68 results found
Mondal R, Torres JF, Hughes G, et al., 2022, Air curtains for reduction of natural convection heat loss from a heated plate: A numerical investigation, International Journal of Heat and Mass Transfer, Vol: 189, ISSN: 0017-9310
Concentrating solar power (CSP) plants encounter inefficiencies at all stages of electricity generation. Convection from the solar-thermal receiver is a significant mode of heat loss in CSP systems, and is challenging to mitigate. This study investigates the reduction of convection losses by using a planar jet that disrupts the buoyant flow arising from the heated surface of an external CSP receiver. An isothermal flat plate with a height of 1.8 m was used to model the receiver, and a planar jet air curtain with a nozzle thickness of 3 mm was introduced near the upper edge of the wall. A computational fluid dynamics model was first validated and subsequently implemented to conduct a parametric study on the heat transfer from the isothermal plate with an air curtain varying four parameters: jet speed, jet angle, plate temperature and plate inclination. The results showed that the air curtain generates a stagnation zone adjacent to the wall which successfully reduces local convective heat losses. The effectiveness of an air curtain is defined here as the relative reduction in the local heat loss due to the air curtain, compared to the case of natural convection alone. A local maximum of 31.2% effectiveness is achieved in the stagnation zone below the jet outlet for a vertical wall with a jet speed of 2.5 ms−1 and jet angle of 45∘. The air curtain effectiveness at the stagnation region was found to decrease with increasing jet speeds, whereas the effectiveness increased near the laminar-to-turbulent transition region with increasing jet speed. Smaller air curtain angles relative to the wall resulted in lower effectiveness. A 45∘ air curtain on a vertical wall can offer performance benefits that are similar in magnitude to inclining a wall from the vertical. A higher wall temperature was accompanied by better effectiveness near the jet outlet, particularly in the stagnation region, while lower wall temperatures produced higher effectiveness further from the jet. T
Higton TD, Burridge HC, Hughes GO, 2021, Natural ventilation flows established by a localised heat source in a room with a doorway and a high-level vent, Building and Environment, Vol: 203, Pages: 1-9, ISSN: 0360-1323
Ventilation flows generated by a localised heat source within a room containing two openings to the ambient environment are examined. The openings are representative of a doorway and a high-level vent, and a steady two-layer stratification of well-mixed fluid is established within the room for all cases considered. Classical displacement ventilation flow is observed when the interface between the two layers is above the height of the doorway. Displacement ventilation flow can persist when the interface within the room is below the height of the doorway; in general, however, an unbalanced exchange flow forms across the doorway and the ventilating flow is found to be dependent on the doorway aspect ratio, the doorway height relative to the room height, the effective area of the high-level vent (relative to the square of the room height) and the rate of entrainment into the plume generated by the localised heat source. An analytical model is presented which predicts the ventilation rates and temperature structures within the room for these flows. Results from analogue experiments demonstrate good agreement with the model for a wide range of the parameter space relevant to the full-scale application.
Abbasi-Shavazi E, Torres J, Hughes G, et al., 2020, Experimental correlation of natural convection losses from a scale-model solar cavity receiver with non-isothermal surface temperature distribution, Solar Energy, Vol: 198, Pages: 355-375, ISSN: 0038-092X
Correlations for natural convection heat loss from solar cavity receivers are widely based on isothermal surface temperature assumptions, which do not occur in practice due to the local heat balance varying with position. An open question thus exists regarding the suitability of such correlations for non-isothermal conditions. This paper addresses this issue by presenting a new Nusselt correlation developed from an experimental investigation of natural convection heat loss from a non-isothermal scale-model cylindrical cavity receiver. Cavities that are considered in this work have length-to-diameter ratios of 1 and 2, are operated at peak temperatures ranging from 355 °C to 650 °C, and exhibit temperature differences along the cavity wall between 40 °C and 342 °C. Stagnation and convection zones, as well as view factor profiles, are observed to contribute to the wall temperature distribution as the cavity is inclined downwards. An energy balance undertaken for steady state provides insight into the effects of non-uniform surface temperature distribution and inclination-dependent surface areas on radiative and convective losses. Natural convection heat loss results from this work are compared with widely-used correlations from the literature that assume isothermal wall conditions, and systematic discrepancies are observed. The proposed Nusselt correlation which accounts for the temperature non-uniformity, cavity inclination and geometric aspect ratio is evaluated against experimental data from this and other studies. It is found to produce excellent predictions of Nusselt numbers for cylindrical cavity receivers in the Grashof number range of 2.6 × 105 to 1.4 × 107.
