Diagnosing mixing in stratified turbulent flows with a locally defined available potential energy

2014 ◽  
Vol 740 ◽  
pp. 114-135 ◽  
Author(s):  
Alberto Scotti ◽  
Brian White
Keyword(s):  
Potential Energy ◽  
Turbulent Flows ◽  
Boussinesq Approximation ◽  
Mixing Efficiency ◽  
Available Potential Energy ◽  
Energy Cycle ◽  
Lorenz Energy Cycle ◽  
The Mean ◽  
Definition Of ◽  
Special Circumstances

AbstractA local available potential energy (APE) density useful as suitable diagnostic tool in turbulent stratified flows is considered under the Boussinesq approximation. The local APE is positive, and in the limit of infinitesimal perturbation from an equilibrium state recovers the Lorenz energy cycle definition of APE. In a turbulent stratified flow, the APE can be Reynolds-decomposed into non-trivial mean and turbulent components, which are connected to the mean and turbulent kinetic energy by suitably defined fluxes. We show that the turbulent buoyancy flux $\overline{w'b'}$ and the rate of production of turbulent APE coincide only under very special circumstances. The framework is applied to derive some global bounds on the mixing efficiency of some representative flows.

scholarly journals Biases in Thorpe-Scale Estimates of Turbulence Dissipation. Part II: Energetics Arguments and Turbulence Simulations

2015 ◽  
Vol 45 (10) ◽  
pp. 2522-2543 ◽  
Author(s):  
Alberto Scotti
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Turbulent Flows ◽  
Companion Paper ◽  
Mean Flow ◽  
Available Potential Energy ◽  
Ozmidov Scale ◽  
Thorpe Scale ◽  
The Mean ◽  
Shear Driven Flows

AbstractThis paper uses the energetics framework developed by Scotti and White to provide a critical assessment of the widely used Thorpe-scale method, which is used to estimate dissipation and mixing rates in stratified turbulent flows from density measurements along vertical profiles. This study shows that the relevant displacement scale in general is not the rms value of the Thorpe displacement. Rather, the displacement field must be Reynolds decomposed to separate the mean from the turbulent component, and it is the turbulent component that ought to be used to diagnose mixing and dissipation. In general, the energetics of mixing in an overall stably stratified flow involves potentially complex exchanges among the available potential energy and kinetic energy associated with the mean and turbulent components of the flow. The author considers two limiting cases: shear-driven mixing, where mixing comes at the expense of the mean kinetic energy of the flow, and convective-driven mixing, which taps the available potential energy of the mean flow to drive mixing. In shear-driven flows, the rms of the Thorpe displacement, known as the Thorpe scale is shown to be equivalent to the turbulent component of the displacement. In this case, the Thorpe scale approximates the Ozmidov scale, or, which is the same, the Thorpe scale is the appropriate scale to diagnose mixing and dissipation. However, when mixing is driven by the available potential energy of the mean flow (convective-driven mixing), this study shows that the Thorpe scale is (much) larger than the Ozmidov scale. Using the rms of the Thorpe displacement overestimates dissipation and mixing, since the amount of turbulent available potential energy (measured by the turbulent displacement) is only a fraction of the total available potential energy (measured by the Thorpe scale). Corrective measures are discussed that can be used to diagnose mixing from knowledge of the Thorpe displacement. In a companion paper, Mater et al. analyze field data and show that the Thorpe scale can indeed be much larger than the Ozmidov scale.

scholarly journals On the meaning of mixing efficiency for buoyancy-driven mixing in stratified turbulent flows

2015 ◽  
Vol 781 ◽  
pp. 261-275 ◽  
Author(s):  
Megan S. Davies Wykes ◽  
Graham O. Hughes ◽  
Stuart B. Dalziel
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Turbulent Flows ◽  
Density Profile ◽  
Direct Conversion ◽  
Density Field ◽  
Gravitational Potential Energy ◽  
Mixing Efficiency ◽  
Local Flow ◽  
Available Potential Energy

