Upscale Energy Research Articles

Quantifying the linear damping in two-dimensional turbulence

Linear damping is widely applied in experiments and fluid models to describe the large-scale dissipation that absorbs upscale energy transfers in two-dimensional turbulence. However, in many systems, it is not justified that linear damping is a good model and it is hard to obtain the damping coefficient from directly measurable quantities. A method based on the measurable third-order structure function is proposed to justify the form of linear damping and determine the damping coefficient.

Deep model simulation of polar vortices in gas giant atmospheres

ABSTRACTThe Cassini and Juno probes have revealed large coherent cyclonic vortices in the polar regions of Saturn and Jupiter, a dramatic contrast from the east–west banded jet structure seen at lower latitudes. Debate has centred on whether the jets are shallow, or extend to greater depths in the planetary envelope. Recent experiments and observations have demonstrated the relevance of deep convection models to a successful explanation of jet structure, and cyclonic coherent vortices away from the polar regions have been simulated recently including an additional stratified shallow layer. Here we present new convective models able to produce long-lived polar vortices. Using simulation parameters relevant for giant planet atmospheres we find flow regimes of geostrophic turbulence (GT) in agreement with rotating convection theory. The formation of large-scale coherent structures occurs via 3D upscale energy transfers. Our simulations generate polar characteristics qualitatively similar to those seen by Juno and Cassini: They match the structure of cyclonic vortices seen on Jupiter; or can account for the existence of a strong polar vortex extending downwards to lower latitudes with a marked spiral morphology, and the hexagonal pattern seen on Saturn. Our findings indicate that these vortices can be generated deep in the planetary interior. A transition differentiating these two polar flows regimes is described, interpreted in terms of force balances and compared with shallow atmospheric models characterizing polar vortex dynamics in giant planets. In addition, heat transport properties are investigated, confirming recent scaling laws obtained with reduced models of GT.

The Interaction Between the Turbulence and Gravity Wave Observed in the Middle Stratosphere Based on the Round‐Trip Intelligent Sounding System

AbstractBased on the round‐trip intelligent sounding system, the structure function and spectrum analysis method were carried out to analyze the scale interactions between the small‐scale gravity wave and turbulence in the middle stratosphere. The result showed that the generation of turbulence was closely related to the Kelvin‐Helmholtz (KH) billows. An upscale energy cascade occurred on the spatial scale of KH billows, while a downscale energy cascade occurred on a larger spatial scale (gravity wave scale), which resulted in the breaking of the gravity wave and generation of turbulence. From the multilevel signal measurement, the obvious interactions between turbulence and gravity can be found. The two‐dimensional turbulence that the inverse energy cascade in 2‐D exists simultaneously with a direct enstrophy cascade to the small scales was found, which is considered to be the first‐hand observation result of relevant height.

Shape and size of large-scale vortices: A generic fluid pattern in geophysical fluid dynamics

Planetary rotation organizes fluid motions into coherent, long-lived swirls, known as large-scale vortices (LSVs), which play an important role in the dynamics and long-term evolution of geophysical and astrophysical fluids. Here, using direct numerical simulations, we show that LSVs in rapidly rotating mixed convective and stably stratified fluids, which approximates the two-layer, turbulent-stratified dynamics of many geophysical and astrophysical fluids, have a generic shape and that their size can be predicted. We show that LSVs emerge in the convection zone from upscale energy transfers and can penetrate into the stratified layer. At the convective-stratified interface, the LSV cores have a positive buoyancy anomaly. Due to the thermal wind constraint, this buoyancy anomaly leads to winds in the stratified layer that decay over a characteristic vertical length scale. Thus LSVs take the shape of a depth-invariant cylinder with a finite-size radius in the turbulent layer and of a penetrating half dome in the stratified layer. Importantly, we demonstrate that when LSVs penetrate all the way through the stratified layer and reach a boundary that is no-slip, they saturate by boundary friction. We provide a prediction for the penetration depth and maximum radius of LSVs as a function of the LSV vorticity, the stratified layer depth, and the stratification. Our results, which apply for cyclonic LSVs, suggest that LSVs in slowly rotating stars and Earth's liquid core are confined to the convective layer, while in Earth's atmosphere and oceans they can penetrate far into the stratified layer.