Hughes G, Gayen B, Griffiths R, 2020, Available potential energy in Rayleigh-Bénard convection
The energy budget for thermally-equilibrated Rayleigh-Bénard convection is developed theoretically, with explicit consideration of the role of available potential energy. The analysis shows that about half of the available potential energy generated by the thermal forcing is dissipated viscously by turbulence at high Rayleigh number. The remainder is consumed by diffusion acting to homogenise the temperature field. The results of direct numerical simulations of convection at Rayleigh numbers ranging from 108 to 1013 are also presented in support of this analysis. An important conclusion is that Rayleigh-Bénard convection may be viewed as a highly efficient mechanism of turbulent mixing in a stratified fluid.
Hughes G, Gayen B, Griffiths R, 2020, Available potential energy in Rayleigh-Bénard convection
Copyright © ETC 2013 - 14th European Turbulence Conference.All rights reserved. The energy budget for thermally-equilibrated Rayleigh-Bénard convection is developed theoretically, with explicit consideration of the role of available potential energy. The analysis shows that about half of the available potential energy generated by the thermal forcing is dissipated viscously by turbulence at high Rayleigh number. The remainder is consumed by diffusion acting to homogenise the temperature field. The results of direct numerical simulations of convection at Rayleigh numbers ranging from 108 to 1013 are also presented in support of this analysis. An important conclusion is that Rayleigh-Bénard convection may be viewed as a highly efficient mechanism of turbulent mixing in a stratified fluid.
Davies Wykes M, Hogg C, Partridge J, et al., 2019, Energetics of mixing for the filling box and the emptying-filling box, Environmental Fluid Mechanics, Vol: 19, Pages: 819-831, ISSN: 1567-7419
The mixing efficiency of a plume in a filling box and an emptying-filling box is calculated for both transient and steady states. The mixing efficiency of a plume in a filling box in an asymptotic state is 1/2, independent of the details of this state or how the plume is modelled. The mixing efficiency of a plume in an emptying-filling box in steady state is 1−ξ , where ξ=h/H , the depth of the ambient layer h normalised by the height of the box H. A deeper mixed layer therefore corresponds to a higher mixing efficiency. These results shed light on the interpretation of mixing efficiencies of open and closed systems.
Craske J, Hughes G, 2019, On the robustness of emptying filling boxes to sudden changes in the wind, Journal of Fluid Mechanics, Vol: 868, ISSN: 0022-1120
We determine the smallest instantaneous increase in the strength of an opposing windthat is necessary to permanently reverse the forward displacement flow that is drivenby a two-layer thermal stratification. With an interpretation in terms of the flow’s ener-getics, the results clarify why the ventilation of a confined space with a stably-stratifiedbuoyancy field is less susceptible to being permanently reversed by the wind than theventilation of a space with a uniform buoyancy field. For large opposing wind strengthswe derive analytical upper and lower bounds for the system’s marginal stability, which ex-hibit a good agreement with the exact solution, even for modest opposing wind strengths.The work extends a previous formulation of the problem (Lishman & Woods 2009,Build-ing and Env.44, pp. 666-673) by accounting for the transient dynamics and energeticsassociated with the homogenisation of the interior, which prove to play a significant rolein buffering temporal variations in the wind.