The concept of a mixing efficiency is widely used to relate the amount of irreversible diabatic mixing in a stratified flow to the amount of energy available to support mixing. This common measure of mixing in a flow is based on the change in the background potential energy, which is the minimum gravitational potential energy of the fluid that can be achieved by an adiabatic rearrangement of the instantaneous density field. However, this paper highlights examples of mixing that is primarily ‘buoyancy-driven’ (i.e. energy is released to the flow predominantly from a source of available potential energy) to demonstrate that the mixing efficiency depends not only on the specific characteristics of the turbulence in the region of the flow that is mixing, but also on the density profile in regions remote from where mixing physically occurs. We show that this behaviour is due to the irreversible and direct conversion of available potential energy into background potential energy in those remote regions (a mechanism not previously described). This process (here termed ‘relabelling’) occurs without requiring either a local flow or local mixing, or any other process that affects the internal energy of that fluid. Relabelling is caused by initially available potential energy, associated with identifiable parcels of fluid, becoming dynamically inaccessible to the flow due to mixing elsewhere. These results have wider relevance to characterising mixing in stratified turbulent flows, including those involving an external supply of kinetic energy.

Energetics and mixing in buoyancy-driven near-bottom stratified flow

2019 ◽  
Vol 869 ◽  
pp. 214-237
Author(s):  
Pranav Puthan ◽  
Masoud Jalali ◽  
Vamsi K. Chalamalla ◽  
Sutanu Sarkar
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Energy Loss ◽  
Convective Instability ◽  
Mixing Efficiency ◽  
Time Interval ◽  
Mean Flow ◽  
Available Potential Energy ◽  
Long Time ◽  
The Mean

Turbulence and mixing in a near-bottom convectively driven flow are examined by numerical simulations of a model problem: a statically unstable disturbance at a slope with inclination $\unicode[STIX]{x1D6FD}$ in a stable background with buoyancy frequency $N$ . The influence of slope angle and initial disturbance amplitude are quantified in a parametric study. The flow evolution involves energy exchange between four energy reservoirs, namely the mean and turbulent components of kinetic energy (KE) and available potential energy (APE). In contrast to the zero-slope case where the mean flow is negligible, the presence of a slope leads to a current that oscillates with $\unicode[STIX]{x1D714}=N\sin \unicode[STIX]{x1D6FD}$ and qualitatively changes the subsequent evolution of the initial density disturbance. The frequency, $N\sin \unicode[STIX]{x1D6FD}$ , and the initial speed of the current are predicted using linear theory. The energy transfer in the sloping cases is dominated by an oscillatory exchange between mean APE and mean KE with a transfer to turbulence at specific phases. In all simulated cases, the positive buoyancy flux during episodes of convective instability at the zero-velocity phase is the dominant contributor to turbulent kinetic energy (TKE) although the shear production becomes increasingly important with increasing  $\unicode[STIX]{x1D6FD}$ . Energy that initially resides wholly in mean available potential energy is lost through conversion to turbulence and the subsequent dissipation of TKE and turbulent available potential energy. A key result is that, in contrast to the explosive loss of energy during the initial convective instability in the non-sloping case, the sloping cases exhibit a more gradual energy loss that is sustained over a long time interval. The slope-parallel oscillation introduces a new flow time scale $T=2\unicode[STIX]{x03C0}/(N\sin \unicode[STIX]{x1D6FD})$ and, consequently, the fraction of initial APE that is converted to turbulence during convective instability progressively decreases with increasing $\unicode[STIX]{x1D6FD}$ . For moderate slopes with $\unicode[STIX]{x1D6FD}<10^{\circ }$ , most of the net energy loss takes place during an initial, short ( $Nt\approx 20$ ) interval with periodic convective overturns. For steeper slopes, most of the energy loss takes place during a later, long ( $Nt>100$ ) interval when both shear and convective instability occur, and the energy loss rate is approximately constant. The mixing efficiency during the initial period dominated by convectively driven turbulence is found to be substantially higher (exceeds 0.5) than the widely used value of 0.2. The mixing efficiency at long time in the present problem of a convective overturn at a boundary varies between 0.24 and 0.3.