Internal Subseasonal Variability in the South China Sea Revealed by Eddy‐Resolving Numerical Simulations

AbstractOceanic subseasonal variabilities in the South China Sea (SCS) derive from both external forcing and internal variability. There have been extensive studies on a range of external forcings, which are composed of local and remote components. In this study, the internal subseasonal variabilities in SCS are examined using an eddy‐resolving model. It is found that the internal subseasonal variabilities are pronounced in the northern SCS, which account for about half of total observed subseasonal variabilities. Particularly to the west of Luzon Strait, the internal subseasonal variabilities are enhanced on the periphery of a ring region. On the contrary, internal subseasonal variabilities are minimal in the center, which is mainly attributable to an upscale energy transfer. As a result, a mean jet is generated which transports heat and eddy kinetic energy along the edge of the ring region. We posit that the impact of internal subseasonal variabilities is significant for the background state in the region where the intense tropical cyclones occur over the northern SCS every year.

Tilted drifting jets over a zonally sloped topography: effects of vanishing eddy viscosity

Oceanic multiple jets are seen to possess spatio-temporal variability imposed by varying bottom topography resulting in jets that can drift and merge. The dynamics of multiple jets over a topographic zonal slope is studied in a two-layer quasi-geostrophic model. The jets tilt from the zonal direction and drift meridionally. In addition to the tilted jets, other large-scale spatial patterns are observed, which are extracted using the principal component analysis. The variances of these patterns are strongly influenced by the values of eddy viscosity and bottom friction parameters. The contribution of the tilted jets to the full flow field decreases with decreasing friction and viscosity parameters, and purely zonal large-scale modes, propagating in the meridional direction, populate the flow field. Linear stability analysis and two-dimensional kinetic-energy spectrum analysis suggest that the zonal modes gain energy from ambient eddies as well as from the tilted jets through nonlinear interactions. However, viscous dissipation and bottom friction tend to suppress the nonlinear interactions, which results in the inhibition of the upscale energy transfer from eddies to the zonal modes. These simulations suggest that, in the presence of topography, alternating jet patterns may be sustained through interactions among various large-scale modes. This is different from the classical zonal jet formation arguments, in which direct eddy forcing maintains the jets.

The intrinsic nonlinear multiscale interactions among the mean flow, low frequency variability and mesoscale eddies in the Kuroshio region

Using a new functional analysis tool, multiscale window transform (MWT), and the MWT-based localized multiscale energetics analysis and canonical transfer theory, this study reconstructs the Kuroshio system on three scale windows, namely, the mean flow window, the interannual-scale (low-frequency) window, and the transient eddy window, and investigates the climatological characteristics of the intricate nonlinear interactions among these windows. Significant upscale energy transfer is observed east of Taiwan, where the mean Kuroshio current extracts kinetic energy from both the interannual and eddy windows. It is found that the canonical transfer from the interannual variability is an intrinsic source that drives the eddy activities in this region. The multiscale variabilities of the Kuroshio in the East China Sea (ECS) are mainly controlled by the interaction between the mean flow and the eddies.The mean flow undergoes mixed instabilities (i.e., both barotropic and baroclinic instabilities) in the southern ECS, while it is barotropically stable but baroclinically unstable to the north. The multiscale interactions are found to be most intense south of Japan, where strong mixed instabilities occur; both the canonical transfers from the mean flow and the interannual scale are important mechanisms to fuel the eddies. It is also found that the interannual-scale energy mainly comes from the barotropically unstable jet, rather than the upscale energy transfer from the high frequency eddies.

