Zonal Energy Research Articles

Wind forcing of the ocean and the Atlantic meridional overturning circulation

Wind forcing of the oceans is analysed for a millennium-length period of a simulation with a global coupled model. The time mean value of the zonal wind energy input to the oceans was found to be 0.97 TW, similar to other estimates, with maximum inputs in the Southern Ocean and Equatorial Pacific Ocean. The meridional wind energy input was also evaluated. The time series of the zonal wind energy input consisted of white noise, with marked multiannual and multidecadal variability, and had a range of 1.6 between minimum and maximum values. Seasonal variations in the wind energy input were most marked in the Pacific Ocean. Composites of the various climatic terms involved in the wind energy input, for maximum and minimum values of the input time series, identified distinct differences in anomaly values, particularly over the Southern Ocean. The temporal variability of the Pacific equatorial wind energy input was clearly identified with ENSO events. The model reproduced the observed structure of the Atlantic meridional overturning circulation surprisingly well. The time series of this circulation exhibited interannual to centennial variability. Correlations, both instantaneous and lagged, failed to identify any meaningful relationship between the temporal variability of the circulation and the wind energy input to the Southern Ocean. The optimum correlation was found between time smoothed versions of the time series for this circulation and the heat input to the North Atlantic Ocean, implying, as noted elsewhere, that this heat input is the principal driver of the temporal variability of the circulation.

On-off intermittent regulation of plasma turbulence

A standard low-dimensional model of the dynamical regulation of plasma turbulence including zonal flows is considered in a statistical sense by taking into account the fluctuating nature of the source driving the system. The probability distribution functions of the turbulent kinetic energy and the zonal flows energy are derived. The dynamics become on-off intermittent close to the bifurcation thresholds. In its low confinement mode, without zonal flows, the system can also display random finite amplitude burst close to marginal stability, a result reminiscent of the self-organized-criticality paradigm applied to flux-driven plasma turbulence.

Alternating zonal jets and energy fluxes in barotropic wind-driven gyres

Abstract The barotropic β-plane vorticity equation is considered under steady large scale (double-gyre) and small scale (stochastic) forcing. For both forcings, regimes are found in which alternating zonal jets appear. For steady large scale forcing, this regime is characterized by weak forcing and weak dissipation. Attention is focused on energy cascades due to the nonlinear and β terms and the jets are found to be associated with to a near compensation in these cascades over a range of wavenumbers. Additionally, interaction between flow forced at large scale and flow forced at small scale is examined.

Gyrokinetic Study of the Local Entropy Dynamics in Turbulent Plasmas with Zonal Flow

An entropy balance equation that maintains the dynamics in the radial direction is derived to study the role of zonal flows in turbulent transport. The equation describes the dynamics not only of the entropy density production related to zonal flow and local heat flux, but also of entropy density convection. We investigated these spatio-temporal dynamics of entropy in ion temperature gradient driven turbulence based on a global gyrokinetic Vlasov simulations in a slab geometry. The contribution of zonal flow to entropy production is observed to be small in the strong instability case, whereas the zonal flow energy is sufficiently large. We also found that the entropy density with n = 2 in the Hermite polynomial expansion in velocity space plays an important role in convecting the entropy density, causing turbulent spreading.

Energy Spectrum Characteristics of Boreal Summer Intraseasonal Oscillations: Climatology and Variations during the ENSO Developing and Decaying Phases*

