Energy Cascades and Loss of Balance in a Reentrant Channel Forced by Wind Stress and Buoyancy Fluxes

2015 ◽  
Vol 45 (1) ◽  
pp. 272-293 ◽  
Author(s):  
Roy Barkan ◽  
Kraig B. Winters ◽  
Stefan G. Llewellyn Smith
Keyword(s):  
Kinetic Energy ◽  
Wind Stress ◽  
General Circulation ◽  
Large Fraction ◽  
Energy Cascade ◽  
Turbulence Theory ◽  
Inverse Energy Cascade ◽  
Loss Of Balance ◽  
Small Scales ◽  
Eddy Field

AbstractA large fraction of the kinetic energy in the ocean is stored in the “quasigeostrophic” eddy field. This “balanced” eddy field is expected, according to geostrophic turbulence theory, to transfer energy to larger scales. In order for the general circulation to remain approximately steady, instability mechanisms leading to loss of balance (LOB) have been hypothesized to take place so that the eddy kinetic energy (EKE) may be transferred to small scales where it can be dissipated. This study examines the kinetic energy pathways in fully resolved direct numerical simulations of flow in a flat-bottomed reentrant channel, externally forced by surface buoyancy fluxes and wind stress in a configuration that resembles the Antarctic Circumpolar Current. The flow is allowed to reach a statistical steady state at which point it exhibits both a forward and an inverse energy cascade. Flow interactions with irregular bathymetry are excluded so that bottom drag is the sole mechanism available to dissipate the upscale EKE transfer. The authors show that EKE is dissipated preferentially at small scales near the surface via frontal instabilities associated with LOB and a forward energy cascade rather than by bottom drag after an inverse energy cascade. This is true both with and without forcing by the wind. These results suggest that LOB caused by frontal instabilities near the ocean surface could provide an efficient mechanism, independent of boundary effects, by which EKE is dissipated. Ageostrophic anticyclonic instability is the dominant frontal instability mechanism in these simulations. Symmetric instability is also important in a “deep convection” region, where it can be sustained by buoyancy loss.

Barotropic and baroclinic inverse kinetic energy cascade in the Antarctic Circumpolar Current

2021 ◽  
Author(s):  
Hongjie Li ◽  
Yongsheng Xu
Keyword(s):  
Kinetic Energy ◽  
General Circulation ◽  
Antarctic Circumpolar Current ◽  
General Circulation Models ◽  
Energy Cascade ◽  
Turbulence Theory ◽  
Inverse Cascade ◽  
Spectral Flux ◽  
Circumpolar Current ◽  
The Antarctic

AbstractStratified geostrophic turbulence theory predicts an inverse energy cascade for the barotropic (BT) mode. Satellite altimetry has revealed a net inverse cascade in the baroclinic (BC) mode. Here the spatial variabilities of BT and BC kinetic energy fluxes in the Antarctic Circumpolar Current (ACC) were investigated using ECCO2 data, which synthesizes satellite data and in situ measurements with an eddy-permitting general circulation models containing realistic bathymetry and wind forcing. The BT and BC inverse kinetic energy cascades both reveal complex spatial variations that could not be explained fully by classical arguments. For example, the BC injection scales match better with most unstable scales than with the first-mode deformation scales, but the opposite is true for the BT mode. In addition, the BT and BC arrest scales do not follow the Rhines scale well in term of spatial variation, but show better consistency with their own energy-containing scales. The reverse cascade of the BT and BC modes was found related to their EKE, and better correlation was found between the BT inverse cascade and barotropization. Speculations of the findings were proposed. however, further observations and modeling experiments are needed to test these interpretations. Spectral flux anisotropy exhibits a feature associated with oceanic jets that is consistent with classical expectations. Specifically, the spectral flux along the along-stream direction remains negative at scales up to that of the studied domain (~2000km), while that in the perpendicular direction becomes positive close to the scale of the width of a typical jet.

scholarly journals Energy cascade for highly anisotropic turbulence in the Stable Boundary Layer

2021 ◽  
Author(s):  
Federica Gucci ◽  
Lorenzo Giovannini ◽  
Dino Zardi ◽  
Nikki Vercauteren
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Stable Boundary Layer ◽  
Energy Cascade ◽  
Isotropic Case ◽  
Limiting State ◽  
Stable Boundary ◽  
Turbulence Anisotropy ◽  
Small Scales ◽  
Energy Exchanges

