Available potential energy and mixing in density-stratified fluids

Winters, Kraig B.; Lombard, Peter N.; Riley, James J.; D’Asaro, Eric A.

doi:10.1017/s002211209500125x

Cited by 478 publications

(368 citation statements)

References 5 publications

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“…8), suggestive of mixing processes. A scale for the energy required to cause such mixing is given by the change in background potential energy of the water column through adiabatic redistribution of density (Winters et al, 1995). Lacking salinity profiles close to the timing of the event, we idealize the system as two layers, with warm freshwater above and cool saltwater below, and utilize the moored temperature time series to estimate the portion of the water column that mixed across the interface, represented by the change in depth of the thermocline.…”

Section: January 2012 Eventmentioning

confidence: 99%

Dynamic response of an Arctic epishelf lake to seasonal and long-term forcing: implications for ice shelf thickness

et al. 2017

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Abstract. Changes in the depth of the freshwater-seawater interface in epishelf lakes have been used to infer long-term changes in the minimum thickness of ice shelves; however, little is known about the dynamics of epishelf lakes and what other factors may influence their depth. Continuous observations collected between 2011 and 2014 in the Milne Fiord epishelf lake, in the Canadian Arctic, showed that the depth of the halocline varied seasonally by up to 3.3 m, which was comparable to interannual variability. The seasonal depth variation was controlled by the magnitude of surface meltwater inflow and the hydraulics of the inferred outflow pathway, a narrow basal channel in the Milne Ice Shelf. When seasonal variation and an episodic mixing of the halocline were accounted for, long-term records of depth indicated there was no significant change in thickness of ice along the basal channel from 1983 to 2004, followed by a period of steady thinning at 0.50 m a −1 between 2004 and 2011. Rapid thinning at 1.15 m a −1 then occurred from 2011 to 2014, corresponding to a period of warming regional air temperatures. Continued warming is expected to lead to the breakup of the ice shelf and the imminent loss of the last known epishelf lake in the Arctic.

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Section: January 2012 Eventmentioning

confidence: 99%

Dynamic response of an Arctic epishelf lake to seasonal and long-term forcing: implications for ice shelf thickness

et al. 2017

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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].…”

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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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“…APE is the difference between the actual potential energy [(5d)] and the potential energy if density is conserved, but all isopycnals are flat. In practice, this calculation is done by a sorting methodology similar to that in Winters et al (1995). For each x # W grid point, its related volume is computed.…”

Section: B Model Diagnosticsmentioning

confidence: 99%

Surface Cooling, Winds, and Eddies over the Continental Shelf

Brink

2017

Journal of Physical Oceanography

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Models show that surface cooling over a sloping continental shelf should give rise to baroclinic instability and thus tend toward gravitationally stable density stratification. Less is known about how alongshore winds affect this process, so the role of surface momentum input is treated here by means of a sequence of idealized, primitive equation numerical model calculations. The effects of cooling rate, wind amplitude and direction, bottom slope, bottom friction, and rotation rate are all considered. All model runs lead to instability and an eddy field. While instability is not strongly affected by upwelling-favorable alongshore winds, wind-driven downwelling substantially reduces eddy kinetic energy, largely because the downwelling circulation plays a similar role to baroclinic instability by flattening isotherms and so reducing available potential energy. Not surprisingly, cross-shelf winds appear to have little effect. Analysis of the model runs leads to quantitative relations for the wind effect on eddy kinetic energy for the equilibrium density stratification (which increases as the cooling rate increases) and for eddy length scale.

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Available potential energy and mixing in density-stratified fluids

Cited by 478 publications

References 5 publications

Dynamic response of an Arctic epishelf lake to seasonal and long-term forcing: implications for ice shelf thickness

Dynamic response of an Arctic epishelf lake to seasonal and long-term forcing: implications for ice shelf thickness

Completing the Mechanical Energy Pathways in Turbulent Rayleigh-Bénard Convection

Surface Cooling, Winds, and Eddies over the Continental Shelf

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