Abstract The geographic-dependence characteristics of the energy spectrum of the boreal summer intraseasonal oscillation (BSISO; May–October) over the Indo–western Pacific region were analyzed using 25-yr (1979–2003) observational data. The BSISO energy spectrum distribution exhibits a distinctive regional characteristic. The stationary and eastward-propagating modes are most pronounced at the equator (5°S–5°N), while the westward-propagating modes are dominant in the off-equatorial region (10°–20°N). While the eastward intraseasonal oscillation (ISO) spectrum agglomerates on the 30–60-day period and zonal wavenumber 1, the westward mode covers wider spatial (wavenumber) and temporal (period) range. Along the Arabian Sea, Bay of Bengal, and South China Sea (SCS) latitudes, the dominant wavenumber 1 mode is the eastward (westward) propagation at the 30–60-day (10–20 day) period; for zonal wavenumber 2, the dominant mode is the westward propagation at both the 30–60-day and 10–20-day periods. Compared to the absolute amplitude of both zonal and meridional mode energy spectrum, northward propagation is the most predominant mode in boreal summer over the Indo–western Pacific regions. The strongest northward-propagating BSISO signal appears in the eastern tropical Indian Ocean. The variation of BSISO differs significantly in the El Niño and La Niña developing and decaying phases. During the El Niño (La Niña) developing summer, the eastward propagation is enhanced (weakened) at the equator, while the northward propagation is also strengthened (weakened) over the western Pacific (east of 140°E). During the El Niño (La Niña) decaying summer, the eastward propagation weakens (strengthens) at the equator, opposite to that in the developing summer; the westward propagation off the equator and the northward propagation over SCS and the western Pacific are suppressed (enhanced). The amplitude of the BSISO variation is stronger in the decaying summer than that in the developing summer. This asymmetry in BSISO variations is primarily attributed to the asymmetry of the background mean flow change associated with the developing and decaying phases of ENSO.

Explaining the global distribution of peak‐spectrum variability of sea surface height

A 14‐year satellite observation of sea surface height (SSH) reveals an interesting pattern. Along any latitude, there is a frequency at which the SSH power spectrum peaks, regardless of which hemisphere or oceanic basin. This peak‐spectrum frequency is nearly identical to the critical frequency at which the zonal energy propagation of Rossby waves becomes stagnant. The interior ocean adjusts to atmospheric forcing by radiating energy away through Rossby waves. There are two distinct groups of Rossby waves, long ones carry the energy to the west while short ones send the energy to the east. At the critical frequency, these two waves merge and their zonal energy propagation becomes stagnant. Consequently, the energy from atmospheric forcing may accumulate in the ocean interior, and thus result in a spectrum peak.

Long-term MST radar observations of vertical wave number spectra of gravity waves in the tropical troposphere over Gadanki (13.5° N, 79.2° E): comparison with model spectra

Abstract. The potential utility of Mesosphere-Stratosphere-Troposphere (MST) radar measurements of zonal, meridional and vertical winds for divulging the gravity wave vertical wave number spectra is discussed. The data collected during the years 1995–2004 are used to obtain the mean vertical wave number spectra of gravity wave kinetic energy in the tropical troposphere over Gadanki (13.5° N, 79.2° E). First, the climatology of 3-dimensional wind components is developed using ten years of radar observations, for the first time, over this latitude. This climatology brought out the salient features of background tropospheric winds over Gadanki. Further, using the second order polynomial fit as background, the day-to-day wind anomalies are estimated. These wind anomalies in the 4–14 km height regions are used to estimate the profiles of zonal, meridional and vertical kinetic energy per unit mass, which are then used to estimate the height profile of total kinetic energy. Finally, the height profiles of total kinetic energy are subjected to Fourier analysis to obtain the monthly mean vertical wave number spectra of gravity wave kinetic energy. The monthly mean vertical wave number spectra are then compared with a saturation spectrum predicted by gravity wave saturation theory. A slope of 5/3 is used for the model gravity wave spectrum estimation. In general, the agreement is good during all the months. However, it is noticed that the model spectrum overestimates the PSD at lower vertical wave numbers and underestimates it at higher vertical wave numbers, which is consistently observed during all the months. The observed discrepancies are attributed to the differences in the slopes of theoretical and observed gravity wave spectra. The slopes of the observed vertical wave number spectra are estimated and compared with the model spectrum slope, which are in good agreement. The estimated slopes of the observed monthly vertical wave number spectra are in the range of −2 to −2.8. The significance of the present study lies in using the ten years of data to estimate the monthly mean vertical wave number spectra of gravity waves, which will find their application in representing the realistic gravity wave characteristics in atmospheric models.