scholarly journals Available Potential Energy and the General Circulation: Partitioning Wind, Buoyancy Forcing, and Diapycnal Mixing

2015 ◽  
Vol 45 (6) ◽  
pp. 1510-1531 ◽  
Author(s):  
Varvara E. Zemskova ◽  
Brian L. White ◽  
Alberto Scotti
Keyword(s):  
Potential Energy ◽  
General Circulation ◽  
Surface Generation ◽  
Mixing Rate ◽  
Diapycnal Mixing ◽  
Available Potential Energy ◽  
Global Rate ◽  
Energy Cycle ◽  
The Mean ◽  
Surface Buoyancy

AbstractThe ocean energy cycle is calculated using a new available potential energy (APE) decomposition, which partitions adiabatic buoyancy fluxes from diapycnal mixing, applied to results from the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2), eddy-permitting ocean state estimate and observed surface buoyancy fluxes from the WHOI OAFlux project. Compared with the traditional Lorenz energy cycle, this framework provides a more accurate estimate of the background potential energy (PE) of the global oceans and the surface generation and interior fluxes of APE. Calculations of the global energy budget using 16 yr of ECCO2 output suggest that the adiabatic portion of the general circulation is maintained by a balance between the mean wind-driven upwelling that increases APE (+0.27 TW) and time-fluctuating processes, including mesoscale eddies, which release APE (−0.27 TW). The APE generated by surface buoyancy fluxes (0.46 TW) is comparable to the generation by the mean winds. The global rate of irreversible mixing (0.46 TW), which balances surface APE generation, is consistent with previous estimates of the diapycnal fluxes associated with maintaining deep stratification (see Munk and Wunsch) and a global diapycnal diffusivity of O(1 × 10−4) m2 s−1. However, the net contribution of diapycnal mixing to the total potential energy is negligible, which suggests that mixing, contrary to one current paradigm, does not place a global demand on kinetic energy dissipation. However, there are regions where mixing is significant, for example, between 3000 and 5000 m (in ECCO2), where mixing increases PE by 0.1 TW. The work provides a new framework for separating adiabatic–diabatic fluxes and for monitoring the global rate of diapycnal mixing rate using measurable surface properties such as SST and heat flux.

scholarly journals An Estimate of the Lorenz Energy Cycle for the World Ocean Based on the STORM/NCEP Simulation

2012 ◽  
Vol 42 (12) ◽  
pp. 2185-2205 ◽  
Author(s):  
Jin-Song von Storch ◽  
Carsten Eden ◽  
Irina Fast ◽  
Helmuth Haak ◽  
Daniel Hernández-Deckers ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
General Circulation ◽  
World Ocean ◽  
Eddy Kinetic Energy ◽  
Available Potential Energy ◽  
Energy Cycle ◽  
Lorenz Energy Cycle ◽  
Surface Buoyancy ◽  
Mean Kinetic Energy

