatorward flow of air with lower energy and entropy content. Because of its turbulent nature, this circulation can only be described in some averaged sense. Here, we show that the total mass transport by the circulation is twice as large when averaged on moist isentropes than when averaged on dry isentropes. The additional mass transport on moist isentropes corresponds to a poleward flow of warm moist air near Earth's surface that rises into the upper troposphere within mid- latitudes and accounts for up to half of the air in the upper troposphere in polar regions.
Thermodynamic consistency of the anelastic approximation for a moist atmosphere
O. Pauluis
J Atmos Sci 65 2719--2729 (2008)
The primary goal of this paper is to validate the use of the anelastic approximation for fluids with a complex equation of state such as moist air or seawater. The anelastic approximation is based on a leading-order expansion of the equations of motion for a compressible fluid in terms of density. Its application to atmospheric flows has been based on a dry framework that treats phase transitions as an external energy source. However, cloudy air is more accurately described as a two-phase fluid in which condensed water and water vapor are in thermodynamic equilibrium. Thermodynamic equilibrium reduces to three the number of state variables necessary to describe the thermodynamic state of moist air, and leads to a discontinuity in the partial derivatives of the equation of state at the saturation point. A version of the anelastic approximation for a moist atmosphere is derived here by considering the atmospheric density as a small perturbation from a moist-adiabatic reference profile, and using moist entropy and total water content as prognostic variables, with buoyancy determined from the complete nonlinear equation of state.The key finding of this paper is that this implementation of the anelastic approximation conserves energy. The total energy is equal to the sum of the kinetic energy and the thermodynamic energy. The latter is found to be equal to the sum of the enthalpy and geopotential energy of the parcel. Furthermore, the state relationships between this thermodynamic energy, entropy, and other state variables are the same as those for moist air after replacing the total pressure with the reference state pressure. This guarantees that, as long as the pressure perturbation remains small, the thermodynamic behavior of a fluid under the anelastic approximation is fully consistent with both the first and second laws of thermodynamics.Two implications of this finding are also discussed. First, it is shown that the first and second laws of thermodynamics constrain the vertically integrated buoyancy flux. This is equivalent to deriving the total work performed in a compressible atmosphere from its entropy and energy budgets. Second, it is argued that an anelastic model can be built with temperature or enthalpy as a prognostic variable instead of entropy. The rate of change for this new state variable can be obtained from energy conservation, so that such a model explicitly obeys the first law of thermodynamics. The entropy in this model is equal to the entropy of the parcel evaluated at the reference pressure, and its evolution obeys the second law of thermodynamics.
Precipitation fronts and the reflection and transmission of tropical disturbances
O. Pauluis and D. M. W. Frierson and A. J. Majda
Q J Roy Meteor Soc 134 913--930 (2008)
This paper investigates the interactions between precipitation and the circulation in an idealized model for the tropical atmosphere where convection is represented by a quasi-equilibrium closure. When studying large-scale circulation in the Tropics, the governing equations can be further simplified by making the strict quasi-equilibrium assumption which considers that convection acts to instantaneously adjust the atmospheric temperature profile to a moist adiabatic lapse rate. It is shown here that, under this assumption, the interface between the precipitating and non-precipitating regions exhibits a discontinuity in the precipitation rate and vertical velocity. Furthermore, this interface, referred to as a precipitation front, moves at a velocity distinct from the propagation speed of dry and moist disturbances. The theory predicts the existence of three types of precipitation fronts: drying fronts, slow moistening fronts and fast moistening fronts. In previous studies, numerical simulations have demonstrated the existence of the three types of front, and have also confirmed that the precipitation front theory offers a good approximation for the behaviour of the interface between dry and moist regions for finite value of the convective adjustment time.A new framework is proposed here in which the encounter of an atmospheric disturbance and the edge of a precipitation region is recast as a Riemann problem. It is shown that, for any precipitation fronts, there are three incident characteristics but only two outgoing characteristics. This makes it possible to solve simultaneously for the intensity of the outgoing invariants and the propagation speed of the front. This also implies that atmospheric disturbances will be partially transmitted and partially reflected when encountering a precipitation front. For small perturbations, linear reflection and transmission coefficients can be computed analytically. These results also indicate that that disturbances can be amplified through over-transmission or over-reflection. These theoretical results are confirmed in numerical simulations of an idealized Walker circulation. A solution that includes a stationary precipitation front is perturbed by adding a small-amplitude gravity wave, convectively coupled gravity wave, or moisture disturbance. All numerical simulations exhibit reflection and transmission of the incoming signal, and one simulation shows a case of over-transmission of the incoming disturbance. Copyright (C) 2008 Royal Meteorological Society.