Propagation and reflection of gravity waves in a meridionally sheared wind field

Although the properties of gravity waves propagating in a vertically sheared flow have been extensively studied, the effects of a horizontally sheared wind on gravity wave propagations were seldom reported. In this paper, according to the linear theory, the characteristics of gravity wave reflection in a meridionally sheared zonal background wind field are discussed, which are evidently different from those of wave reflected by a vertically sheared flow. By numerical simulations, we present the whole process of a gravity wave packet reflection in a meridionally sheared wind. When the wave reaches the reflecting level, the zonal disturbance velocity in the evanescent region shows an evanescent wave configuration, which is consistent with the Airy function form predicted by the linear theory; while the meridional disturbance velocity exhibits rather different wave structures. The wave number spectra of zonal and meridional disturbance velocities also show different characteristics in the reflection process. The energy center of the wave packet is reflected in a position nearer than the reflecting level predicted by the linear theory. While the wave propagates along (against) the meridionally sheared wind, the meridional perturbation kinetic energy and total wave energy decrease (increase), whereas, the zonal perturbation kinetic energy increases (decreases); and an energy exchange between the wave potential and wave kinetic energies can be observed. Earth rotation has a slight influence on the energy transfer between the wave and the background flow. If the wind shear beyond the reflecting level isn't strong enough, part components of the incident wave may steadily penetrate across the reflecting level, and yields a transmission wave. A large amplitude gravity wave propagating in a meridionally sheared wind can obviously induce a mean flow, which strengthens slightly the wave reflection, indicating that the transmission rate slightly decreases with the increasing amplitude of the incident wave. This differs from the reflection of waves in a vertical sheared wind field, in which the mean flow induced by the large amplitude wave significantly enhances the wave transmission effect. In the meridionally sheared flow, the transmission rate seems to mainly depend on the sheared wind and the parameters and spectral components of the incident waves.

Modeling ventilated double skin façade—A zonal approach

This article presents the application of the zonal approach for modeling airflow and temperature in a ventilated double skin facades (DSF). The zonal airflow equation, power-law, was employed to calculate the airflow through the shading device and cavities. The zonal energy equation was used to evaluate the temperature distribution in the DSF system. The predicted temperature distributions were verified using measured values and parametric studies were conducted to identify the influence of height, flow rate and presence of venetian blinds on the inlet–outlet temperature difference. The influence of changing the values of each parameter was found to be more apparent during the day than during the night. The inlet–outlet temperature difference increased as height of the DSF increased and when venetian blinds were installed but it was found to decrease as the airflow rate increased . The results had revealed that the zonal approach can be employed to provide information on the performance of DSF faster and at very low computational resource.

Two-Layer Baroclinic Eddy Heat Fluxes: Zonal Flows and Energy Balance

Abstract The eddy heat flux generated by statistically equilibrated baroclinic turbulence supported on a uniform, horizontal temperature gradient is examined using a two-layer β-plane quasigeostrophic model. The dependence of the eddy diffusivity of temperature, Dτ, on external parameters such as β, bottom friction κ, the deformation radius λ, and the velocity jump 2U, is provided by numerical simulations at 110 different points in the parameter space β* = βλ2/U and κ* = κλ/U. There is a special “pivot” value of β*, βpiv* ≈ 11/16, at which Dτ depends weakly on κ*. But otherwise Dτ has a complicated dependence on both β* and κ*, highlighted by the fact that reducing κ* leads to increases (decreases) in Dτ if β is less than (greater than) βpiv*. Existing heat-flux parameterizations, based on Kolmogorov cascade theories, predict that Dτ is nonzero and independent of κ* in the limit κ* → 0. Simulations show indications of this regime provided that κ* ≤ 0.04 and 0.25 ≤ β* ≤ 0.5. All important length scales in this problem, namely the mixing length, the scale of the energy containing eddies, the Rhines scale, and the spacing of the zonal jets, converge to a common value as bottom friction is reduced. The mixing length and jet spacing do not decouple in the parameter regime considered here, as predicted by cascade theories. The convergence of these length scales is due to the formation of jet-scale eddies that align along the eastward jets. The baroclinic component of these eddies helps force the zonal mean flow, which occurs through nonzero Reynolds stress correlations in the upper layer, as opposed to the barotropic mode. This behavior suggests that the dynamics of the inverse barotropic cascade are insufficient to fully describe baroclinic turbulence.