The asymmetric eddy–background flow interaction in the North Pacific storm track

Using a recently developed methodology, namely the multiscale window transform (MWT) and the MWT‐based theory of canonical transfer and localized multiscale energetics analysis, we investigate in an eddy‐following way the nonlinear eddy–background flow interaction in the North Pacific storm track, based on the ERA‐40 reanalysis data from the European Centre for Medium‐Range Weather Forecasts. It is found that more than 50% of the storms occur on the northern flank of the jet stream, about 40% are around the jet centre, and very few (less than 5%) happen on the southern flank. For storms near or to the north of the jet centre, their interaction with the background flow is asymmetric in latitude. In higher latitudes, strong downscale canonical available potential energy transfer happens, especially in the mid‐troposphere, which reduces the background baroclinicity and decelerates the jet; in lower latitudes, upscale canonical kinetic energy transfer intensifies at the jet centre, accelerating the jet and enhancing the middle‐level baroclinicity. The resultant effect is that the jet strengthens but narrows, leading to an anomalous dipolar pattern in the fields of background wind and baroclinicity. For the storms on the southern side of the jet, the baroclinic canonical transfer is rather weak. On average, the local interaction begins about 3 days before a storm arrives at the site of observation, achieves its maximum as the storm arrives, and then weakens.

Numerical Investigation of Turbulent Kinetic Energy Dynamics in Chemically-Reacting Homogeneous Turbulence

In this work, we investigate numerically the temporal evolution of Turbulent Kinetic Energy (TKE) of a chemically-reacting n-heptane and air mixture in statistically Homogeneous Isotropic Turbulence (HIT). Our specific focus is on the concurrent view of TKE evolution in both physical and scale (Fourier) spaces to identify the impact of reaction-induced heat release on turbulence. The simulation parameters are selected to represent the combustion characteristics of heavy hydrocarbon fuels under engine conditions. Results indicate that pressure dilatation work dominates the TKE evolution during the period of strong heat release and its dominance is attributed to the strong volumetric dilatation associated with the presence of reaction fronts in physical space. Viscous dissipation and viscous dilatation terms become much stronger with increasing heat release, primarily due to the increase in strain-rate and dilatation at the vicinity of the reaction fronts, but their magnitudes are still small compared to that of pressure dilatation work. In addition, the analysis in Fourier space shows that pressure dilatation work dominates the evolution of TKE not only in the mean, but also over a wide range of scales. The spectrum of pressure dilatation shows a power-law behavior, which is a direct consequence of the localized sheet-like reaction fronts in physical space. It is also shown that viscous dissipation spectrum initially removes kinetic energy at small scales when heat release is weak, but starts to remove kinetic energy at intermediate and later at large scales due to the presence of localized reaction fronts during the strong heat release period. More interestingly, it is observed that the inter-scale kinetic energy transfer spectrum moves energy from less dissipative scales (small scales) to scales where kinetic energy is more effectively removed by viscous dissipation work (large scales) during the period of strong heat release, which indicates possible up-scale kinetic energy transfer in Fourier space.

Energy transfer in turbulence under rotation

It is known that rapidly rotating turbulent flows are characterized by the emergence of simultaneous upscale and downscale energy transfer. Indeed, both numerics and experiments show the formation of large-scale anisotropic vortices together with the development of small-scale dissipative structures. However the organization of interactions leading to this complex dynamics remains unclear. Two different mechanisms are known to be able to transfer energy upscale in a turbulent flow. The first is characterized by two-dimensional interactions among triads lying on the two-dimensional, three-component (2D3C) manifold, namely on the Fourier plane perpendicular to the rotation axis. The second mechanism is three-dimensional and consists of interactions between triads with the same sign of helicity (homochiral). Here, we present a detailed numerical study of rotating flows using a suite of high Reynolds number direct numerical simulations within different parameter regimes to analyze both upscale and downscale cascade ranges. We find that the upscale cascade at wave numbers close to the forcing scale is generated by increasingly dominant homochiral interactions which couple the three-dimensional bulk and the 2D3C plane. This coupling produces an accumulation of energy in the 2D3C plane, which then transfers energy to smaller wave numbers thanks to the two-dimensional mechanism. In the forward cascade range, we find that the energy transfer is dominated by heterochiral triads and is dominated primarily by interaction within the fast manifold where $k_z\ne0$. We further analyze the energy transfer in different regions in the real-space domain. In particular, we distinguish high-strain from high-vorticity regions and we uncover that while the mean transfer is produced inside regions of strain, the rare but extreme events of energy transfer occur primarily inside the large-scale column vortices.

