Conversion Of Available Potential Energy Research Articles

Spectral Budget of Rotational and Divergent Kinetic Energy in Global Analyses

Abstract To study the multiscale interactions between rotational and divergent components of atmospheric motion, a new formulation of spectral budget of rotational kinetic energy (RKE) and divergent kinetic energy (DKE) based on the primitive equations in the pressure coordinate is derived, with four main characteristics: 1) horizontal kinetic energy (HKE) spectral transfer is exactly divided into spectral transfer of RKE and DKE, 2) the exact spectral conversion term between DKE and RKE is constructed, 3) the Coriolis term is considered, and 4) both the baroclinic conversion from available potential energy (APE) and the vertical flux of HKE act only on DKE. With this new formulation, outputs from ERA5 global reanalysis are investigated. At planetary scales, HKE spectral transfer, mainly attributed to β effect, is dominated by downscale DKE transfer. At synoptic scales, it is dominated by an upscale transfer of RKE energized by conversion of DKE mainly due to the Coriolis effect. The ultimate source of DKE in the upper troposphere is conversion of APE, while in the stratosphere it is the vertical flux. At mesoscales, the spectral transfers of RKE and DKE are both downscale, and conversion from RKE to DKE exists at sub-800-km scales in the upper troposphere, which is mainly attributed to the contribution from relative vorticity. At different heights, the intersection scales of RKE and DKE spectra are affected by the scales of positive peaks of the local spectral conversion from DKE to RKE around total wavenumber 10. Significance Statement The purpose of this study is to explore more physical insights on the dynamics underlying the atmospheric energy spectra from the perspective of rotational and divergent components of motion. We derive a new formulation of the spectral rotational and divergent kinetic energy budget in the pressure coordinate for the global atmosphere, with application to ERA5 global reanalysis. Our results reveal the differences of spectral energy budget between rotational and divergent motions at different heights and scales. This new formulation provides a good tool for revealing the multiscale cascade and interaction between atmospheric rotational and divergent motions. Future work should investigate these dynamical processes with higher-resolution simulations and datasets.

ПРОСТРАНСТВЕННО-ВРЕМЕННАЯ ИЗМЕНЧИВОСТЬ ГИДРОФИЗИЧЕСКИХ И ЭНЕРГЕТИЧЕСКИХ ХАРАКТЕРИСТИК ЦИРКУЛЯЦИИ ЧЕРНОГО МОРЯ ПРИ ДОМИНИРОВАНИИ ДВИЖЕНИЙ РАЗНЫХ МАСШТАБОВ

Simulation results of the Black Sea dynamics for two periods when the annual mean circulation corresponded to the basin-scale and eddy regimes (2011 and 2016) are considered in the paper. Numerical experiments are carried out using the MHI model and considering the realistic atmospheric forcing from SKIRON. The seasonal variability of dynamic and thermohaline fields, as well as the kinetic and available potential energy, and their conversion rates are estimated. According to the model data on the seasonal mean distribution of currents velocity, it is found that in 2011 the RIM Current is detected in all seasons, and the most intense mesoscale eddies developed on its periphery over the continental slope in the warm period of the year; in 2016, separate cyclonic jets in the area of the continental slope are observed in the northern and southwestern parts of the basin during cold seasons, and mesoscale eddies are propagated in the central part of the sea throughout the year. The change in the mean current kinetic energy is determined by the circulation regime: energy maxima are revealed in the spring of 2011 and in the winter of 2016, when the mean current was the most intense. The distribution of the mean available potential energy is predominantly seasonal, the time variability is qualitatively similar for both modes and is provided by an increase in the density anomaly due to seawater heating. The eddy kinetic energy characterizing the mesoscale variability depends both on the circulation regime and on the season. In the spring 2011, the mean current and eddy kinetic energies are comparable; in 2016, the maximum eddy energy exceeded the mean current kinetic energy. In autumn and winter, for both calculations, the increase in eddy energy occurs due to the energy transfer from the wind and the mean current through the barotropic instability mechanism. In summer when wind activity weakens, in the basin-scale circulation mode, mesoscale variability is supported by commensurate contributions from barotropic and baroclinic instability; in the eddy circulation mode – mainly due to the conversion of available potential energy through baroclinic instability.