Abstract This paper presents an estimate of the oceanic Lorenz energy cycle derived from a simulation forced by 6-hourly fluxes obtained from NCEP–NCAR reanalysis-1. The total rate of energy generation amounts to 6.6 TW, of which 1.9 TW is generated by the time-mean winds and 2.2 TW by the time-varying winds. The dissipation of kinetic energy amounts to 4.4 TW, of which 3 TW originate from the dissipation of eddy kinetic energy. The energy exchange between reservoirs is dominated by the baroclinic pathway and the pathway that distributes the energy generated by the time-mean winds. The former converts 0.7 to 0.8 TW mean available potential energy to eddy available potential energy and finally to eddy kinetic energy, whereas the latter converts 0.5 TW mean kinetic energy to mean available potential energy. This energy cycle differs from the atmospheric one in two aspects. First, the generation of the mean kinetic and mean available potential energy is each, to a first approximation, balanced by the dissipation. The interaction of the oceanic general circulation with mesoscale eddies is hence less crucial than the corresponding interaction in the atmosphere. Second, the baroclinic pathway in the ocean is facilitated not only by the surface buoyancy flux but also by the winds through a conversion of 0.5 TW mean kinetic energy to mean available potential energy. In the atmosphere, the respective conversion is almost absent and the baroclinic energy pathway is driven solely by the differential heating.

Study of the Mechanisms of Vortex Variability in the Lofoten Basin Based on the Energy Analysis

2021 ◽  
Vol 37 (3) ◽  
Author(s):  
V. S. Travkin ◽  
◽  
T. V. Belonenko ◽  
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Baroclinic Instability ◽  
Positive Trend ◽  
Barotropic Instability ◽  
Available Potential Energy ◽  
Conversion Rates ◽  
Order Of Magnitude ◽  
The Mean ◽  
Mean Kinetic Energy

Purpose. The Lofoten Basin is one of the most energetic zones of the World Ocean characterized by high activity of mesoscale eddies. The study is aimed at analyzing different components of general energy in the basin, namely the mean kinetic and vortex kinetic energy calculated using the integral of the volume of available potential and kinetic energy of the Lofoten Vortex, as well as variability of these characteristics. Methods and Results. GLORYS12V1 reanalysis data for the period 2010–2018 were used. The mean kinetic energy and the eddy kinetic one were analyzed; and as for the Lofoten Vortex, its volume available potential and kinetic energy were studied. The mesoscale activity of eddies in winter is higher than in summer. Evolution of the available potential energy and kinetic energy of the Lofoten Vortex up to the 1000 m horizon was studied. It is shown that the vortex available potential energy exceeds the kinetic one by an order of magnitude, and there is a positive trend with the coefficient 0,23⋅1015 J/year. It was found that in the Lofoten Basin, the intermediate layer from 600 to 900 m made the largest contribution to the potential energy, whereas the 0–400 m layer – to kinetic energy. The conversion rates of the mean kinetic energy into the vortex kinetic one and the mean available potential energy into the vortex available potential one (barotropic and baroclinic instability) were analyzed. It is shown that the first type of transformation dominates in summer, while the second one is characterized by its increase in winter. Conclusions. The vertical profile shows that the kinetic energy of eddies in winter is higher than in summer. The available potential energy of a vortex is by an order of magnitude greater than the kinetic energy. An increase in the available potential energy is confirmed by a significant positive trend and by a decrease in the vortex Burger number. The graphs of the barotropic instability conversion rate demonstrate the multidirectional flows in the vortex zone with the dipole structure observed in a winter period, and the tripole one – in summer. The barotropic instability highest intensity is observed in summer. The baroclinic instability is characterized by intensification of the regime in winter that is associated with weakening of stratification in this period owing to winter convection.

The Lorenz Energy Cycle: Trends and the Impact of Modes of Climate Variability

2021 ◽  
Author(s):  
Qiyun Ma ◽  
Valerio Lembo ◽  
Christian Franzke
Keyword(s):  
Kinetic Energy ◽  
Climate Variability ◽  
Potential Energy ◽  
Atmospheric Circulation ◽  
Southern Hemisphere ◽  
Transient Eddy ◽  
Energy Cycle ◽  
Conversion Rates ◽  
Lorenz Energy Cycle ◽  
Modes Of Climate Variability