Jets and large-scale vortices in rotating Rayleigh-Bénard convection

One of the most prominent dynamical features of turbulent, rapidly-rotating convection is the formation of large-scale coherent structures, driven by Reynolds stresses resulting from the small-scale convective flows. In spherical geometry, such structures consist of intense zonal flows that are invariant along the rotation axis. In planar geometry, long-lived, depth-invariant structures also form at large scales, but, in the absence of horizontal anisotropy, they consist of vortices that grow to the domain size. In this work, through the introduction of horizontal anisotropy into a numerical model of planar rotating convection by the adoption of unequal horizontal box sizes (i.e. $L_x \le L_y$, where the $xy$-plane is horizontal), we investigate whether unidirectional flows and large-scale vortices can coexist. We find that only a small degree of anisotropy is required to bring about a transition from dynamics dominated by persistent large-scale vortices to dynamics dominated by persistent unidirectional flows parallel to the shortest horizontal direction. When the anisotropy is sufficiently large, the unidirectional flow consists of multiple jets, generated on a timescale smaller than a global viscous timescale, thus signifying that the upscale energy transfer does not spontaneously feed the largest available mode in the system. That said, the multiple jets merge on much longer timescales. Large-scale vortices of size comparable with $L_x$ systematically form in the flanks of the jets and can be persistent or intermittent. This indicates that large-scale vortices, either coexisting with jets or not, are a robust dynamical feature of planar rotating convection.

Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-Graining Approach

AbstractA coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates, and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer, rely on the assumption of statistical homogeneity or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space and is not restricted by those assumptions. This paper describes how the framework can be applied to ocean flows. Energy transfer between scales is not unique because of a gauge freedom. Here, it is argued that a Galilean-invariant subfilter-scale (SFS) flux is a suitable quantity to properly measure energy scale transfer in the ocean. It is shown that the SFS definition can yield answers that are qualitatively different from traditional measures that conflate spatial transport with the scale transfer of energy. The paper presents geographic maps of the energy scale transfer that are both local in space and allow quasi-spectral, or scale-by-scale, dynamics to be diagnosed. Utilizing a strongly eddying simulation of flow in the North Atlantic Ocean, it is found that an upscale energy transfer does not hold everywhere. Indeed certain regions near the Gulf Stream and in the Equatorial Countercurrent have a marked downscale transfer. Nevertheless, on average an upscale transfer is a reasonable mean description of the extratropical energy scale transfer over regions of O(103) km in size.

Dynamics of a hybrid morphing wing with active open loop vibrating trailing edge by time-resolved PIV and force measures

A quantitative characterization of the effects obtained by high frequency–low amplitude trailing edge actuation is presented. Particle image velocimetry, pressure and aerodynamic forces measurements are carried out on a wing prototype equipped with shape memory alloys and trailing edge piezoelectric-actuators, allowing simultaneously high deformations (bending) in low frequency and higher-frequency vibrations. The effects of this hybrid morphing on the forces have been quantified and an optimal actuation range has been identified, able to increase lift and decrease drag. The present study focuses more specifically on the effects of the higher-frequency vibrations of the trailing edge region. This actuation allows manipulation of the wake turbulent structures. It has been shown that specific frequency and amplitude ranges achieved by the piezoelectric actuators are able to produce a breakdown of larger coherent eddies by means of upscale energy transfer from smaller-scale eddies in the near wake. It results a thinning of the shear layers and the wake’s width, associated to reduction of the form drag, as well as a reduction of predominant frequency peaks of the shear-layer instability. These effects have been shown by means of frequency domain analysis and Proper Orthogonal Decomposition.