Radiosonde observations of vertical wave number spectra for gravity waves in the lower atmosphere over Central China

Abstract. Vertical wave number spectra of inertial gravity waves in the troposphere and lower stratosphere over six stations at latitudes from 20° N to 40° N were statistically studied by using the data from Radiosonde observation on a twice daily basis at 08:00 and 20:00 LT. Statistically, the spectral characteristics seem to be independent of the local observation time, and show considerable conformity between the spectral of zonal and meridional kinetic energy densities. Compared with the spectra of the kinetic energy density, the spectra of the potential energy density are steeper. in addition the characteristic wave numbers of the spectra also show considerable consistency among the observations at different stations. As for the spectral slopes, they are systematically smaller (in magnitude) than the canon value of –3, and exhibit slight height, seasonal and latitudinal variability. In addition to these universal characteristics, the spectral structures also exhibit departures and variations, and most of the departures and variations are related to the strong tropospheric jets. Generally, in the case of strong shear due to the tropospheric jet, there usually occur larger characteristic wave numbers and smaller spectral slopes. These departures seem to be persistent and climatological rather than transitory, indicating the significant impacts of the sheared background winds on the spectral structures of gravity waves.

Barotropic Beta-Plane Turbulence in a Regime with Strong Zonal Jets Revisited

The problem of quantification of barotropic beta-plane turbulence driven by small-scale stochastic forcing into regimes dominated by quasi-periodic zonal jets is revisited. It is shown that the large-scale relative vorticity in such regimes is organized into a sequence of zonal bands. Its zonal mean profile varies approximately linearly within the bands. Its mean negative slope β∗ is less than the meridional gradient of the Coriolis parameter β, and depends on the external parameters (friction, forcing, and β). The neighboring bands are connected through the vorticity fronts where the zonal mean meridional gradient is large and positive. The frontal-band vorticity structure defines piecewise parabolic profiles of asymmetric eastward and westward jets, and strong peaks in the low-k interval of turbulent zonal energy spectra, which store most of the zonal energy. The slope of their envelope depends on the structure of the frontal zones and is always steeper than −4. The presence of peaks invalidates the recent hypothesis on the universal power-law scaling Ez(k) = Czβ2k−5, Cz = O(1), for the zonal energy spectra of beta-plane turbulence in strongly anisotropic regimes. The power-law intervals could appear at large k and are linked to uncorrelated fluctuations of band profiles. It is shown that they could contain a part that slopes close to −5. However, its Cz is not universal and depends on the external parameters. A simple kinematic model of multijet beta-plane flows is proposed that explains the shape of the coherent part of zonal energy spectra and asymmetry between westward and eastward jets generated by vorticity bands, and quantifies the zonal wavenumber of jets kj in terms of the ratio of zonal enstrophy to zonal energy.

Scaling, spectra and zonal jets in beta-plane turbulence

A beta-plane approximation of the two-dimensional quasigeostrophic model describes a single layer (barotropic) fluid subjected to a latitudinally varying Coriolis parameter or topography. Rhines (1975) initiated the study of beta-plane turbulence. He predicted the inverse energy cascade into predominantly zonal modes, hence an array of eastward–westward jets, and estimated the jet number (celebrated Rhines scale). He also proposed a k−5 scaling law of zonal energy spectra. Our paper re-examines scaling, spectra, and zonal structure of beta-plane turbulence, based on theoretical predictions and numeric experiments. We show that the inverse cascade gives rise to strong organized zonal jets that evolve a peculiar frontal-band (“saw-tooth”) vorticity profile. Such structure affects all spectral properties of the system, by creating organized sequences of spectral peaks, and thus confounds any putative “scaling behavior.” The frontal-band structure appears consistently in all stochastically forced beta-plane flows, independent of dissipation and/or other details. But the resulting turbulent quasiequilibrium is not unique, its gross parameters (jets number, mean vorticity gradient) retain memory of the initial state and/or history.

Holocene annual mean temperature changes in Estonia and their relationship to solar insolation and atmospheric circulation patterns