&lt;p&gt;The atmospheric circulation is driven by heat transport from the tropics to the polar regions, implying energy conversions between available potential and kinetic energy through various mechanisms. The processes of energy transformations can be quantitatively investigated in the global climate system through the Lorenz energy cycle formalism. In this study, we examine these variations and the impacts of modes of climate variability on the Lorenz energy cycle by using reanalysis data from the Japanese Meteorological Agency (JRA-55). We show that the atmospheric circulation is overall becoming more energetic and efficient. For instance, we find a statistically significant trend in the eddy available potential energy, especially in the transient eddy available potential energy in the Southern Hemisphere. We find significant trends in the conversion rates between zonal available potential and kinetic energy, consistent with an expansion of the Hadley cell, and in the conversion rates between eddy available potential and kinetic energy, suggesting an increase in mid-latitudinal baroclinic instability. We also show that planetary-scale waves dominate the stationary eddy energy, while synoptic-scale waves dominate the transient eddy energy with a significant increasing trend. Our results suggest that interannual variability of the Lorenz energy cycle is determined by modes of climate variability. We find that significant global and hemispheric energy fluctuations are caused by the El Nino-Southern Oscillation, the Arctic Oscillation, the Southern Annular Mode, and the meridional temperature gradient over the Southern Hemisphere.&lt;/p&gt;

scholarly journals Scaling Laws and Regime Transitions of Macroturbulence in Dry Atmospheres

2008 ◽  
Vol 65 (7) ◽  
pp. 2153-2173 ◽  
Author(s):  
Tapio Schneider ◽  
Christopher C. Walker
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Surface Potential ◽  
Scaling Laws ◽  
Potential Temperature ◽  
Eddy Kinetic Energy ◽  
Eddy Flux ◽  
Available Potential Energy ◽  
Mean Fields ◽  
The Mean

Abstract In simulations of a wide range of circulations with an idealized general circulation model, clear scaling laws of dry atmospheric macroturbulence emerge that are consistent with nonlinear eddy–eddy interactions being weak. The simulations span several decades of eddy energies and include Earth-like circulations and circulations with multiple jets and belts of surface westerlies in each hemisphere. In the simulations, the eddy available potential energy and the barotropic and baroclinic eddy kinetic energy scale linearly with each other, with the ratio of the baroclinic eddy kinetic energy to the barotropic eddy kinetic energy and eddy available potential energy decreasing with increasing planetary radius and rotation rate. Mean values of the meridional eddy flux of surface potential temperature and of the vertically integrated convergence of the meridional eddy flux of zonal momentum generally scale with functions of the eddy energies and the energy-containing eddy length scale, with a few exceptions in simulations with statically near-neutral or neutral extratropical thermal stratifications. Eddy energies scale with the mean available potential energy and with a function of the supercriticality, a measure of the near-surface slope of isentropes. Strongly baroclinic circulations form an extended regime in which eddy energies scale linearly with the mean available potential energy. Mean values of the eddy flux of surface potential temperature and of the vertically integrated eddy momentum flux convergence scale similarly with the mean available potential energy and other mean fields. The scaling laws for the dependence of eddy fields on mean fields exhibit a regime transition between a regime in which the extratropical thermal stratification and tropopause height are controlled by radiation and convection and a regime in which baroclinic entropy fluxes modify the extratropical thermal stratification and tropopause height. At the regime transition, for example, the dependence of the eddy flux of surface potential temperature and the dependence of the vertically integrated eddy momentum flux convergence on mean fields changes—a result with implications for climate stability and for the general circulation of an atmosphere, including its tropical Hadley circulation.