2007
Sources and sinks of available potential energy in a moist atmosphere
O. Pauluis
J Atmos Sci 64 2627--2641 (2007)
Available potential energy (APE) is defined as the difference between the total static energy of the atmosphere and that of a reference state that minimizes the total static energy after a sequence of reversible adiabatic transformations. Determining the rate at which APE is generated in the atmosphere allows one to estimate the amount of kinetic energy that can be generated by atmosphere flows. Previous expressions for the sources and sinks of APE rely on a dry framework and are limited by the fact that they require prior knowledge of the distribution of latent heat release by atmospheric motion. In contrast, this paper uses a moist APE framework to derive a general formula for the sources and sinks of APE that can be equally applied to dry and moist circulations.Two key problems are addressed here. First, it is shown that any reorganization of the reference state due to diabatic heating or addition of water does not change its total static energy. This property makes it possible to determine the rate of change in APE even in the absence of an analytic formula for the reference state, as is the case in a moist atmosphere. Second, the effects of changing the total water content of an air parcel are also considered in order to evaluate the changes of APE due to precipitation, evaporation, and diffusion of water vapor. Based on these new findings, one can obtain the rate of change of APE from that of atmospheric entropy, water content, and pressure.This result is used to determine the sources and sinks of APE due to different processes such as external energy sources, frictional dissipation, diffusion of sensible heat and water vapor, surface evaporation, precipitation, and reevaporation. These sources and sinks are then discussed in the context of an idealized atmosphere in radiative-convective equilibrium. For a moist atmosphere, the production of APE by the surface energy flux is much larger than any observational or theoretical estimates of frictional dissipation, and, as is argued here, must be balanced by a comparable sink of APE due to the diffusion of water vapor from unstable to stable air parcels.
Resolving convection in a global hypohydrostatic model
S. Garner and D. M. W. Frierson and I. M. Held and O. Pauluis and G. K. Vallis
J Atmos Sci 64 2061--2075 (2007)
Convection cannot be explicitly resolved in general circulation models given their typical grid size of 50 km or larger. However, by multiplying the vertical acceleration in the equation of motion by a constant larger than unity, the horizontal scale of convection can be increased at will, without necessarily affecting the larger-scale flow. The resulting hypohydrostatic system has been recognized for some time as a way to improve numerical stability on grids that cannot well resolve nonhydrostatic gravity waves. More recent studies have explored its potential for better representing convection in relatively coarse models.The recent studies have tested the rescaling idea in the context of regional models. Here the authors present global aquaplanet simulations with a low-resolution, nonhydrostatic model free of convective parameterization, and describe the effect on the global climate of very large rescaling of the vertical acceleration. As the convection expands to resolved scales, a deepening of the troposphere, a weakening of the Hadley cell, and a moistening of the lower troposphere is found, compared to solutions in which the moist convection is essentially hydrostatic. The growth rate of convective instability is reduced and the convective life cycle is lengthened relative to synoptic phenomena. This problematic side effect is noted in earlier studies and examined further here.
2006
The hypohydrostatic rescaling and its impacts on modeling of atmospheric convection
O. Pauluis and D. M. W. Frierson and S. T. Garner and I. M. Held and G. K. Vallis
Theoretical and Computational Fluid Dynamics 20 485--499 (2006)
The atmospheric circulation spans a wide range of spatial scales, including the planetary scale (similar to 10,000 km), synoptic scale (similar to 2,000 km), mesoscale (similar to 200 km), and convective scales (< 20 km). The wide scale separation between convective motions, responsible for the vertical energy transport, and the planetary circulation, responsible for the meridional energy transport, has prevented explicit representation of convective motions in global atmospheric models. Kuang et al. (Geophys. Res. Lett. 32: L02809, 2005) have suggested a way to circumvent this limitation through a rescaling that they refer to as Diabatic Acceleration and REscaling (DARE). We focus here on a modified version of the procedure that we refer to as hypohydrostatic rescaling. These two strategies are equivalent for inviscid and adiabatic flow in the traditional meteorological setting in which the vertical component of the Coriolis acceleration is ignored, but they differ when atmospheric physics is taken into account. It is argued here that, while the hypohydrostatic rescaling preserves the dynamics of the planetary scale circulation, it increases the horizontal scale of convective motions. This drastically reduces the computational cost for explicit simulation of hypohydrostatic convection in a global atmospheric model. A key question is whether explicit simulations of hypohydrostatic convection could offer a valid alternative to convective parameterization in global models. To do so, radiative-convective equilibrium is simulated with a high-resolution non-hydrostatic model using different model resolutions and values of the rescaling parameter. When the behavior of hypohydrostatic convection is compared with coarse-resolution simulations of convection, the latter set of simulations reproduce more accurately the result from a reference high-resolution simulation. This is particularly true for the convective velocity and cloud ice distributions. Scaling arguments show that hypohydrostatic rescaling increases the convective overturning time. In particular, this convective slowdown associated with the hypohydrostatic rescaling is more significant than the slowdown resulting from under-resolving the convective elements. These results cast doubt on the practical value of the hypohydrostatic rescaling as an alternative to convective parameterization.
