scholarly journals A Cascade-Type Global Energy Conversion Diagram Based on Wave–Mean Flow Interactions

2006 ◽  
Vol 63 (12) ◽  
pp. 3277-3295 ◽  
Author(s):  
Sachiyo Uno ◽  
Toshiki Iwasaki
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Wave Energy ◽  
General Circulation ◽  
Diabatic Heating ◽  
Mean Flow ◽  
Available Potential Energy ◽  
Flow Interactions ◽  
Northern Hemispheric ◽  
Cascade Type

A cascade-type energy conversion diagram is proposed for the purpose of diagnosing the atmospheric general circulation based on wave–mean flow interactions. Mass-weighted isentropic zonal means facilitate the expression of nongeostrophic wave effects, conservation properties, and lower boundary conditions. To gain physical insights into energetics based on the nonacceleration theorem, the wave energy W is defined as the sum of the eddy available potential energy PE and the eddy kinetic energy KE. The mainstream of the energy cascade is as follows: The diabatic heating produces the zonal mean available potential energy PZ, which is converted into the zonal mean kinetic energy KZ through the mean meridional circulation. The KZ is mainly converted to W through zonal wave–mean flow interactions and the rest is dissipated through friction. Not only the dynamical conversion but also the diabatic heating generates W, which is dissipated through friction. A diagnosis package is designed to analyze actual atmospheric data on the standard pressure surfaces. A validation study of the package is made by using the output from a general circulation model. The scheme accurately expresses tendencies of the zonal mean and eddy available potential energy equations, showing the diagnosis capability. On shorter time scales, PE changes in accordance with KE, good correlation indicating the relevance of the definition of wave energy. A preliminary study is made of the climate in December–February (DJF), and June–August (JJA), using the NCEP–NCAR reanalysis. The dynamical wave energy generation rate C(KZ, W) is about 60% of the conversion rate C(PZ, KZ), which means that KZ is dissipated through friction at a rate of about 40%. In the extratropics, C(KZ, W) is almost equal to C(PZ, KZ), as is expected from quasigeostrophic balance. In the subtropics, however, C(KZ, W) is much smaller than C(PZ, KZ), which suggests the importance of nongeostrophic effects on the energetics. The energetics is substantially different between the two solstices. Both C(PZ, KZ) and C(KZ, W) are about 30% larger in DJF than those in JJA, reflecting differences in wave activity. Stationary waves contribute considerably to energy conversions in the Northern Hemispheric winter, while baroclinic instability waves do more in the Southern Hemispheric winter than in the Northern Hemispheric winter.

scholarly journals Energy of Midlatitude Transient Eddies in Idealized Simulations of Changed Climates

2008 ◽  
Vol 21 (22) ◽  
pp. 5797-5806 ◽  
Author(s):  
Paul A. O’Gorman ◽  
Tapio Schneider
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Radiative Forcing ◽  
General Circulation ◽  
Thermal Structure ◽  
Circulation Model ◽  
Static Stability ◽  
Eddy Kinetic Energy ◽  
Available Potential Energy ◽  
Wide Range

Abstract As the climate changes, changes in static stability, meridional temperature gradients, and availability of moisture for latent heat release may exert competing effects on the energy of midlatitude transient eddies. This paper examines how the eddy kinetic energy in midlatitude baroclinic zones responds to changes in radiative forcing in simulations with an idealized moist general circulation model. In a series of simulations in which the optical thickness of the longwave absorber is varied over a wide range, the eddy kinetic energy has a maximum for a climate with mean temperature similar to that of present-day earth, with significantly smaller values both for warmer and for colder climates. In a series of simulations in which the meridional insolation gradient is varied, the eddy kinetic energy increases monotonically with insolation gradient. In both series of simulations, the eddy kinetic energy scales approximately linearly with the dry mean available potential energy averaged over the baroclinic zones. Changes in eddy kinetic energy can therefore be related to the changes in the atmospheric thermal structure that affect the mean available potential energy.

scholarly journals A Detailed Normal-Mode Energetics of the General Circulation of the Atmosphere

2012 ◽  
Vol 69 (9) ◽  
pp. 2718-2732 ◽  
Author(s):  
C. A. F. Marques ◽  
J. M. Castanheira
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Normal Mode ◽  
General Circulation ◽  
Department Of Energy ◽  
Japan Meteorological Agency ◽  
Available Potential Energy ◽  
Conversion Rates ◽  
Zonal Wavenumber ◽  
New Formulation