Dynamics of Urbanization and Temperature Increase in Middle East-An Empirical Investigation

Growth patterns are the important channels, through which the society and economy interact. Climate change could lead to such disruption, if unsystematic growth has not been controlled to a limit. Recent scientific evidences have shown that Middle East region is in the midst of climate change vulnerability by endangering its oil cashed growth strategy. But economic research has given very scant attention towards such incident by correlating with urbanization. In this context, we argue that the upscale energy demand, industrialization and unbalanced urbanization strategies could potentially impact the region in long run in forms of climate change. We further argue that the behavioral changes in terms of percapita urbanization growth and increasing import have impacted the region unlike never before. Even our cross-sectional dependency test has shown that the region?s heat wave problem is worth of deep concerns. From a policy perspective, we suggest that the region as whole should be proactive in terms of starting effective implementation of green energy plan, clean energy investment and production of bio-fuel. In order to counter the negative cost of heat wave as predicted, the region must combinedly put forward and ratify a climate change strategy to monitor the development on an annual basis.

Spectral structure of 5 year time series of horizontal wind speed at the Boulder Atmospheric Observatory

AbstractWe investigate the spectral structures of 5 year, 1 min time series of horizontal wind speeds at 100 and 10 m heights at the Boulder Atmospheric Observatory tower located in the eastern slope of the Rocky Mountains, USA. In the full‐scale spectra, the diurnal spectral peak, which is usually insignificant at a coastal or offshore site, is the most significant at both heights. The spectrum is enhanced on the low‐frequency side of the diurnal peak during winter, but on the high‐frequency side during summer, which indicates frequent synoptic weather events during winter supplanted by mesoscale events during summer. In terms of the spectral density in the spectral gap of Van der Hoven (1957), separating boundary layer turbulence from the synoptic‐scale fluctuations, at a frequency between 10−4 and 10−3 Hz, we rank the daily time series at 100 m height and sample the summer top and winter bottom 10 percentile cases. The winter cases of the reduced spectral density in the gap region present the f−3 spectrum (f is frequency) and negatively skewed velocity increment distributions, which are the signatures of enstrophy (the integral of squared vorticity) cascade of turbulent two‐dimensional (2‐D) flows. In contrast, the summer cases of the enhanced spectral density present the f−5/3 spectrum and positively skewed velocity increment distributions, which are the signatures of upscale energy cascade of 2‐D flows. In these mesoscale events that fill up the gap, the turbulence intensity‐wind speed relationship is very sensitive to the choice of the averaging period.

The effects of Ekman pumping on quasi-geostrophic Rayleigh–Bénard convection

Numerical simulations of three-dimensional rapidly rotating Rayleigh–Bénard convection are performed by employing an asymptotic quasi-geostrophic model that incorporates the effects of no-slip boundaries through (i) parametrized Ekman pumping boundary conditions and (ii) a thermal wind boundary layer that regularizes the enhanced thermal fluctuations induced by pumping. The fidelity of the model, obtained by an asymptotic reduction of the Navier–Stokes equations that implicitly enforces a pointwise geostrophic balance, is explored for the first time by comparisons of simulations against the findings of direct numerical simulations (DNS) and laboratory experiments. Results from these methods have established Ekman pumping as the mechanism responsible for significantly enhancing the vertical heat transport. This asymptotic model demonstrates excellent agreement over a range of thermal forcing for Prandtl number $Pr\approx 1$ when compared with results from experiments and DNS at maximal values of their attainable rotation rates, as measured by the Ekman number ($E\approx 10^{-7}$); good qualitative agreement is achieved for $Pr>1$. Similar to studies with stress-free boundaries, four spatially distinct flow morphologies exists. Despite the presence of frictional drag at the upper and/or lower boundaries, a strong non-local inverse cascade of barotropic (i.e. depth-independent) kinetic energy persists in the final regime of geostrophic turbulence and is dominant at large scales. For mixed no-slip/stress-free and no-slip/no-slip boundaries, Ekman friction is found to attenuate the efficiency of the upscale energy transport and, unlike the case of stress-free boundaries, rapidly saturates the barotropic kinetic energy. For no-slip/no-slip boundaries, Ekman friction is strong enough to prevent the development of a coherent dipole vortex condensate. Instead, vortex pairs are found to be intermittent, varying in both time and strength. For all combinations of boundary conditions, a Nastrom–Gage type of spectrum of kinetic energy is found, where the power-law exponent changes from ${\approx}-3$ to ${\approx}-5/3$, i.e. from steep to shallow, as the spectral wavenumber increases.

