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Nilton O. Rennó

Abstract

Pauluis et al. argue that frictional dissipation of energy around falling hydrometeors is an important entropy source in the tropical atmosphere. Their calculations suggest that the frictional dissipation around hydrometeors is about ⅓ of the work available from a reversible convective heat engine. Moreover, based on the residual of the energy budget of a numerical model, not shown in their note, the authors argue that irreversible entropy sources due to diffusion of water vapor and phase changes reduce the mechanical work available from the convective heat engine by about ⅔. Pauluis et al. conclude that only a tiny fraction of the energy potentially available from a convective heat engine is used to perform work.

Rennó and Ingersoll show that frictional heating can be easily included in the heat engine framework via increases in the thermodynamic efficiency of a reversible heat engine. It is shown that the effect of any other irreversible process is merely to reduce the thermodynamic efficiency of a reversible convective heat engine. Thus, the framework proposed by Rennó and Ingersoll is valid even when the heat engine is as irreversible as suggested by Pauluis et al. Since irreversible entropy sources reduce the mechanical work available from the convective heat engine, the study of Pauluis et al. implies that the bulk thermodynamic efficiency of the tropical atmosphere is only a tiny fraction of that predicted by the framework proposed by Rennó and Ingersoll. Both theoretical and observational evidence that the calculations performed by Pauluis et al. overestimate the irreversible entropy changes in the real tropical atmosphere is shown. Moreover, evidence that numerical models are highly dissipative when compared with nature is shown. Therefore, the interpretation of Pauluis et al. that the reversible heat engine framework grossly overestimates the rate at which work is performed by tropical convective systems is not agreed with.

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Nilton O. Rennó

Abstract

Emanuel and Bister discussed results of numerical experiments in which the radiative cooling rate of the atmosphere was arbitrarily specified. They suggested that the scaling theory for atmospheric convection proposed by Rennó and Ingersoll is not consistent with these results and proposed an alternative theory. Klein, in turn, argued that the results of these numerical experiments are consistent with the scaling theory proposed by Rennó and Ingersoll. The author shows further evidence in support of Klein’s arguments. Furthermore, it is shown that the alternative scaling theory proposed by Emanuel and Bister, though interesting, possesses a thermodynamic inconsistency.

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David K. Adams and Nilton O. Rennó
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Nilton O. Rennó and Howard B. Bluestein

Abstract

It is shown that the simple thermodynamic theory for dust devils, proposed by Rennó et al., also applies to waterspouts. The theory is based on the thermodynamics of heat engines and predicts the central pressure and the wind speed of these convective vortices. Moreover, it provides a simple physical interpretation of their general characteristics. In particular, the heat engine theory shows that convective vortices are more likely to form in the regions where the occurrence of the warmest and moistest updrafts and the coldest and driest downdrafts are supported by the local environment. These are the regions where both the heat input into the convective heat engine is maximum and the solenoidal generation of vorticity is the greatest. This explains why waterspouts are frequently observed near the boundaries between relatively warm and relatively cold waters. Moreover, since the work done by the convective heat engine is equal to the total heat input multiplied by the thermodynamic efficiency, the theory shows that another necessary condition for the formation of intense vortices is the presence of intense convection.

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Nilton O. Rennó and Andrew P. Ingersoll

Abstract

On many planets there is a continuous heat supply to the surface and a continuous emission of infrared radiation to space by the atmosphere. Since the heat source is located at higher pressure than the heat sink, the system is capable of doing mechanical work. Atmospheric convection is a natural heat engine that might operate in this system. Based on the heat engine framework, a simple theory is presented for atmospheric convection that predicts the buoyancy, the vertical velocity, and the fractional area covered by either dry or moist convection in a state of statistical equilibrium. During one cycle of the convective heat engine, heat is taken from the surface layer (the hot source) and a portion of it is rejected to the free troposphere (the cold sink) from where it is radiated to space. The balance is transformed into mechanical work. The mechanical work is expended in the maintenance of the convective motions against mechanical dissipation. Ultimately, the energy dissipated by mechanical friction is transformed into heat. Then, a fraction of the dissipated energy is radiated to space while the remaining portion is recycled by the convecting air parcels. Increases in the fraction of energy dissipated at warmer temperature, at the expense of decreases in the fraction of energy dissipated at colder temperatures, lead to increases in the apparent efficiency of the convective heat engine. The volume integral of the work produced by the convective heat engine gives a measure of the statistical equilibrium amount of convective available potential energy (CAPE) that must be present in the planet's atmosphere so that the convective motions can be maintained against viscous dissipation. This integral is a fundamental global number qualifying the state of the planet in statistical equilibrium conditions. For the earth's present climate, the heat engine framework predicts a CAPE value of the order of 1000 J kg−1 for the tropical atmosphere. This value is in agreement with observations. It also follows from our results that the total amount of CAPE present in a convecting atmosphere should increase with increases in the global surface temperature (or the atmosphere's opacity to infrared radiation).