Pye J, Abbasi E, Arjomandi M, et al., 2019, Towards Testing of a Second-Generation Bladed Receiver, 24th International Conference on Concentrating Solar Power and Chemical Energy Systems (SolarPACES), Publisher: AMER INST PHYSICS, ISSN: 0094-243X
Abbasi Shavazi E, Torres J, Hughes G, et al., 2018, Convection heat transfer from an inclined narrow flat plate with uniform flux boundary conditions, 21st Australasian Fluid Mechanics Conference, Publisher: Australasian Fluid Mechanics Society
Natural convection from flat plates finds diverse applications in engineering and natural systems. While previous studies have considered natural convection from isothermal vertical plates in air and tilted plates in water subject to uniform flux, little attention has been given to natural convection from inclined narrow plates in air. This work reports onexperiments undertaken on an inclined narrow plate with uniform flux boundary conditions. The spatial distribution of temperature along the length of the plate was measured for a range of imposed uniform flux values and inclination angles, ranging between vertical and downward-facing horizontal. The temperature profile along the plate indicates convective heat transfer rates associated with the development of the flow from a laminar to a turbulent regime. An interesting result of increased convection loss at a downward-facing inclination was observed, and is shown to be associated with the absence of sidewalls. Smoke visualisation of the flow was undertaken and the transition from laminar to turbulent flow was observed.
Abbasi Shavazi E, Torres JF, Hughes GO, et al., 2018, Convection heat transfer from an inclined narrow flat plate with uniform flux boundary conditions
Natural convection from flat plates finds diverse applications in engineering and natural systems. While previous studies have considered natural convection from isothermal vertical plates in air and tilted plates in water subject to uniform flux, little attention has been given to natural convection from inclined narrow plates in air. This work reports on experiments undertaken on an inclined narrow plate with uniform flux boundary conditions. The spatial distribution of temperature along the length of the plate was measured for a range of imposed uniform flux values and inclination angles, ranging between vertical and downward-facing horizontal. The temperature profile along the plate indicates convective heat transfer rates associated with the development of the flow from a laminar to a turbulent regime. An interesting result of increased convection loss at a downward-facing inclination was observed, and is shown to be associated with the absence of sidewalls. Smoke visualisation of the flow was undertaken and the transition from laminar to turbulent flow was observed.
Burridge HC, Sehmbi G, Fiuza Dosil D, et al., 2017, Determining the venting efficiency of simple chimneys for buoyant plumes, 38th AIVC Conference
We present preliminary results from an examination of the capture and venting of a buoyant plume by a chimney. The aim is to enable improved management of indoor pollutant sources –for instance, the plume rising from a cooking pan in a kitchen or a cooking fire in a hut. Using the principle of dynamic similarity, we precisely and controllably model the behaviour of indoor plumes by using saline solutions ejected into an enclosure containing freshwater. These well-established laboratory analogue techniques enable the location and concentration of tracer in the plume to be easily tracked, reflecting the evolution of pollutants carried in the plume. Focusing on a plume within a room containing a quiescent ambient environment, we identify two physical mechanisms potentially responsible for driving the removal of pollutants. The first, we describe as the capture of the plume, a process driven by the direct interaction between the plume and the evacuation opening; the second, we describe as the draining flow driven by a buoyant layer of fluid which may accumulate at the ceiling and is then evacuated through the effects of buoyancy. We first demonstrate that the addition of a simple cylindrical chimney that hangs downwards from an opening in the (analogue) ceiling increases the venting efficiency of these potentially polluting plumes.We go on to examine how the capture efficiency of these simple chimneys varies as the relative size of the plume and the chimney are altered, and demonstrate that simple model can provide predictionsof the observed variation in capture efficiency.
Logie WR, Abbasi-Shavazi E, Hughes G, et al., 2017, Turbulent contribution to heat loss in cavity receivers, SolarPACES 2016, Publisher: AIP, ISSN: 0094-243X
For the prediction of convective heat loss from solar concentrating receiver cavities a number of empirical correlations exist. Geometry and the inclination angle determine the degree to which natural convection can infiltrate the cavity and remove stably stratified hot air out through the aperture. This makes the task of defining characteristic lengths for such Nusselt correlations difficult, neither does their use offer insight as to how one might reduce heat loss through the use of baffles, air curtains or small aperture-to-cavity-area ratios. Computational Fluid Dynamics (CFD) can assist in the design of better cavity receivers as long as the rules upon which it rests are respected. This paper is an exploration of the need for turbulence modelling in cavity receivers using some common linear eddy viscosity closure schemes. Good agreement was obtained with the CFD software OpenFOAMO® 3.0.1 for a deep cavity aperture but it under-predicted a shallow cavity. The experiments used for validation were in the Grashof region Gr ≈ 10 6 , well below the region for transition to turbulence between 10 8 < Gr < 10 9 .