Energetics of the Climate System

2019 ◽  
Author(s):  
Jin-Song von Storch
Keyword(s):  
Kinetic Energy ◽  
General Circulation ◽  
General Circulation Models ◽  
Eddy Kinetic Energy ◽  
Energy Cycle ◽  
Lorenz Energy Cycle ◽  
The Mean ◽  
Realistic Data ◽  
Mean Kinetic Energy ◽  
Energy Pathways

The energetics considerations based on Lorenz’s available potential energy A focus on identification and quantification of processes capable of converting external energy sources into the kinetic energy of atmospheric and oceanic general circulations. Generally, these considerations consist of: (a) identifying the relevant energy compartments from which energy can be converted against friction to kinetic energy of motions of interests; (b) formulating for these energy compartments budget equations that describe all possible energy pathways; and (c) identifying the dominant energy pathways using realistic data. In order to obtain a more detailed description of energy pathways, a partitioning of motions, for example, into a “mean” and an “eddy” component, or into a diabatic and an adiabatic component, is used. Since the budget equations do not always suggest the relative importance of all possible pathways, often not even the directions, data that describe the atmospheric and the oceanic state in a sufficiently accurate manner are needed for evaluating the energy pathways. Apart from the complication due to different expressions of A, ranging from the original definition by Lorenz in 1955 to its approximations and to more generally defined forms, one has to balance the complexity of the respective budget equations that allows the evaluation of more possible energy pathways, with the quality of data available that allows sufficiently accurate estimates of energy pathways. With regard to the atmosphere, our knowledge, as inferred from the four-box Lorenz energy cycle, has consolidated in the last two decades, by, among other means, using data assimilation products obtained by combining observations with realistic atmospheric general circulation models (AGCMs). The eddy kinetic energy, amounting to slightly less than 50% of the total kinetic energy, is supported against friction through a baroclinic pathway “fueled” by the latitudinally dependent diabatic heating. The mean kinetic energy is supported against friction by converting eddy kinetic energy via inverse cascades. For the ocean, our knowledge is still emerging. The description through the four-box Lorenz energy cycle is approximative and was only estimated from a simulation of a 0.1° oceanic general circulation models (OGCM) realistically forced at the sea surface, rather than from a data assimilation product. The estimates obtained so far suggest that the oceanic eddy kinetic energy, amounting almost 75% of the total oceanic kinetic energy, is supported against friction through a baroclinic pathway similar to that in the atmosphere. However, the oceanic baroclinic pathway is “fueled” to a considerable extent by converting mean kinetic energy supported by winds into mean available potential energy. Winds are also the direct source of the kinetic energy of the mean circulation, without involving noticeable inverse cascades from transients, at least not for the ocean as a whole. The energetics of oceanic general circulation can also be examined by separating diabatic from adiabatic processes. Such a consideration is thought to be more appropriate for understanding the energetics of the oceanic meridional overturning circulation (MOC), since this circulation is sensitive to density changes induced by diabatic mixing. Further work is needed to quantify the respective energy pathways using realistic data.

scholarly journals Energy Conversion Routes in the Western Mediterranean Sea Estimated from Eddy–Mean Flow Interactions

2019 ◽  
Vol 49 (1) ◽  
pp. 247-267 ◽  
Author(s):  
Esther Capó ◽  
Alejandro Orfila ◽  
Evan Mason ◽  
Simón Ruiz
Keyword(s):  
Energy Conversion ◽  
Mediterranean Sea ◽  
Western Mediterranean ◽  
Mean Flow ◽  
Physical Mechanisms ◽  
Western Mediterranean Sea ◽  
Energy Cycle ◽  
Flow Interactions ◽  
Lorenz Energy Cycle ◽  
The Mean

AbstractEnergy conversion routes are investigated in the western Mediterranean Sea from the eddy–mean flow interactions. The sources of eddy kinetic energy are analyzed by applying a regional formulation of the Lorenz energy cycle to 18 years of numerical simulation at eddy-resolving resolution (3.5 km), which allows for identifying whether the energy exchange between the mean and eddy flow is local or nonlocal. The patterns of energy conversion between the mean and eddy kinetic and potential energy are estimated in three subregions of the domain: the Alboran Sea, the Algerian Basin, and the northern basin. The spatial characterization of the energy routes hints at the physical mechanisms involved in maintaining the balance, suggesting that flow–topography interaction is strongly linked to eddy growth in most of the domain.

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