The Instabilities and Multiscale Energetics Underlying the Mean–Interannual–Eddy Interactions in the Kuroshio Extension Region

AbstractUsing a recently developed energetics diagnostic methodology, namely, the localized multiscale energy and vorticity analysis (MS-EVA), this study investigates the intricate nonlinear mutual interactions among the decadally modulating mean flow, the interannual fluctuations, and the transient eddies in the Kuroshio Extension region. It is found that the mean kinetic energy maximizes immediately east of the Izu–Ogasawara Ridge, while the transient eddy kinetic energy does not peak until 400 km away downstream. The interannual variabilities, which are dominated by a jet-trapped Rossby wave mode, provide an energy reservoir comparable to the other counterparts. In the upstream, strong localized barotropic and baroclinic transfers from the mean flow to the eddies are observed, whereas those from the interannual variabilities are not significant. Besides fueling the eddies, the unstable mean jet also releases energy to the interannual-scale processes. Between 144° and 154°E, both transfers from the mean flow and the interannual variabilities are important for the eddy development. Farther downstream, eddies are found to drive the mean flow on both the kinetic energy (KE) and available potential energy (APE) maps. They also provide KE to the interannual variabilities but obtain APE from the latter. The gained eddy APE is then converted to eddy KE through buoyancy conversion. Upscale energy transfers are observed in the northern and southern recirculation gyre (RG) regions. In these regions, the interannual–eddy interaction exhibits different scenarios: the eddies lose KE to the interannual processes in the northern RG region, while gaining KE in the southern RG region.

An experimental study of multiple zonal jet formation in rotating, thermally driven convective flows on a topographic beta-plane

A series of rotating, thermal convection experiments were carried out on the Coriolis platform in Grenoble, France, to investigate the formation and energetics of systems of zonal jets through nonlinear eddy/wave-zonal flow interactions on a topographic β-plane. The latter was produced by a combination of a rigid, conically sloping bottom and the rotational deformation of the free upper surface. Convection was driven by a system of electrical heaters laid under the (thermally conducting) sloping bottom and led to the production of intense, convective vortices. These were observed to grow in size as each experiment proceeded and led to the development of weak but clear azimuthal jet-like flows, with a radial scale that varied according to the rotation speed of the platform. Detailed analyses reveal that the kinetic energy-weighted radial wavenumber of the zonal jets, kJy, scales quite closely either with the Rhines wavenumber as kJy ≃ 2(βT/2urms)1/2, where urms is the rms total or eddy velocity and βT is the vorticity gradient produced by the sloping topography, or the anisotropy wavenumber as kJy≃1.25(βT3/ϵ)1/5, where ϵ is the upscale turbulent energy transfer rate. Jets are primarily produced by the direct quasi-linear action of horizontal Reynolds stresses produced by trains of topographic Rossby waves. The nonlinear production rate of zonal kinetic energy is found to be strongly unsteady, however, with fluctuations of order 10-100 times the amplitude of the mean production rate for all cases considered. The time scale of such fluctuations is found to scale consistently with either an inertial time scale, τp∼1./urmsβT, or the Ekman spin-down time scale. Kinetic energy spectra show some evidence for a k−5/3 inertial subrange in the isotropic component, suggestive of a classical Kolmogorov-Batchelor-Kraichnan upscale energy cascade and a steeper spectrum in the zonal mean flow, though not as steep as k−5, as anticipated for fully zonostrophic flow. This is consistent with a classification of all of these flows as marginally zonostrophic, as expected for values of the zonostrophy parameter Rβ ≃ 1.6–1.7, though a number of properties related to flow anisotropy were found to vary significantly and systematically within this range.

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.

Upscale energy transfer and flow topology in free-surface turbulence.

Free-surface turbulence, albeit constrained onto a two-dimensional space, exhibits features that barely resemble predictions of simplified two-dimensional modeling. We demonstrate that, in a three-dimensional open channel flow, surface turbulence is characterized by upscale energy transfer, which controls the long-term evolution of the larger scales. We are able to associate downscale and upscale energy transfer at the surface with the two-dimensional divergence of velocity. We finally demonstrate that surface compressibility confirms the strongly three-dimensional nature of surface turbulence.