<p>The broad variety of phenomena occurring on multiple scales under stably stratified conditions and their complex interactions make it difficult to get a full description of the Stable Boundary Layer (SBL). Near-surface turbulence may be intermittent and highly anisotropic even at small scales. By studying the invariants of the anisotropy Reynolds stress tensor, it is possible to analyse the eddy kinetic energy distribution over the three components of the flow. Recent analyses of SBL turbulence data highlighted a prevalence of one-component limiting state of anisotropy. The causes of this particular limiting state are not fully understood, but there is evidence that submeso activity influences turbulence topology.<span> </span></p><p>This open question motivated the present work, that addresses the issue from the point of view of space dimensionality. In large-scale atmospheric and oceanic dynamics it is well known that turbulent motions may transfer energy both to the large and to the small scales, according to density stratification and rotation. These two properties act as constraints on the flow, giving it a 2D structure, and leading turbulence to be more complex than the homogeneous and isotropic case. For a SBL in low-wind speed conditions, atmospheric stratification might be very strong and we investigate if some of the peculiar characteristics of this regime might be related to a quasi-2D dynamics, with the occurrence of an inverse energy cascade, typical of 2D-like turbulence.</p><p>Energy exchanges across larger and smaller scales are studied by analysing the direction of the momentum flux with different methods, including a coarse-graining approach based on Large Eddy Simulation (LES) theory. The SnoHATS dataset was used to this purpose, where two vertically-separated horizontal arrays of sonic anemometers over the Plaine Morte Glacier (Switzerland) allowed the computation of the full three-dimensional velocity gradient. In order to fully characterize the energy exchanges according to different states of turbulence anisotropy, energy conversion processes between eddy kinetic and potential energy have also been considered and analysed at different heights. To this purpose, the dataset FLOSSII was used, providing turbulence measurements up to 30 m above a flat grass surface, often covered by snow.<span> </span></p><p>Results seem to suggest that turbulent kinetic energy in the SBL is distributed mainly in one component more as a consequence of wave-turbulence interactions than of development of 2D-like turbulence. This gives insights on mechanisms driving turbulence anisotropy that might be used to improve turbulence parameterizations in the SBL.</p>

scholarly journals Ocean Eddy Energetics in the Spectral Space as Revealed by High-Resolution General Circulation Models

2019 ◽  
Vol 49 (11) ◽  
pp. 2815-2827
Author(s):  
Shengpeng Wang ◽  
Zhao Jing ◽  
Qiuying Zhang ◽  
Ping Chang ◽  
Zhaohui Chen ◽  
...  
Keyword(s):  
Energy Conversion ◽  
General Circulation ◽  
Surface Wind ◽  
Circulation Model ◽  
General Circulation Models ◽  
Ocean General Circulation Model ◽  
Energy Cascade ◽  
Spectral Space ◽  
Inverse Energy Cascade ◽  
Barotropic Energy Conversion

AbstractIn this study, the global eddy kinetic energy (EKE) budget in horizontal wavenumber space is analyzed based on 1/10° ocean general circulation model simulations. In both the tropical and midlatitude regions, the barotropic energy conversion from background flow to eddies is positive throughout the wavenumber space and generally peaks at the scale (Le) where EKE reaches its maximum. The baroclinic energy conversion is more pronounced at midlatitudes. It exhibits a dipolar structure with positive and negative values at scales smaller and larger than Le, respectively. Surface wind power on geostrophic flow results in a significant EKE loss around Le but deposits energy at larger scales. The interior viscous dissipation and bottom drag inferred from the pressure flux convergence act as EKE sink terms. The latter is most efficient at Le while the former is more dominant at smaller scales. There is an evident mismatch between EKE generation and dissipation in the spectral space especially at the midlatitudes. This is reconciled by a dominant forward energy cascade on the equator and a dominant inverse energy cascade at the midlatitudes.

