Production Of Available Potential Energy Research Articles

Turbulent Convection Insights from Small-Scale Thermal Forcing with Zero Net Heat Flux at a Horizontal Boundary.

A large-scale circulation, a turbulent boundary layer, and a turbulent plume are noted features of convection at large Rayleigh numbers under differential heating on a single horizontal boundary. These might be attributed to the forcing, which in all studies has been limited to a unidirectional gradient over the domain scale. We instead apply forcing on a length scale smaller than the domain, and with variation in both horizontal directions. Direct numerical simulations show turbulence throughout the domain, a regime transition to a dominant domain-scale circulation, and a region of logarithmic velocity in the boundary layer, despite zero net heat flux. The results show significant similarities to Rayleigh-Bénard convection, demonstrate the significance of plume merging, support the hypothesis that the key driver of convection is the production of available potential energy without necessarily supplying total potential energy, and imply that contributions to domain-scale circulation in the oceans need not be solely from the large-scale gradients of forcing.

Large‐scale character of an atmosphere in rotating radiative‐convective equilibrium

AbstractA rotating radiative‐convective equilibrium on a sphere is reached using a global atmospheric model with prescribed globally uniform sea surface temperature and no insolation. In such an equilibrium state, multiple tropical cyclone‐like vortices coexist in the extratropics, moving slowly poleward and westward. Many vortices have a lifetime longer than 2 months and travel from the tropics to the polar regions. The typical spacing of simulated tropical cyclone‐like vortices is comparable to the deformation radius, while the production of available potential energy is at a scale slightly smaller than those vortices. It is hypothesized that the growth of tropical cyclone‐like vortices is driven by the self‐aggregation of convection, while baroclinic instability destabilizes any vortices that grow significantly larger than the deformation radius. A weak Hadley circulation dominates in the deep tropics, and an eastward propagating wave number 1 Kelvin‐like mode having a period of 30–40 days develops at the equator. The weak Hadley circulation is found to emerge from an initially quiescent atmosphere due to poleward momentum transport by the vortices.

Moist versus Dry Baroclinic Instability in a Simplified Two-Layer Atmospheric Model with Condensation and Latent Heat Release

AbstractThe authors undertake a detailed analysis of the influence of water vapor condensation and latent heat release upon the evolution of the baroclinic instability. The framework consists in a two-layer rotating shallow-water model with moisture coupled to dynamics through mass exchange between the layers due to condensation/precipitation. The model gives all known in literature models of this kind as specific limits. It is fully nonlinear and ageostrophic. The reference state is a baroclinic Bickley jet. The authors first study its “dry” linear instability and then use the most unstable mode to initialize high-resolution numerical simulations of the life cycle of the instability in nonprecipitating (moisture being a passive tracer) and precipitating cases. A new-generation well-balanced finite-volume scheme is used in these simulations.The evolution in the nonprecipitating case follows the standard cyclonic wave-breaking life cycle of the baroclinic instability, which is reproduced with a high fidelity. In the precipitating case, the onset of condensation significantly increases the growth rate of the baroclinic instability at the initial stages due to production of available potential energy by the latent heat release. Condensation occurs in frontal regions and wraps up around the cyclone, which is consistent with the moist cyclogenesis theory and observations. Condensation induces a clear-cut cyclone–anticyclone asymmetry. The authors explain the underlying mechanism and show how it modifies the equilibration of the flow at the late stages of the saturation of the instability. In spite of significant differences in the evolution, only weak differences in various norms of the perturbations remain between precipitating and nonprecipitating cases at the end of the saturation process.

Available Potential Energy and Irreversible Mixing in the Meridional Overturning Circulation

Abstract The overturning circulation of the global oceans is examined from an energetics viewpoint. A general framework for stratified turbulence is used for this purpose; first, it highlights the importance of available potential energy in facilitating the transfer of kinetic energy to the background potential energy (defined as the adiabatically rearranged state with no motion). Next, it is shown that it is the rate of transfer between different energy reservoirs that is important for the maintenance of the ocean overturning, rather than the total amount of potential or kinetic energy. A series of numerical experiments is used to assess which energy transfers are significant in the overturning circulation. In the steady state, the rate of irreversible diapycnal mixing is necessarily balanced by the production of available potential energy sourced from surface buoyancy fluxes. Thus, the external inputs of available potential energy from surface buoyancy forcing and of kinetic energy from other sources (such as surface winds and tides, and leading to turbulent mixing) are both necessary to maintain the overturning circulation.

Further studies of the properties of cellular convection in a conditionally unstable atmosphere

The problem of convection in an atmosphere which is stable for dry adiabatic descending motion but unstable for saturated ascending motion is analyzed, with a view to the determinations of the preferred areas of the ascending and descending regions and the distributions of the convection currents. Two somewhat different approaches have been formulated, one is based on an integral relation obtained from the governing linearized differential equation while the other is based on the energy integral. It is found that the area of the ascending region tends to decrease while that of the descending region tends to increase with increasing static stability for unsaturated motion, but both of them are finite under all realistic conditions. On the other hand, when the mean lapse-rate is far above the moist-adiabatic lapse-rate, the consideration of the maximum efficiency in the production of available potential energy gives a much larger preferred area ratio, which tends to approach a constant value for every given static stability factor in the descending region. The theory predicts that for large stability factor R ′ 2 (> 100) in the descending region the area ratio A a / A d increases linearly with the ratio R 1 / R ′ 2 of the stability factors whereas for smaller R ′ 2 (< 100) A a / A d increases more slowly. The predicted area ratio of the ascending and descending regions may vary from 1/2 to 1/30 from nearly neutral to normal conditions in the atmosphere, which agree quite closely with that obtained from satellite observations when reasonable values of eddy viscosity and eddy conductivity are assumed. Alternatively, we may also make use of this theory and the observed area ratio to determine the appropriate eddy viscosity coefficient, if the static stability factor in either the ascending or the descending region is known. The nonlinear heat transfer has also been analyzed. DOI: 10.1111/j.2153-3490.1965.tb00204.x

TROPOSPHERIC HEAT SOURCES AND SINKS AT WASHINGTON, D.C., SUMMER 1961, RELATED TO THE PHYSICAL FEATURES AND ENERGY BUDGET OF THE CIRCULATION

Estimates of atmospheric heating in the troposphere at Washington, D.C., for each successive 12 hr. during June and July 1961, were used to study the relation between local heating and the large-scale features of the circulation, to determine the local production of available potential energy, and to assist in interpreting cloud and radiation data from meteorological satellites. Some interesting inter-connections are found between heating and the circulation: e.g., it is shown that there is a very critical phase relation between heating and the temperature field which is important in determining the generation or destruction of the atmosphere's potential energy. This suggests that special care is needed in designing numerical computations of diabatic heating. A major effort should be directed to interpreting satellite data in terms of the atmospheric heat budget, because such global estimates may be useful (using a procedure suggested in this paper) in determining the world-wide distribution of regions of maintenance or destruction of potential energy.