Pye J, Coventry J, Venn F, et al., 2017, Experimental testing of a high-flux cavity receiver, SolarPACES 2016, Publisher: AIP Publishing, ISSN: 0094-243X
A new tubular cavity receiver for direct steam generation, 'SG4', has been built and tested on-sun based on integrated optical and thermal modelling. The new receiver achieved an average thermal efficiency of 97.1±2.1% across several hours of testing, and reduced the losses by more than half, compared to the modelled performance of the previous SG3 receiver and dish. Near-steady-state outlet steam temperatures up to 560°C were achieved during the tests.
Pye J, Coventry J, Ho C, et al., 2017, Optical and thermal performance of bladed receivers, SolarPACES 2016, Publisher: AIP Publishing, ISSN: 0094-243X
Bladed receivers use conventional receiver tube-banks rearranged into bladed/finned structures, and offer better light trapping, reduced radiative and convective losses, and reduced tube mass, based on the presented optical and thermal analysis. Optimising for optical performance, deep blades emerge. Considering thermal losses leads to shallower blades. Horizontal blades perform better, in both windy and no-wind conditions, than vertical blades, at the scales considered so far. Air curtains offer options to further reduce convective losses; high flux on blade-tips is still a concern.
Hughes GO, Linden PF, 2016, Mixing efficiency in run-down gravity currents, Journal of Fluid Mechanics, Vol: 809, Pages: 691-704, ISSN: 0022-1120
This paper presents measurements of mixing efficiency of the two counter-flowing gravitycurrents created by symmetric lock exchange in a channel. The novel feature of thiswork is that the buoyancy Reynolds number of the currents is higher than in previousexperiments, so that the mixing is not significantly affected by viscosity. We find thatthe mixing efficiency asymptotes to 0.08 at high Reynolds numbers. We present a modelof the mixing based on the evolution of idealized mean profiles of velocity and density atthe interface between the two currents, the results of which are in good agreement withthe measurements of mixing efficiency.
Dossmann Y, Rosevear MG, Griffiths RW, et al., 2016, Experiments with mixing in stratified flow over a topographic ridge, Journal of Geophysical Research: Oceans, Vol: 121, Pages: 6961-6977, ISSN: 2169-9275
The interaction of quasi-steady abyssal ocean flow with submarine topography is expected to generate turbulent mixing in the ocean. This mixing may occur locally, close to topography, or via breaking quasi-steady lee waves that can carry energy into the ocean interior. There is currently no theoretical, or empirically derived, prediction for the relative amounts of local and interior mixing. We report measurements of the mixing rate in laboratory experiments with a topographic ridge towed through a density stratification. The experiments span three parameter regimes including linear lee waves, nonlinear flow and an evanescent regime in which wave radiation is weak. Full field density measurements provide the depth-dependence of energy loss to turbulent mixing, allowing separation of the local mixing in the turbulent wake and remote mixing by wave radiation. Remote mixing is significant only for a narrow band of forcing parameters where the flow speed is resonant with internal waves; in all other parameter regimes local mixing close to the topography is dominant. The results suggest that mixing by local nonlinear mechanisms close to abyssal ocean topography may be much greater than the remote mixing by quasi-steady lee waves.
Hughes GO, Pye J, Kaufer M, et al., 2016, Reduction of convective losses in solar cavity receivers, SolarPACES 2015, Publisher: AIP
Two design innovations are reported that can help improve the thermal performance of a solar cavity receiver.These innovations utilise the natural variation of wall temperature inside the cavity and active management of airflow inthe vicinity of the receiver. The results of computational fluid dynamics modelling and laboratory-scale experimentssuggest that the convective loss from a receiver can be reduced substantially by either mechanism. A further benefit isthat both radiative and overall thermal losses from the cavity may be reduced. Further work to assess the performance ofsuch receiver designs under operational conditions is discussed.