Quantifying mixing and available potential energy in vertically periodic simulations of stratified flows

Abstract

Modulations of North American and European Weather Variability and Extremes by Interdecadal Variability of the Atmospheric Circulation over the North Atlantic Sector

AbstractThe dominant mode of wintertime interdecadal covariability between subseasonal surface air temperature (SAT) variability and midtropospheric circulation over the North Atlantic sector is identified through maximum covariance analysis applied to century-long reanalysis data. This mode highlights a tendency for subseasonal temperature variability over Europe and eastern North America to be enhanced during decades when the negative phase of the North Atlantic Oscillation (NAO) prevails. This interdecadal NAO is characterized by a stationary Rossby wave train that originates from the subtropical Atlantic, propagates northward into the subpolar Atlantic, and finally refracts toward Europe and the Middle East. A decadal increase in precipitation in the subtropics under the enhanced supply of heat and moisture from the Gulf Stream and its surroundings appears to act as a source for this wave train. The influence of the interdecadal NAO on subseasonal SAT variability is explained primarily by the modulated efficiency of baroclinic conversion of available potential energy from the background atmospheric flow to subseasonal eddies. The combination of enhanced subseasonal variability and low winter-mean temperature anomalies associated with the negative phase of the interdecadal NAO increases the frequency of cold extremes affecting Europe and the eastern United States.

The Seasonality of Submesoscale Energy Production, Content, and Cascade

AbstractSubmesoscale processes in the upper ocean vary seasonally, in tight correspondence with mixed layer thickness variability. Based on a global high‐resolution MITgcm simulation, seasonal evaluation of strong vorticity and spectral analysis of the kinetic energy in the Kuroshio Extension System show the strongest submesoscales occur in March, implying a lag of about a month behind mixed layer thickness maximum in February. An analysis of spectral energy sources and transfers indicates that the seasonality of the submesoscale energy content is a result of the competition between the conversion of available potential energy into submesoscale kinetic energy via a buoyancy production/vertical buoyancy flux associated with mixed layer instability and nonlinear energy transfers to other scales associated with an energy cascade. The buoyancy production is seasonally in phase with the mixed layer depth, but the transfers of energy across scales makes energizing the reservoir of submesoscale kinetic energy lag behind by a month.

Energetics of the Western Hemisphere Circulation Pattern

Abstract The Western Hemisphere (WH) circulation pattern, identified by self-organizing maps cluster analysis, is a low-frequency atmospheric regime that influences the fluctuations of large-scale circulation over the North Pacific–North American–North Atlantic areas. The reanalysis datasets from ECMWF are used to estimate the energetics of the WH pattern in this study. The composite results based on monthly WH events reveal that the kinetic energy (KE) associated with the WH pattern is maintained through the barotropic conversion from the climatological-mean westerlies, mainly in the Atlantic jet exit regions. The KE could also be gained through the barotropic feedback forcing from transient eddies. The corresponding baroclinic conversion of available potential energy (APE) from the climatological-mean state, which contributes most efficiently to the energy maintenance of the WH pattern, is obvious in the middle and lower troposphere, owing to the thermal contrast of the colder continent and warmer ocean over the North America–North Atlantic sector. The baroclinic conversion associated with the heat flux on the climatological temperature gradient is consistent with the southwestward-tilting height anomalies from 850 to 500 hPa. The baroclinic feedback from transient eddies contributes negatively to the energy conversion and destroys the maintenance of the WH pattern.

