Available Potential Energy and the Maintenance of the General Circulation

Lorenz, Edward N.

doi:10.3402/tellusa.v7i2.8796

Cited by 937 publications

(701 citation statements)

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“…Ignoring the diabatic terms and the meridional advection, the time derivative of the eddy total energy (ETE) can be written as the sum of a barotropic and a baroclinic conversion rate (Lorenz 1955;Rivière et al 2013). Its formulation in the present quasigeostrophic framework is…”

Section: Synoptic Feedbackmentioning

confidence: 99%

Positive and Negative Eddy Feedbacks Acting on Midlatitude Jet Variability in a Three-Level Quasigeostrophic Model

Robert

Rivière

Codron

2017

Journal of the Atmospheric Sciences

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The variability of midlatitude jets is investigated in a long-term integration of a dry three-level quasigeostrophic model on the sphere. As for most observed jets, the leading EOF of the zonal-mean wind corresponds to latitudinal shifts of the jet, and the second EOF to pulses of the jet speed. The first principal component (PC1) is also more persistent than the second one (PC2); this longer persistence arises from different eddy feedbacks both in the short term (i.e., within a few days following the peak of the PCs) and in the long term. The short-term eddy feedbacks come from two distinct mechanisms. First, a planetary waveguide effect acts as a negative feedback on both PCs. The positive phases of PC1 and PC2, which correspond to poleward-shifted and accelerated jets, respectively, are first driven then canceled by planetary waves reflecting on the equatorward flank of the jet. A similar process occurs for the negative phases when planetary waves reflect on the poleward flank of the jet. Second, synoptic waves also exert a short-term negative feedback on PC2: when the jet accelerates, the enhanced meridional wind shear increases the barotropic sink of eddy energy and depletes it very rapidly, therefore preventing synoptic eddies from maintaining the accelerated jet. Finally, at lags longer than their typical time scale, synoptic eddies drive a positive feedback on PC1 only. This feedback can be explained by a baroclinic mechanism in which the jet shift modifies the baroclinicity, causing, first, eddy heat flux anomalies and, then, momentum convergence anomalies. This feedback is absent for PC2, despite some changes in the baroclinicity.

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Section: Synoptic Feedbackmentioning

confidence: 99%

Positive and Negative Eddy Feedbacks Acting on Midlatitude Jet Variability in a Three-Level Quasigeostrophic Model

Robert

Rivière

Codron

2017

Journal of the Atmospheric Sciences

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“…APE is a subset of the total gravitational potential energy (GPE) and is the form essential for motions [9][10][11]. A complete mechanical energy framework has been recently developed for the case of horizontal convection forced by differential heating at one horizontal boundary [12,13] and recently extended to RBC [14].…”

mentioning

confidence: 99%

“…The potential energy is further decomposed into background potential energy (BPE) E b ¼ g R z Ã dV (which cannot drive motion) and available potential energy, E a ¼ E p À E b [9,10]. The BPE of a volume of fluid corresponds to E p for a state of no motion, or gravitational equilibrium, in which fluid parcels have been adiabatically rearranged to new vertical positions z Ã ¼ z Ã ðÞ.…”

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confidence: 99%

Completing the Mechanical Energy Pathways in Turbulent Rayleigh-Bénard Convection