Henley RW, Hughes GO, 2016, SO2 flux and the thermal power of volcanic eruptions, Journal of Volcanology and Geothermal Research, Vol: 324, Pages: 190-199, ISSN: 0377-0273
A description of the dynamics, chemistry and energetics governing a volcanic system can be greatlysimplified if the expansion of magmatic gas can be assumed to be adiabatic as it rises towards thesurface. The conditions under which this assumption is valid are clarified by analysis of the transferof thermal energy into the low conductivity wallrocks traversed by fractures and vents from a gasphase expanding over a range of mass flux rates. Adiabatic behavior is predicted to be approachedtypically within a month after perturbations in the release of source gas have stabilized, thistimescale being dependent upon only the characteristic length scale on which the host rock isfractured and the thermal diffusivity of the rock. This analysis then enables the thermal energytransport due to gas release from volcanoes to be evaluated using observations of SO2 flux withreference values for the H2O:SO2 ratio of volcanic gas mixtures discharging through hightemperature fumaroles in arc and mantle-related volcanic systems. Thermal power (MWH/s)estimates for gas discharge are 101.8 to 104.1 MWH during quiescent, continuous degassing of arcvolcanoes and 103.7 to 107.3MWH for their eruptive stages, the higher value being the PlineanPinatubo eruption in 1991. Fewer data are available for quiescent stage mantle-related volcanoes(Kilauea 102.1MWH) but for eruptive events power estimates range from 102.8 MWH to 105.5MWH.These estimates of thermal power and mass of gas discharges are commensurate with powerestimates based on the total mass of gas ejected during eruptions. The sustained discharge ofvolcanic gas during quiescent and short-lived eruptive stages can be related to the hydrodynamicstructure of volcanic systems with large scale gaseous mass transfer from deep in the crust coupledwith episodes of high level intrusive activity and gas release.
Hughes GO, 2016, Inside the head and tail of a turbulent gravity current, JOURNAL OF FLUID MECHANICS, Vol: 790, ISSN: 0022-1120
Pye J, Hughes GO, Abbasi E, et al., 2016, Development of a higher-efficiency tubular cavity receiver for direct steam generation on a dish concentrator, SolarPACES2015
Zhang JJ, Pye JD, Hughes GO, 2016, ACTIVE AIR FLOW CONTROL TO REDUCE CAVITY RECEIVER HEAT LOSS, 9th ASME International Conference on Energy Sustainability, Publisher: AMER SOC MECHANICAL ENGINEERS
Wykes MSD, Hughes GO, Dalziel SB, 2015, On the meaning of mixing efficiency for buoyancy-driven mixing in stratified turbulent flows, JOURNAL OF FLUID MECHANICS, Vol: 781, Pages: 261-275, ISSN: 0022-1120
Vreugdenhil CA, Hogg AMC, Griffiths RW, et al., 2015, Adjustment of the meridional overturning circulation and its dependence on depth of mixing, Journal of Physical Oceanography, Vol: 46, Pages: 731-747, ISSN: 0022-3670
The relative roles of advective processes and mixing on the temporal adjustment of the meridional overturning circulation are examined, in particular the effects of mixing in either the abyssal or upper ocean. Laboratory experiments with convectively driven overturning and imposed stirring rates show that the circulation adjusts toward an equilibrium state on time scales governed by mixing in the upper boundary layer region but independent of the mixing rate in the bulk of the interior. The equilibrium state of the stratification is dependent only on the rate of mixing in the boundary layer. An idealized high-resolution ocean model shows adjustment (of a two-cell circulation) dominated primarily by the advective ventilation time scale, consistent with a view of the circulation determined by water mass transformation occurring primarily near the surface. Both the experiments and the model results indicate that adjustments of the circulation are controlled by surface buoyancy uptake (or rejection) and that the nonequilibrium circulation is dominated by advective processes, especially if the average abyssal ocean diffusivity is less than 3 × 10-5 m2 s-1.