Intensification of Upper-Ocean Submesoscale Turbulence through Charney Baroclinic Instability

AbstractThis study focuses on the description of an oceanic variant of the Charney baroclinic instability, arising from the joint presence of (i) an equatorward buoyancy gradient that extends from the surface into the ocean interior and (ii) reduced subsurface stratification, for example, as produced by wintertime convection or subduction. This study analyzes forced dissipative simulations with and without Charney baroclinic instability (C-BCI). In the former, C-BCI strengthens near-surface frontal activity with important consequences in terms of turbulent statistics: increased variance of vertical vorticity and velocity and increased vertical turbulent fluxes. Energetic consequences are explored. Despite the atypical enhancement of submesoscale activity in the simulation subjected to C-BCI, and contrary to several recent studies, the downscale energy flux at the submesoscale en route to dissipation remains modest in the flow energetic equilibration. In particular, it is modest vis à vis the global energy input to the system, the eddy kinetic energy input through conversion of available potential energy, and the classical inverse cascade of kinetic energy. Linear stability analysis suggests that the southern flank of the Gulf Stream may be conducive to oceanic Charney baroclinic instability in spring, following mode water formation and upper-ocean destratification.

Vertical Structure and Energetics of the Western Pacific Teleconnection Pattern

Abstract The western Pacific (WP) pattern, characterized by north–south dipolar anomalies in pressure over the Far East and western North Pacific, is known as one of the dominant teleconnection patterns in the wintertime Northern Hemisphere. Composite analysis reveals that monthly height anomalies exhibit baroclinic structure with their phase lines tilting southwestward with height in the lower troposphere. The anomalies can thus yield not only a poleward heat flux across the climatological thermal gradient across the strong Pacific jet but also a westward heat flux across the climatological thermal gradient between the North Pacific and the cooler Asian continent. The resultant baroclinic conversion of available potential energy (APE) from the climatological-mean flow contributes most efficiently to the APE maintenance of the monthly WP pattern, acting against strong thermal damping effects by anomalous heat exchanges with the underlying ocean and anomalous precipitation in the subtropics and by the effect of anomalous eddy heat flux under modulated storm-track activity. Kinetic energy (KE) of the pattern is maintained through barotropic feedback forcing associated with modulated activity of transient eddies and the conversion from the climatological-mean westerlies, both of which act against frictional damping. The net feedback forcing by transient eddies is therefore not particularly efficient. The present study suggests that the WP pattern has a characteristic of a dynamical mode that can maintain itself through efficient energy conversion from the climatological-mean fields even without external forcing, including remote influence from the tropics.

Linear stability and energetics of rotating radial horizontal convection

The effect of rotation on horizontal convection in a cylindrical enclosure is investigated numerically. The thermal forcing is applied radially on the bottom boundary from the coincident axes of rotation and geometric symmetry of the enclosure. First, a spectral element method is used to obtain axisymmetric basic flow solutions to the time-dependent incompressible Navier–Stokes equations coupled via a Boussinesq approximation to a thermal transport equation for temperature. Solutions are obtained primarily at Rayleigh number $\mathit{Ra}=10^{9}$ and rotation parameters up to $Q=60$ (where $Q$ is a non-dimensional ratio between thermal boundary layer thickness and Ekman layer depth) at a fixed Prandtl number $\mathit{Pr}=6.14$ representative of water and enclosure height-to-radius ratio $H/R=0.4$. The axisymmetric solutions are consistently steady state at these parameters, and transition from a regime unaffected by rotation to an intermediate regime occurs at $Q\approx 1$ in which variation in thermal boundary layer thickness and Nusselt number are shown to be governed by a scaling proposed by Stern (1975, Ocean Circulation Physics. Academic). In this regime an increase in $Q$ sees the flow accumulate available potential energy and more strongly satisfy an inviscid change in potential energy criterion for baroclinic instability. At the strongest $Q$ the flow is dominated by rotation, accumulation of available potential energy ceases and horizontal convection is suppressed. A linear stability analysis reveals several instability mode branches, with dominant wavenumbers typically scaling with $Q$. Analysis of contributing terms of an azimuthally averaged perturbation kinetic energy equation applied to instability eigenmodes reveals that energy production by shear in the axisymmetric mean flow is negligible relative to that produced by conversion of available potential energy from the mean flow. An evolution equation for the quantity that facilitates this exchange, the vertical advective buoyancy flux, reveals that a baroclinic instability mechanism dominates over $5\lesssim Q\lesssim 30$, whereas stronger and weaker rotations are destabilised by vertical thermal gradients in the mean flow.