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David K. Adams and Nilton O. Rennó

Abstract

A recent article by J. I. Yano has indicated that there is an inconsistency in the original formulation of the quasi-equilibrium theory of Arakawa and Schubert. He argues that this inconsistency results from a contradiction in the two asymptotic limits of the theory; that is, the fractional area covered by convection, and the ratio of the convective adjustment and large-scale timescales cannot simultaneously go to zero, σ → 0 and τ ADJ/τ LS → 0. Yano cites the heat engine theory proposed by Rennó and Ingersoll as “formally establishing” this contradiction. It is demonstrated in this paper that the quasi-equilibrium framework originally developed by Arakawa and Schubert is perfectly consistent with the heat engine theory for steady-state convection, that is, when the timescale associated with the large-scale forcing τ LS approximates the effective adjustment timescale of the large-scale ensemble of convective clouds τ EFF. Indeed, the quasi-equilibrium framework states that, on the large scale, the atmosphere is in quasi steady state.

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Nilton O. Rennó and Earle R. Williams

Abstract

Measurements were made to determine the level of origin of air parcels participating in natural convection. Lagrangian measurements of conservative variables are ideal for this purpose. A simple remotely piloted vehicle was developed to make in situ measurements of pressure, temperature, and humidity in the convective boundary layer. These quasi-Lagrangian measurements clearly show that convective plumes originate in the superadiabatic surface layer. The observed boundary layer plumes have virtual temperature excesses of about 0.4 K in a tropical region (Orlando, Florida) and of about 1.5 K in a desert region (Albuquerque, New Mexico). The water vapor contribution to parcel buoyancy was appreciable in Orlando but in Albuquerque was insignificant. These observations indicate that convective available potential energy should he determined by adiabatically lifting air parcels from the surface layer, at screen level.

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Douglas G. Halleaux, Jeffery M. Sussman, and Nilton O. Rennó

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This article describes a Prandtl tube system developed at the University of Michigan to measure the static pressure, the total (or stagnation) pressure, and the velocity in flows whose direction and intensity change rapidly. The ever-changing wind vectors in convective vortices are a challenge for making accurate measurements on them. Accurate measurements of the static pressure are particularly problematic because they require the sensor air intake to be aligned perpendicular to the wind direction. This article describes calibrations and tests of the Michigan Prandtl System (MPS) and, in particular, the characterization of the errors in the static pressure measurements as a function of misalignments between the Prandtl tube and the wind vector. This article shows that the MPS measures the pressure with a relative error of 3.5% for wind flows whose direction is within about 10° of the MPS tube direction. It also shows that the MPS adjusts to changes in wind direction of 90° in about 1.5 s, the average rate of change expected in a typical dust devil of about 15 m of radius traveling at 10 m s−1 (Rennó et al.). Field tests indicate that misalignments between the MPS and the wind vector are usually smaller than ~30° during measurements in dust devils and that these misalignments always cause increases in the static pressure measured and decreases in the total pressure measured.

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Steven L. Mullen, Jeffrey T. Schmitz, and Nilton O. Rennó

Abstract

Intraseasonal fluctuations associated with the Mexican monsoon system are examined for the semiarid Sonoran Desert region. Daily rain gauge accumulations, radiosonde reports, satellite imagery, and global analyses are all analyzed. Composite wet and dry periods during July and August of 1985–92 are compared, and the statistical significance of differences between the composite fields are assessed.

Significant differences exist between many of the wet and dry fields over the Sonoran Desert. As the monsoon shifts from dry to wet conditions, the subtropical ridge moves ∼5° lat northward, and the middle- and upper-tropospheric (700–300 mb) winds back from southwesterly to southeasterly. The midtropospheric transport of water vapor from the southeast strengthens, and the precipitable water values increase by as much as ∼1.2 cm (∼0.5 in.). Middle-tropospheric air parcels ascend into the region from the southeast, while low-level air parcels continue to stream inland from the Gulf of California and up the slopes of the Sierra Madre Occidental. The surface and midtropospheric air parcels rise at an average rate of ∼50–75 mb per day and would saturate within 2 days if undiluted. This combination of conditions leads to a more unstable atmosphere and an increase in convective activity.

Spectral analysis of precipitation data for southeast Arizona indicates that 75% of the temporal variance is contained in fluctuations longer than 7 days and that a statistically significant peak exists in the 12–18-day band. These results suggest that large-scale, low-frequency dynamics might play an important role in modulating the variability of convective activity over the Sonoran Desert.

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Nilton O. Rennó, Matthew L. Burkett, and Matthew P. Larkin

Abstract

Based on the heat engine framework, a simple scaling theory for dust devils is proposed and compared to observations. This theory provides a simple physical interpretation for many of the observed characteristics of dust devils. In particular, it predicts the potential intensity and the diurnal variation of dust devil occurrence. It also predicts that the intensity of dust devils depends on the product of two thermodynamic efficiencies, corresponding respectively to vertical and horizontal temperature gradients.

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