Saenz JA, Tailleux R, Butler ED, et al., 2015, Estimating Lorenz’s Reference State in an Ocean with a Nonlinear Equation of State for Seawater, Journal of Physical Oceanography, Vol: 45, Pages: 1242-1257, ISSN: 0022-3670
The study of the mechanical energy budget of the oceans using the Lorenz available potential energy (APE) theory is based on knowledge of the adiabatically rearranged Lorenz reference state of minimum potential energy. The compressible and nonlinear character of the equation of state for seawater has been thought to cause the reference state to be ill defined, casting doubt on the usefulness of APE theory for investigating ocean energetics under realistic conditions. Using a method based on the volume frequency distribution of parcels as a function of temperature and salinity in the context of the seawater Boussinesq approximation, which is illustrated using climatological data, the authors show that compressibility effects are in fact minor. The reference state can be regarded as a well-defined one-dimensional function of depth, which forms a surface in temperature, salinity, and density space between the surface and the bottom of the ocean. For a very small proportion of water masses, this surface can be multivalued and water parcels can have up to two statically stable levels in the reference density profile, of which the shallowest is energetically more accessible. Classifying parcels from the surface to the bottom gives a different reference density profile than classifying in the opposite direction. However, this difference is negligible. This study shows that the reference state obtained by standard sorting methods is equivalent to, though computationally more expensive than, the volume frequency distribution approach. The approach that is presented can be applied systematically and in a computationally efficient manner to investigate the APE budget of the ocean circulation using models or climatological data.
Abbasi-Shavazi E, Hughes GO, Pye JD, 2015, Investigation of heat loss from a solar cavity receiver, International Conference on Concentrating Solar Power and Chemical Energy Systems (SolarPACES), Publisher: ELSEVIER SCIENCE BV, Pages: 269-278, ISSN: 1876-6102
Gayen B, Hughes GO, Griffiths RW, 2015, Mechanical energy budget of turbulent rayleigh-benard convection
Turbulent Rayleigh-Bénard convection (RBC) is examined in terms of its mechanical energy budget. Three-dimensional large-eddy and direct numerical simulations are conducted at moderately large Rayleigh numbers. An expanded view of the mechanical energy pathways for RBC convection is developed for the the first time by recognising that mechanical energy includes gravitational potential energy and that the available component of this potential energy (APE) is the energy source for convection. The partitioning of energy pathways between large and small scales of motion is also analysed based on their corresponding temporal scales. The relative magnitudes of different pathways change significantly over the range of Rayleigh numbers Ra ∼ 107 - 1013. At Ra < 107 small-scale turbulent motions are energized directly from APE via turbulent buoyancy flux while kinetic energy is dissipated at comparable rates by both the large- and small-scale motions. In contrast, at Ra ≥ 1010 most of the APE goes into kinetic energy of the large-scale flow, and the large scales undergo shear instabilities that sustain small-scale turbulence. At large Ra one half of the total APE supply goes to viscous dissipation of kinetic energy and the other half to mixing of the thermal field. Therefore, mixing efficiency approaches 50% at large Ra, as also predicted by a scaling analysis. At large Rayleigh number the viscous dissipation is largely in the interior, while the irreversible mixing is largely confined to the unstable boundary layers. The inclusion of the mechanical energy in the budget provides new information on the roles of different length scales and on the mechanics of the interior and boundary layer.
Gayen B, Griffiths RW, Hughes GO, 2014, Stability transitions and turbulence in horizontal convection, JOURNAL OF FLUID MECHANICS, Vol: 751, Pages: 698-724, ISSN: 0022-1120
Stewart KD, Saenz JA, Hogg AM, et al., 2014, Effect of topographic barriers on the rates of available potential energy conversion of the oceans, OCEAN MODELLING, Vol: 76, Pages: 31-42, ISSN: 1463-5003
McIntosh A, Hughes G, Pye J, 2014, Use of an air curtain to reduce heat loss from an inclined open-ended cavity
The use of an air curtain directed across the aperture of an inclined open-ended cavity is examined as a method to reduce convective losses from a heated cavity. Computational fluid dynamics (CFD) simulations were conducted in two-dimensions for a range of air curtain velocities and axial cavity orientations. The greatest relative reduction in convective losses with an air curtain resulted when the cavity aperture plane was vertical (i.e. horizontal cavity axis). For cavities whose axis was inclined to the horizontal, convective losses could still be lowered with an air curtain, but reduced jet velocities were required for optimum performance.
Gayen B, Hughes GO, Griffiths RW, 2013, Completing the Mechanical Energy Pathways in Turbulent Rayleigh-Bénard Convection, Physical Review Letters, Vol: 111, ISSN: 1079-7114
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 large- and 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%.
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