Abstract An energetics formulation is here introduced that enables an explicit evaluation for the conversion rates between available potential energy and kinetic energy, the nonlinear interactions of both energy forms, and their generation and dissipation rates, in both the zonal wavenumber and vertical mode domains. The conversion rates between available potential energy and kinetic energy are further decomposed into the contributions by the rotational (Rossby) and divergent (gravity) components of the circulation field. The computed energy terms allow one to formulate a detailed energy cycle describing the flow of energy among the zonal mean and eddy components, and also among the barotropic and baroclinic components. This new energetics formulation is a development of the 3D normal-mode energetics scheme. The new formulation is applied on an assessment of the energetics of winter (December–February) circulation in the 40-yr ECMWF Re-Analysis (ERA-40), the 25-yr Japan Meteorological Agency Reanalysis (JRA-25), and the NCEP–Department of Energy Reanalysis 2 (NCEP-R2) datasets.

scholarly journals Energetics of Eddy-Mean Flow Interactions in the Amery Ice Shelf Cavity

2021 ◽  
Vol 8 ◽  
Author(s):  
Yang Wu ◽  
Zhaomin Wang ◽  
Chengyan Liu ◽  
Liangjun Yan
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Ocean Circulation ◽  
Bottom Topography ◽  
Ocean Bottom ◽  
Mean Flow ◽  
Ice Shelf ◽  
Available Potential Energy ◽  
Amery Ice Shelf ◽  
Basal Melting

Previous studies demonstrated that eddy processes play an important role in ice shelf basal melting and the water mass properties of ice shelf cavities. However, the eddy energy generation and dissipation mechanisms in ice shelf cavities have not been studied systematically. The dynamic processes of the ocean circulation in the Amery Ice Shelf cavity are studied quantitatively through a Lorenz energy cycle approach for the first time by using the outputs of a high-resolution coupled regional ocean-sea ice-ice shelf model. Over the entire sub-ice-shelf cavity, mean available potential energy (MAPE) is the largest energy reservoir (112 TJ), followed by the mean kinetic energy (MKE, 70 TJ) and eddy available potential energy (EAPE, 10 TJ). The eddy kinetic energy (EKE) is the smallest pool (5.5 TJ), which is roughly 8% of the MKE, indicating significantly suppressed eddy activities by the drag stresses at ice shelf base and bottom topography. The total generation rate of available potential energy is about 1.0 GW, almost all of which is generated by basal melting and seawater refreezing, i.e., the so-called “ice pump.” The energy generated by ice pump is mainly dissipated by the ocean-ice shelf and ocean-bottom drag stresses, amounting to 0.3 GW and 0.2 GW, respectively. The EKE is generated through two pathways: the barotropic pathway MAPE→MKE→EKE (0.03 GW) and the baroclinic pathway MAPE→EAPE→EKE (0.2 GW). In addition to directly supplying the EAPE through baroclinic pathway (0.2 GW), MAPE also provides 0.5 GW of power to MKE to facilitate the barotropic pathway.

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.

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 Energetics of Eddy–Mean Flow Interactions in the Gulf Stream Region

2015 ◽  
Vol 45 (4) ◽  
pp. 1103-1120 ◽  
Author(s):  
Dujuan Kang ◽  
Enrique N. Curchitser
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gulf Stream ◽  
Mean Flow ◽  
Available Potential Energy ◽  
Flow Energy ◽  
Flow Interaction ◽  
The Mean ◽  
Eddy Field ◽  
Coast Region