2013

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A new, more complete view of the mechanical energy budget for Rayleigh-Bénard convection is developed and examined using three-dimensional numerical simulations at large Rayleigh numbers and Prandtl number of 1. The driving role of available potential energy is highlighted. The relative magnitudes of different energy conversions or pathways change significantly over the range of Rayleigh numbers Ra $ 10 7 -10 13 . At Ra < 10 7 small-scale turbulent motions are energized directly from available potential energy via turbulent buoyancy flux and kinetic energy is dissipated at comparable rates by both the largeand small-scale motions. In contrast, at Ra ! 10 10 most of the available potential energy goes into kinetic energy of the large-scale flow, which undergoes shear instabilities that sustain small-scale turbulence. The irreversible mixing is largely confined to the unstable boundary layer, its rate exactly equal to the generation of available potential energy by the boundary fluxes, and mixing efficiency is 50%. Introduction.-Flow in a horizontal layer of fluid heated uniformly from below and cooled from above-RayleighBénard convection (RBC)-is an idealized problem from which much can be learned about the nature of convective flow and heat transfer. Recent attention has focused on the relative importance of the boundary layer and interior behavior, including flow structures, at very large Rayleigh numbers [1][2][3][4][5][6]. The salient features of the flow can be usefully interpreted in terms of the energy budget, and previous work has considered the kinetic and thermal energy [2,3,7,8]. However, the existing framework is incomplete and provides limited insight into the exchange of mechanical energy among different forms or between fluid motions of different scales. In particular, the nature of the turbulent energy cascade in RBC is still not fully understood [3] and improved models are needed.Convection is caused by the generation of mechanical energy in the form of available potential energy (APE) by boundary buoyancy fluxes. APE is a subset of the total gravitational potential energy (GPE) and is the form essential for motions [9][10][11]. A complete mechanical energy framework has been recently developed for the case of horizontal convection forced by differential heating at one horizontal boundary [12,13] and recently extended to RBC [14]. In RBC there is a release of APE from thermal boundary layers adjacent to the top and bottom boundaries, driving flow at various scales, while complex feedbacks further distribute the potential and kinetic energy among the different scales or, through mixing, to the background potential energy. The role of APE in RBC was recognized in quantifying the overall rate of irreversible mixing [14]. Here we show that an account of GPE, its partition into available and background forms, and its links to kinetic energy at various scales are essential in a full understanding of the turbulent energy cascade and the relative roles of the boundary layer and the interior.

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“…(11), since this force does not work, but indirectly in the pressure work through geostrophic imbalance. Moreover this pressure work can also be interpreted as a local formulation for the so-called baroclinic conversion between the potential energy of the atmosphere and the horizontal kinetic energy, as it was originally proposed by Lorenz (1955) for studying the energetics of the general circulation and applied locally by Arnault and Roux (2009), among others, for studying the energetics of a developing African easterly wave in a finite domain. It is interesting to note for the physical interpretation of this baroclinic conversion term that it can only result from the ageostrophic component of the wind.…”

Section: Budget Of Horizontal Kinetic Energy As Noticed Bymentioning

confidence: 98%

Large-scale dynamical influence of a gravity wave generated over the Antarctic Peninsula – regional modelling and budget analysis

Arnault

2013

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C T The case study of a mountain wave triggered by the Antarctic Peninsula on 6 October 2005, which has already been documented in the literature, is chosen here to quantify the associated gravity wave forcing on the largescale flow, with a budget analysis of the horizontal wind components and horizontal kinetic energy. In particular, a numerical simulation using the Weather Research and Forecasting (WRF) model is compared to a control simulation with flat orography to separate the contribution of the mountain wave from that of other synoptic processes of non-orographic origin. The so-called differential budgets of horizontal wind components and horizontal kinetic energy (after subtracting the results from the simulation without orography) are then averaged horizontally and vertically in the inner domain of the simulation to quantify the mountain wave dynamical influence at this scale. This allows for a quantitative analysis of the simulated mountain wave's dynamical influence, including the orographically induced pressure drag, the counterbalancing wave-induced vertical transport of momentum from the flow aloft, the momentum and energy exchanges with the outer flow at the lateral and upper boundaries, the effect of turbulent mixing, the dynamics associated with geostrophic re-adjustment of the inner flow, the deceleration of the inner flow, the secondary generation of an inertiaÁ gravity wave and the so-called baroclinic conversion of energy between potential energy and kinetic energy.

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Available Potential Energy and the Maintenance of the General Circulation

Cited by 937 publications

References 10 publications

Positive and Negative Eddy Feedbacks Acting on Midlatitude Jet Variability in a Three-Level Quasigeostrophic Model

Positive and Negative Eddy Feedbacks Acting on Midlatitude Jet Variability in a Three-Level Quasigeostrophic Model

Completing the Mechanical Energy Pathways in Turbulent Rayleigh-Bénard Convection

Large-scale dynamical influence of a gravity wave generated over the Antarctic Peninsula – regional modelling and budget analysis

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