Applications of a Moist Nonhydrostatic Formulation of the Spectral Energy Budget to Baroclinic Waves. Part II: The Upper-Tropospheric Energy Spectra

Abstract In this second part of a two-part study, a newly developed moist nonhydrostatic formulation of the spectral energy budget of both kinetic energy (KE) and available potential energy (APE) is employed to investigate the dynamics underlying the mesoscale upper-tropospheric energy spectra in idealized moist baroclinic waves. By calculating the conservative nonlinear spectral fluxes, it is shown that the inclusion of moist processes significantly enhances downscale cascades of both horizontal KE and APE. Moist processes act not only as a source of latent heat but also as an “atmospheric dehumidifier.” The latent heating, mainly because of the depositional growth of cloud ice, has a significant positive contribution to mesoscale APE. However, the dehumidifying reduces the diabatic contribution of the latent heating by 15% at all scales. Including moist processes also changes the direction of the mesoscale conversion between APE and horizontal KE and adds a secondary conversion of APE to gravitational energy of moist species. With or without moisture, the vertically propagating inertia–gravity waves (IGWs) produced in the lower troposphere result in a significant positive contribution to the upper-tropospheric horizontal KE spectra at the large-scale end of the mesoscale. However, including moist processes generates additional sources of IGWs located in the upper troposphere; the upward propagation of the convectively generated IGWs removes much of the horizontal KE there. Because of the restriction of the anelastic approximation, the three-dimensional divergence has no significant contribution. In view of conflicting contributions of various direct forcings, finally, an explicit comparison between the net direct forcing and energy cascade is made.

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

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.

Applications of a Moist Nonhydrostatic Formulation of the Spectral Energy Budget to Baroclinic Waves. Part I: The Lower-Stratospheric Energy Spectra

Abstract The authors investigate the mesoscale dynamics that produce the lower-stratospheric energy spectra in idealized moist baroclinic waves, using the moist nonhydrostatic formulation of spectral energy budget of kinetic energy and available potential energy by J. Peng et al. The inclusion of moist processes energizes the lower-stratospheric mesoscale, helping to close the gap between observed and simulated energy spectra. In dry baroclinic waves, the lower-stratospheric mesoscale is mainly forced by weak downscale cascades of both horizontal kinetic energy (HKE) and available potential energy (APE) and by a weak conversion of APE to HKE. At wavelengths less than 1000 km, the pressure vertical flux divergence also has a significant positive contribution to the HKE; however, this positive contribution is largely counteracted by the negative HKE vertical flux divergence. In moist baroclinic waves, the lower-stratospheric mesoscale HKE is mainly generated by the pressure and HKE vertical flux divergences. This additional HKE is partly converted to APE and partly removed by diffusion. Another negative contribution to the mesoscale HKE is from the forcing of a visible upscale HKE cascade. Besides the conversion of HKE, however, the three-dimensional divergence also has a significant positive contribution to the mesoscale APE. With these two direct APE sources, the lower-stratospheric mesoscale also undergoes a much stronger upscale APE cascade. These results suggest that both downscale and upscale cascades through the mesoscale are permitted in the real atmosphere and the direct forcing of the mesoscale is available to feed the upscale energy cascade.

Energetics Responses to Increases in Greenhouse Gas Concentration

Abstract Increasing greenhouse gas concentrations warm the troposphere. However, it is not clear whether this implies changes in the energetics. To study the energetics responses to CO2 increases, changes in the Lorenz energy cycle (LEC) are evaluated using output from the atmosphere–ocean ECHAM5/Max Planck Institute Ocean Model (MPI-OM). Equilibrium 2 × CO2 experiments and 10-yr transient experiments with 3% increase per year are analyzed. Globally, doubling of CO2 results in a decrease in the LEC strength—defined as the total conversion of available potential energy P into kinetic energy K—but also in an increase in the zonal-mean K. These global changes are a consequence of the strengthening of the LEC in the upper troposphere and the weakening of the cycle below. The two opposite responses result from the simulated warming pattern that shows the strongest warming in the upper tropical troposphere and in the lower troposphere at high latitudes. This warming structure causes changes in the horizontal temperature variance and in mean static stability, which increase zonal-mean P in the upper troposphere and decrease it below, triggering the two opposite responses via changes in baroclinic activity. In general, the lower-region weakening is stronger in the Northern Hemisphere, while the upper-region strengthening, and the increase of zonal-mean P and K, is stronger in the Southern Hemisphere. The former is more pronounced in the transient experiments but decreases in the stabilized 2 × CO2 climate.