Sensitivity of radiative-convective equilibrium simulations to horizontal resolution
O. Pauluis and S. Garner
J Atmos Sci 63 1910--1923 (2006)
This paper investigates the impacts of horizontal resolution on the statistical behavior of convection. An idealized radiative-convective equilibrium is simulated for model resolutions ranging between 2 and 50 km. The simulations are compared based upon the analysis of the mean state, the energy and water vapor transport, and the probability distribution functions for various quantities. It is shown that, at a coarse resolution, the model is unable to capture the mixing associated with shallow clouds. This results in a dry bias in the lower troposphere, and in an excessive amount of water clouds. Despite this deficiency, the coarse resolution simulations are able to reproduce reasonably well the statistical properties of deep convective towers. This is particularly apparent in the cloud ice and vertical velocity distributions that exhibit a very robust behavior.A theoretical scaling for the vertical velocity as function of the grid resolution is derived based upon the behavior of an idealized air bubble. It is shown that the vertical velocity of an ascending air parcel is determined by its aspect ratio, with a wide, flat parcel rising at a much slower pace than a narrow one. This theoretical scaling law exhibits a similar sensitivity to that of the numerical simulations. It is used to renormalize the probability distribution functions for vertical velocity, which show a very good agreement for resolutions up to 16 km. This new scaling law offers a way to improve direct simulations of deep convection in coarse resolution models.
2004
Sensitivity of radiative-convective equilibrium simulations to horizontal resolution
O. Pauluis
J Atmos Sci 61 1161--1173 (2004)
The behavior of the Hadley circulation is analyzed in the context of an idealized axisymmetric atmosphere. It is argued that the cross-equatorial Hadley circulation exhibits two different regimes depending on the depth of the planetary boundary layer and the sea surface temperature gradient in the equatorial regions. The first regime corresponds to a classic direct circulation from the summer to winter hemisphere. The second regime differs in that the return flow rises above the boundary layer in the winter hemisphere and crosses the equator within the free troposphere. This equatorial jump is associated with a secondary maximum in precipitation on the winter side of the equator.The transition between these two regimes can be understood through the dynamical constraints on the low-level flow. Strong virtual temperature gradients are necessary for the return flow to cross the equator within the planetary boundary layer. However, the mass transport driven by such a temperature gradient is highly sensitive to the thickness of the boundary layer. For a weak temperature gradient or a shallow boundary layer, the return flow is prevented from crossing the equator within the the boundary layer and, instead, must do so in the free troposphere. These dynamical constraints act equally in a dry and a moist atmosphere. However, a comparison between dry and moist simulations shows that the equatorial jump is much deeper in a moist atmosphere. This is interpreted as resulting from the feedbacks between the large-scale flow and moist convection, which results in establishing a very weak gross moist stability for the equatorial jump.