We reconstructed annual mean temperature ( T ann) trends from three radiocarbon-dated Holocene pollen stratigraphies from lake sediments in Estonia, northern Europe. The reconstructions were carried out using a North-European pollen-climate calibration model based on weighted averaging partial least-squares regression. The cross-validated prediction error of the model is 0.89°C and the coefficient of determination between observed modern T ann values and those predicted by the model is 0.88. In the reconstruction, the Holocene thermal maximum (HTM) is distinguishable at 8000–4500 cal yr B.P., with the expansion of thermophilous tree species and T ann on average 2.5°C higher than at present. The pollen-stratigraphical data reflect progressively warmer and drier summers during the HTM. Analogously with the modern decadal-scale climatic variability in North Europe, we interpret this as an indication of increasing climatic continentality due to the intensification of anticyclonic circulation and meridional air flow. Post-HTM cooling started abruptly at around 4500 cal yr B.P. All three reconstructions show a transient (ca. 300 years) cooling of 1.5–2.0°C at 8600–8000 cal yr B.P. We tentatively correlate this cold event with the North-Atlantic “8.2 ka event” at 8400–8000 cal yr B.P. Provided that the 8.2 ka event was caused by freshening of the North-Atlantic surface water, our data provide evidence of the climatic and vegetational responsiveness of the boundary of the temperate and boreal zones to the weakening of the North-Atlantic thermohaline circulation and the zonal energy transport over Europe. No other cold events of comparable magnitude are indicated during the last 8000 years.

The geodesic transfer effect on zonal flows in tokamak edge turbulence

Detailed computations of tokamak edge turbulence in three-dimensional, globally consistent flux tube geometry show an inhibition of the standard scenario in which zonal E × B flows generated by the turbulence should lead to transport barrier formation. It is found by comparison to slab geometry and by analysis of the energetics that the zonal flow energy is depleted by toroidal coupling to the pressure through the geodesic curvature. Edge transport barriers would then depend on the physics of a self-consistent equilibrium including neoclassical forcing effects as well as the turbulence.

Extent of partial ice cover due to carbon cycle feedback in a zonal energy balance model

Abstract. A global carbon cycle is introduced into a zonally averaged energy balance climate model. The physical model components are similar to those of Budyko (1969) and Sellers (1969). The new carbon components account for atmospheric carbon dioxide concentrations and the terrestrial and oceanic storage of carbon. Prescribing values for the sum of these carbon components, it is found that inclusion of a closed carbon cycle reduces the range of insolation over which stable partial ice cover solutions may occur. This highly simplified climate model also predicts that the estimated release of carbon from fossil fuel burning over the next hundred years could result in the eventual melting of the ice sheets. Keywords: climate, carbon cycle,zonal model, earth system modelling

The 41 kyr world: Milankovitch's other unsolved mystery

For most of the Northern Hemisphere Ice Ages, from ∼3.0 to 0.8 m.y., global ice volume varied predominantly at the 41,000 year period of Earth's orbital obliquity. However, summer (or summer caloric half year) insolation at high latitudes, which is widely believed to be the major influence on high‐latitude climate and ice volume, is dominated by the 23,000 year precessional period. Thus the geologic record poses a challenge to our understanding of climate dynamics. Here we propose that variations in the insolation gradient between high and low latitudes control high‐latitude climate and ice volume during the late Pliocene and early Pleistocene. The differential heating between high and low latitudes, driven by obliquity, controls the atmospheric meridional flux of heat, moisture, and latent energy, which may exert the dominant control on high‐latitude climate on Milankovitch timescales. In the two‐dimensional zonal energy balance models typically used to study the long‐term evolution of climate, the meridional atmospheric moisture flux is usually kept fixed. The hypothesis that insolation gradients control the poleward energy fluxes, precipitation, and ice volume at high latitudes has never been directly examined within the context of an ice sheet model. In light of what we know about modern energy fluxes and their relative influence on high‐latitude climate, this possibility should be examined.

Arctic Oscillation response to the 1991 Mount Pinatubo eruption: Effects of volcanic aerosols and ozone depletion