The atmospheric circulation and states of maximum entropy production

Energy balance models suggest that the atmospheric circulation operates close to a state of maximum entropy production. Here we support this hypothesis with sensitivity simulations of an atmospheric general circulation model. A state of maximum entropy production is obtained by (i) adjusting boundary layer turbulence and (ii) using a sufficiently high model resolution which allows sufficient degrees of freedom for the atmospheric flow. The state of maximum entropy production is associated with the largest conversion of available potential energy into kinetic energy which is subsequently dissipated by boundary layer turbulence. It exhibits the largest eddy activity in the mid latitudes, resulting in the most effective transport of heat towards the poles and the least equator‐pole temperature difference. These results suggest that GCMs have a fundamental tendency to underestimate the magnitude of atmospheric heat transport and, therefore, overestimate the equator‐pole temperature gradient for the present‐day climate, for the response to global climatic change, and for atmospheres of other planetary bodies.

A possible explanation of countergradient fluxes in homogeneous turbulence

This study addresses the phenomenon of persistent countergradient (PCG) fluxes of momentum and heat (density) as observed in homogeneous turbulence forced by shear and stratification. Countergradient fluxes may occur at large scales when stratification is strong. However, they always occur at small scales, independently of stratification. A conceptional model is introduced to explain PCG fluxes at small scales as the result of the collision of large-scale fluid parcels. The large parcels collide under the driving force of inclined vortex structures (in a shear-dominated flow) or of buoyancy (in a strongly stratified shear flow). This “collision model” also explains the PCG heat flux in an unsheared stratified flow with zero average momentum flux. It is found that the energy of the small-scale PCG motions is provided (i) by quick transport of kinetic energy from the scales of production to relatively slowly dissipating scales if the flow is shear-driven and (ii) by conversion of available potential energy to kinetic energy at small scales when the flow is stratified. The collision mechanism is an inherent property of the turbulence dynamics. Therefore, the PCG fluxes at small scales reflect a universal character of homogeneous turbulence, and are found over a large range of Reynolds numbers. The Prandtl (or Schmidt) number influences the rate of dissipation of temperature (or density) variance but not the dissipation rate of the velocity variance. In stratified flows, therefore, the number directly affects the strength of the PCG heat flux at small scales. It is found, however, that the PCG momentum flux is also altered slightly when the Prandtl number is large enough to sustain small buoyantly moving parcels after collision.

Energetics constraint for linear disturbances development

In development of baroclinic disturbances, baroclinity of basic temperature field varies with conversion of available potential energy. The growth rate which depends on the baroclinity varies as well. However, in previous linear theories, the growth rate was considered constant, so development of disturbances was not constrained by energy sources in the linear theories. In terms of energy conservation and conversion in an isolated atmosphere, we may study the variations in the baroclinity and growth rate and draw the corresponding pictures of perturbation developments in the varying environments. The amplification for the most unstable Eady wave is discussed as an example. It will be found that growth of baroclinic perturbations constrained by energy conservation is significantly different from the growth at the initial constant rate after mature stage.