Numerical instability resulting from infrequent calculation of radiative heating
O. Pauluis and K. Emanuel
Mon.Wea. Rev. 132 673--686 (2004)
Owing to its relative expense, radiative heating is often not calculated for every time step in numerical simulations of the atmosphere. This is justified when the radiation field evolves slowly in comparison to the atmospheric flow. However, when the effects of variable water vapor and clouds are taken into account, the radiation field can change rapidly, and the finite time between calls to the radiation scheme can introduce a destabilizing time lag. In the worst case, this lag gives rise to an exponential numerical instability with a growth rate proportional to the time interval between radiative calculations. In less drastic circumstances, in which the radiation would damp oscillations of the real system, numerical instability occurs when the time interval between calls to the radiation scheme exceeds a critical value that depends on the Doppler-shifted natural oscillation frequency and the radiative damping rate. It is shown that this type of instability occurs in a single-column model as well as in an idealized general circulation model. The critical frequency at which the radiative heating rate should be computed is found to depend on several factors, including the large-scale circulation and the model resolution. Several potential remedies are discussed
Large scale dynamics of precipitation fronts in the tropical atmosphere: A novel relaxation limit
D. M. W. Frierson , A. J. Majda and O. Pauluis
Comm. Math. Sci. 2 591-626 (2004)
A simplified set of equations is derived systematically below for the interaction of large scale flow fields and precipitation in the tropical atmosphere. These equations, the Tropical Climate Model, have the form of a shallow water equation and an equation for moisture coupled through a strongly nonlinear source term. This source term, the precipitation, is of relaxation type in one region of state space for the temperature and moisture, and vanishes identically elsewhere in the state space of these variables. In addition, the equations are coupled nonlinearly to the equations for barotropic incompressible flow. Several mathematical features of this system are developed below including energy principles for solutions and their first derivatives independent of relaxation time. With these estimates, the formal infinitely fast relaxation limit converges to a novel hyperbolic free boundary problem for the motion of precipitation fronts from a large scale dynamical perspective. Elementary exact solutions of the limiting dynamics involving precipitation fronts are developed below and include three families of waves: fast drying fronts as well as slow and fast moistening fronts. The last two families of waves violate Lax’s Shock Inequalities; nevertheless, numerical experiments presented below confirm their robust realizability with realistic finite relaxation times. From the viewpoint of tropical atmospheric dynamics, the theory developed here provides a new perspective on the fashion in which the prominent large scale regions of moisture in the tropics associated with deep convection can move and interact with large scale dynamics in the quasi-equilibrium approximation
2002
O. Pauluis and I. M. Held
J Atmos Sci 59 125--139 (2002)
The entropy budget of an atmosphere in radiative-convective equilibrium is analyzed here. The differential heating of the atmosphere, resulting from surface heat fluxes and tropospheric radiative cooling, corresponds to a net entropy sink. In statistical equilibrium, this entropy sink is balanced by the entropy production due to various irreversible processes such as frictional dissipation, diffusion of heat, diffusion of water vapor, and irreversible phase changes. Determining the relative contribution of each individual irreversible process to the entropy budget can provide important information on the behavior of convection.The entropy budget of numerical simulations with a cloud ensemble model is discussed. In these simulations, it is found that the dominant irreversible entropy source is associated with irreversible phase changes and diffusion of water vapor. In addition, a large fraction of the frictional dissipation results from falling precipitation, and turbulent dissipation accounts for only a small fraction of the entropy production.This behavior is directly related to the fact that the convective heat transport is mostly due to the latent heat transport. In such cases, moist convection acts more as an atmospheric dehumidifier than as a heat engine. The amount of work available to accelerate convective updrafts and downdrafts is much smaller than predicted by studies that assume that moist convection behaves mostly as a perfect heat engine.
O. Pauluis and I. M. Held
J Atmos Sci 59 140--149 (2002)
In moist convection, atmospheric motions transport water vapor from the earth's surface to the regions where condensation occurs. This transport is associated with three other aspects of convection: the latent heat transport, the expansion work performed by water vapor, and the irreversible entropy production due to diffusion of water vapor and phase changes. An analysis of the thermodynamic transformations of atmospheric water yields what is referred to as the entropy budget of the water substance, providing a quantitative relationship between these three aspects of moist convection. The water vapor transport can be viewed as an imperfect heat engine that produces less mechanical work than the corresponding Carnot cycle because of diffusion of water vapor and irreversible phase changes.The entropy budget of the water substance provides an alternative method of determining the irreversible entropy production due to phase changes and diffusion of water vapor. This method has the advantage that it does not require explicit knowledge of the relative humidity or of the molecular flux of water vapor for the estimation of the entropy production. Scaling arguments show that the expansion work of water vapor accounts for a small fraction of the work that would be produced in the absence of irreversible moist processes. It is also shown that diffusion of water vapor and irreversible phase changes can be interpreted as the irreversible counterpart to the continuous dehumidification resulting from condensation and precipitation. This leads to a description of moist convection where it acts more as an atmospheric dehumidifier than as a heat engine.
2001
Comments on "Frictional dissipation in a precipitating atmosphere'' - Reply
O. Pauluis and V. Balaji and I. M. Held
J Atmos Sci 58 1178--1179 (2001)
2000
Frictional dissipation in a precipitating atmosphere
O. Pauluis and V. Balaji and I. M. Held
J Atmos Sci 57 989--994 (2000)
The frictional dissipation in the shear zone surrounding falling hydrometeors is estimated to be 2-4 W m(-2) in the Tropics. A numerical model of radiative-convective equilibrium with resolved three-dimensional moist convection confirms this estimate and shows that the precipitation-related dissipation is much larger than the dissipation associated with the turbulent energy cascade from the convective scale. Equivalently, the work performed by moist convection is used primarily to lift water rather than generate kinetic energy of the convective airflow. This fact complicates attempts to use the entropy budget to derive convective velocity scales.