Observations show that strong equatorial volcanic eruptions have been followed by a pronounced positive phase of the Arctic Oscillation (AO) for one or two Northern Hemisphere winters. It has been previously assumed that this effect is forced by strengthening of the equator‐to‐pole temperature gradient in the lower stratosphere, caused by aerosol radiative heating in the tropics. To understand atmospheric processes that cause the AO response, we studied the impact of the 1991 Mount Pinatubo eruption, which produced the largest global volcanic aerosol cloud in the twentieth century. A series of control and perturbation experiments were conducted with the GFDL SKYHI general circulation model to examine the evolution of the circulation in the 2 years following the Pinatubo eruption. In one set of perturbation experiments, the full radiative effects of the observed Pinatubo aerosol cloud were included, while in another only the effects of the aerosols in reducing the solar flux in the troposphere were included, and the aerosol heating effects in the stratosphere were suppressed. A third set of perturbation experiments imposed the stratospheric ozone losses observed in the post‐Pinatubo period. We conducted ensembles of four to eight realizations for each case. Forced by aerosols, SKYHI produces a statistically significant positive phase of the AO in winter, as observed. Ozone depletion causes a positive phase of the AO in late winter and early spring by cooling the lower stratosphere in high latitudes, strengthening the polar night jet, and delaying the final warming. A positive phase of the AO was also produced in the experiment with only the tropospheric effect of aerosols, showing that aerosol heating in the lower tropical stratosphere is not necessary to force positive AO response, as was previously assumed. Aerosol‐induced tropospheric cooling in the subtropics decreases the meridional temperature gradient in the winter troposphere between 30°N and 60°N. The corresponding reduction of mean zonal energy and amplitudes of planetary waves in the troposphere decreases wave activity flux into the lower stratosphere. The resulting strengthening of the polar vortex forces a positive phase of the AO. We suggest that this mechanism can also contribute to the observed long‐term AO trend being caused by greenhouse gas increases because they also weaken the tropospheric meridional temperature gradient due to polar amplification of warming.

Breaking Rossby waves in the barotropic atmosphere with parameterized baroclinic instability

In this study, we conducted a series of numerical experiments of breaking Rossby waves in thebarotropic atmosphere using a simple barotropic model which implements parametrization ofbaroclinic instability. Exponential growth of unstable modes must terminate eventually whenthe waves become finite amplitude. The non-linear evolution of amplified Rossby waves isexamined by analyzing the potential vorticity (PV) field in order to assess the criterion of theRossby wave breaking in a barotropic model atmosphere. For a control run of the wave-6experiment, growing unstable wavenumber n=6 is saturated when the wave energy attainsapproximately 20% of zonal energy of the basic flow. The energy supply at n=6 is balancedwith energy transfer to zonal flow and to its harmonics of n=12 and 18 by weak non-linearinteractions, maintaining a steady configuration of a surf zone structure. The existence of thenegative meridional gradient of PV is the necessary condition for the wave saturation. We thenattempted to break the waves intentionally by increasing the growth rate of the unstable mode.It is found that the regularity of Rossby wave progression is lost and the overturning of highand low PV centers occurs when the growth rate is increased by 30%. Associated with theRossby wave breaking, not only the harmonic waves but all zonal waves are amplified by thefully non-linear interactions among all waves. It is demonstrated that the transition from theweakly non-linear regime to fully non-linear regime in the energy transfer is the key factor forthe Rossby wave breaking so that the supplied energy is effectively dissipated by all waves.

A life-cycle of nonlinear baroclinic waves represented by a simple 3-D spectral model

In this study, a life-cycle experiment for baroclinic disturbances is carried out for Simmons and Hoskins' 45° jet by integrating a three-dimensional spectral primitive equation model. The utility of the spectral representation in the vertical direction is examined for a fully nonlinear well-established phenomenon. The energy evolution and corresponding energy transformation are analyzed in the framework of the baroclinic-barotropic decomposition of atmospheric energy. According to the result, the initial perturbations of n= 6 grow exponentially drawing zonal baroclinic energy. This early evolution is reasonably described by linear baroclinic instability of the 45° jet. Both of baroclinic energy and barotropic energy of n= 6 increase simultaneously since the unstable mode maintains its consistent structure to grow. The energy flow is characterized as from zonal baroclinic energy via eddy baroclinic energy to eddy barotropic energy. These energy transformations are also synchronized since they are proportional to the eddy energy levels in the linear framework. When the waves reach the finite amplitude, the barotropic conversion increases, tranferring eddy barotropic energy toward zonal barotropic energy. It is shown by the result that the zonal barotropic energy increases when the waves decay, and the zonal jet is accelerated so that the structure becomes more barotropic. It is found by this study that the important baroclinic–barotropic interactions are coupled with baroclinic instability rather than the barotropic conversion. The results are consistent with previous studies. Therefore, we confirm also that the vertical spectral representation is applicable to simulate the nonlinear phenomenon. DOI: 10.1034/j.1600-0870.1995.00113.x