A divergent and rotational kinetic energy budget for January and July

Rotational and divergent kinetic energy (K) exchanges are studied using a budget which partitions the global K into four components: zonal divergent K, zonal rotational K, eddy divergent K, and eddy rotational K. Vertically integrated results are given for the energies, the exchanges between them, and the conversions from available potential energy (APE) using the National Meteorological Center global operational analyses for the five Januarys and the five Julys from 1983 to 1987. Both the January and the July results show that the flow of energy is generally from eddy APE to eddy divergent K and then to eddy rotational K. From the eddy rotational K, energy flows to zonal rotational K and then to zonal divergent K. The conversion of zonal APE to zonal divergent K is seasonally dependent. In January the conversion is indirect (APE is converted to divergent K) and in July it is in the opposite sense. The results also indicate that the amounts of divergent energy in the atmosphere are small compared to the amounts of rotational energy even though the sources and sinks of divergent energy are relatively large, supporting the idea suggested by previous studies that the divergent K plays a “catalytic” role in the conversion of APE to rotational K.

Linear Baroclinic instability with the Geostrophic Momentum Approximation

Abstract The linear Eady model of baroclinic instability with the geostrophic momentum (GM) approximation is solved analytically in physical space and shown to be identical to linear three-dimensional semigeostrophic theory. Both the growth rates and the wavenumber of the short-wave cutoff are larger than those predicted by quasi-geostrophic (QG) theory. This behavior arises because the effective static stability is reduced in the GM case. These results are opposite to those using standard nongeostrophic (NG) theory, and the discrepancy increases with decreasing Richardson number. Energetically, the unstable GM normal modes enhance the conversion of available potential energy compared to the QG modes and also convert available kinetic energy to eddy kinetic energy. With regards to the structure of the unstable modes, the northward tilt with height in the GM case is more consistent with NG theory than is the QG solution which displays no meridional tilt. Additional analysis addresses the effect of assuming...

Maintenance and oscillation mechanisms of summer tropical upper-tropospheric easterlies

The mechanisms of the maintenance and oscillation of 1982 summer tropical 200-hPa mean easterly flow and extra-long waves are investigated in terms of the energy equations in wavenumber-frequency space. Calculation results show that the difference in heating between land and sea and the boundary effect serve as the main source of energy; frictional dissipation as the sink; the conversion of available potential energy into kinetic takes place dominantly in the waves of number 1–2 such transformation is accomplished in just a small amount in zonal mean flow and therefore can be ignored because of the value. In the interaction between wave and zonal mean flow, the latter loses its available potential and gains kinetic energy. The tropical easterly belt over 20°N-5°S is found barotropically stable and that over 10°-5°S, unstable. The waves of number 2 and 1 manifest themselves a primary source and sink of kinetic energy, respectively, in the interplay between waves and between zonal mean flow and wave. It is found that zonal mean flow and the waves of number 1-2 have a roughly 40-and 20-day oscillational period of kinetic energy, respectively, whose primary mechanism is the transfer of barotropic energy, the conversion of baroclinic energy, and the boundary effect.

Effects of Eddy Initial Conditions on Nonlinear Forcing of Planetary Scale Waves by Amplifying Baroclinic Eddies

The previous study of Young and Villere concerning growth of planetary scale waves forced by wave-wave interactions of amplifying intermediate scale baroclinic eddies is extended to investigate effects of different eddy initial conditions. A global, spectral, primitive equation model is used for the calculations. For every set of eddy initial conditions considered, growth rates of planetary modes are considerably greater than growth rates computed from linear instability theory for a fixed zonally independent basic state. However, values of growth rates ranged over a factor of 3 depending on the particular set of eddy initial conditions used. Nonlinear forcing of planetary modes via wave-wave coupling becomes more important than baroclinic growth on the basic state at small values of the intermediate-scale modal amplitudes. The relative importance of direct transfer of kinetic energy from intermediate scales of motion to a planetary mode, compared to baroclinic conversion of available potential energy to kinetic energy within that planetary mode, depends on the individual case. In all cases, however, the transfer of either kinetic or available potential energy to the planetary modes was accomplished principally by wave-wave transfer from intermediate scale eddies, rather than from the zonally averaged state. The zonal wavenumber 2 planetary mode was prominent in all solutions, even in those for which eddy initial conditions were such that a different planetary mode was selectively forced at the start. General characteristics of the structural evolution of the planetary wave components of total heat and momentum flux, and modal structures themselves, were relatively insensitive to variations in eddy initial conditions, even though quantitative details varied from case to case.