AbstractA detailed energetics analysis of the Gulf Stream (GS) and associated eddies is performed using a high-resolution multidecadal regional ocean model simulation. The energy equations for the time-mean and time-varying flows are derived as a theoretical framework for the analysis. The eddy–mean flow energy components and their conversions show complex spatial distributions. In the along-coast region, the cross-stream and cross-bump variations are seen in the eddy–mean flow energy conversions, whereas in the off-coast region, a mixed positive–negative conversion pattern is observed. The local variations of the eddy–mean flow interaction are influenced by the varying bottom topography. When considering the domain-averaged energetics, the eddy–mean flow interaction shows significant along-stream variability. Upstream of Cape Hatteras, the energy is mainly transferred from the mean flow to the eddy field through barotropic and baroclinic instabilities. Upon separating from the coast, the GS becomes highly unstable and both energy conversions intensify. When the GS flows into the off-coast region, an inverse conversion from the eddy field to the mean flow dominates the power transfer. For the entire GS region, the mean current is intrinsically unstable and transfers 28.26 GW of kinetic energy and 26.80 GW of available potential energy to the eddy field. The mesoscale eddy kinetic energy is generated by mixed barotropic and baroclinic instabilities, contributing 28.26 and 9.15 GW, respectively. Beyond directly supplying the barotropic pathway, mean kinetic energy also provides 11.55 GW of power to mean available potential energy and subsequently facilitates the baroclinic instability pathway.

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.

Advancing the simulation of mesoscale eddies: Backscatter schemes in eddy-permitting ocean simulations

2021 ◽  
Author(s):  
Stephan Juricke ◽  
Sergey Danilov ◽  
Marcel Oliver ◽  
Nikolay Koldunov ◽  
Dmitry Sidorenko ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Large Scale ◽  
Mesoscale Eddy ◽  
Ocean Model ◽  
Mean Flow ◽  
Ocean Coupling ◽  
Climate Simulations ◽  
Flow Interactions ◽  
To Come ◽  
Eddy Dynamics

&lt;p&gt;Capturing mesoscale eddy dynamics is crucial for accurate simulations of the large-scale ocean currents as well as oceanic and climate variability. Eddy-mean flow interactions affect the position, strength and variations of mean currents and eddies are important drivers of oceanic heat transport and atmosphere-ocean-coupling. However, simulations at eddy-permitting resolutions are substantially underestimating eddy variability and eddy kinetic energy many times over. Such eddy-permitting simulations will be in use for years to come, both in coupled and uncoupled climate simulations. We present a set of kinetic energy backscatter schemes with different complexity as alternative momentum closures that can alleviate some eddy related biases such as biases in the mean currents, in sea surface height variability and in temperature and salinity. The complexity of the schemes reflects in their computational costs, the related simulation improvements and their adaptability to different resolutions. However, all schemes outperform classical viscous closures and are computationally less expensive than a related necessary resolution increase to achieve similar results. While the backscatter schemes are implemented in the ocean model FESOM2, the concepts can be adjusted to any ocean model including NEMO.&lt;/p&gt;

scholarly journals On the Role of Asymmetric Convective Bursts to the Problem of Hurricane Intensification: Radiation of Vortex Rossby Waves and Wave–Mean Flow Interactions

2014 ◽  
Vol 71 (6) ◽  
pp. 2057-2077 ◽  
Author(s):  
Konstantinos Menelaou ◽  
M. K. Yau
Keyword(s):  
Kinetic Energy ◽  
Thermal Anomaly ◽  
Eddy Kinetic Energy ◽  
Intensity Change ◽  
Mean Flow ◽  
Symmetric Flow ◽  
Thermal Forcing ◽  
Sensitivity Experiments ◽  
Flow Interactions

Abstract The role of asymmetric convection to the intensity change of a weak vortex is investigated with the aid of a “dry” thermally forced model. Numerical experiments are conducted, starting with a weak vortex forced by a localized thermal anomaly. The concept of wave activity, the Eliassen–Palm flux, and eddy kinetic energy are then applied to identify the nature of the dominant generated waves and to diagnose their kinematics, structure, and impact on the primary vortex. The physical reasons for which disagreements with previous studies exist are also investigated utilizing the governing equation for potential vorticity (PV) perturbations and a number of sensitivity experiments. From the control experiment, it is found that the response of the vortex is dominated by the radiation of a damped sheared vortex Rossby wave (VRW) that acts to accelerate the symmetric flow through the transport of angular momentum. An increase of the kinetic energy of the symmetric flow by the VRW is shown also from the eddy kinetic energy budget. Additional tests performed on the structure and the magnitude of the initial thermal forcing confirm the robustness of the results and emphasize the significance of the wave–mean flow interaction to the intensification process. From the sensitivity experiments, it is found that for a localized thermal anomaly, regardless of the baroclinicity of the vortex and the radial and vertical gradients of the thermal forcing, the resultant PV perturbation follows a damping behavior, thus suggesting that deceleration of the vortex should not be expected.

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