Charney isotropy and equipartition in quasi-geostrophic turbulence

2010 ◽  
Vol 656 ◽  
pp. 448-457 ◽  
Author(s):  
ANDREAS VALLGREN ◽  
ERIK LINDBORG
Keyword(s):  
High Resolution ◽  
Kinetic Energy ◽  
Horizontal Velocity ◽  
Energy Cascade ◽  
Two Dimensional ◽  
Inverse Energy Cascade ◽  
Wide Range ◽  
Geostrophic Turbulence ◽  
Decaying Turbulence ◽  
Enstrophy Cascade

High-resolution simulations of forced quasi-geostrophic (QG) turbulence reveal that Charney isotropy develops under a wide range of conditions, and constitutes a preferred state also in β-plane and freely decaying turbulence. There is a clear analogy between two-dimensional and QG turbulence, with a direct enstrophy cascade that is governed by the prediction of Kraichnan (J. Fluid Mech., vol. 47, 1971, p. 525) and an inverse energy cascade following the classic k−5/3 scaling. Furthermore, we find that Charney's prediction of equipartition between the potential and kinetic energy in each of the two horizontal velocity components is approximately fulfilled in the inertial ranges.

Kinetic Energy Conversion in A Wind-forced Submesoscale Flow

2020 ◽  
Author(s):  
Song Li ◽  
Nuno Serra ◽  
Detlef Stammer
Keyword(s):  
Kinetic Energy ◽  
Energy Conversion ◽  
Wind Stress ◽  
Mixed Layer ◽  
Recent Progress ◽  
Cyclonic Eddy ◽  
Major Fraction ◽  
High K ◽  
Eddy Field ◽  
Mean Kinetic Energy

<p>Despite recent progress in measuring the ocean eddy field with satellite missions at the mesoscale (order of 100 km), containing the major fraction of ocean kinetic energy, many questions still remain regarding the generation, conversion and dissipation mechanisms of eddy kinetic energy (K<sub>e</sub>). In this work, we use the output from an idealized 500-m resolution ocean numerical simulation to study the conversion of K<sub>e</sub> in the absence and presence of wind stress forcing. In contrast to the result of the unforced run, K<sub>e</sub> increased approximately nine times in the mixed layer and considerably in the pycnocline in the forced run. Eddies and filaments were seen to re-stratify the mixed layer and wind-induced turbulence at the base of the mixed layer promoted its deepening and therefore dramatically enhanced the exchange between K<sub>e</sub> and eddy available potential energy (P<sub>e</sub>). The wind stress forcing additionally affected the conversion processes between P<sub>e</sub> and mean kinetic energy (K<sub>m</sub>). The wind also excited inertial and superinertial motions throughout almost the whole water column. Although those motions played a major role in the conversion between P<sub>e</sub> and K<sub>e</sub>, the net effect by inertial and superinertial flows was almost null. In addition, we found an asymmetric character in kinetic energy conversion in eddies. Cyclonic and anti-cyclonic eddies showed different behaviour regarding conversion from P<sub>e</sub> and K<sub>e</sub>, which was positive on the high K<sub>e</sub> part in the anti-cyclonic eddy but negative in the cyclonic eddy.</p>

scholarly journals Spontaneous mirror-symmetry breaking induces inverse energy cascade in 3D active fluids

2017 ◽  
Vol 114 (9) ◽  
pp. 2119-2124 ◽  
Author(s):  
Jonasz Słomka ◽  
Jörn Dunkel
Keyword(s):  
Symmetry Breaking ◽  
Mirror Symmetry ◽  
Energy Transport ◽  
Fluid Model ◽  
Energy Cascade ◽  
Turbulence Theory ◽  
Scale Selection ◽  
Inverse Cascade ◽  
Inverse Energy Cascade ◽  
Self Organized

Classical turbulence theory assumes that energy transport in a 3D turbulent flow proceeds through a Richardson cascade whereby larger vortices successively decay into smaller ones. By contrast, an additional inverse cascade characterized by vortex growth exists in 2D fluids and gases, with profound implications for meteorological flows and fluid mixing. The possibility of a helicity-driven inverse cascade in 3D fluids had been rejected in the 1970s based on equilibrium-thermodynamic arguments. Recently, however, it was proposed that certain symmetry-breaking processes could potentially trigger a 3D inverse cascade, but no physical system exhibiting this phenomenon has been identified to date. Here, we present analytical and numerical evidence for the existence of an inverse energy cascade in an experimentally validated 3D active fluid model, describing microbial suspension flows that spontaneously break mirror symmetry. We show analytically that self-organized scale selection, a generic feature of many biological and engineered nonequilibrium fluids, can generate parity-violating Beltrami flows. Our simulations further demonstrate how active scale selection controls mirror-symmetry breaking and the emergence of a 3D inverse cascade.

scholarly journals On the Origins of the Oceanic Ultraviolet Catastrophe

2021 ◽  
Keyword(s):  
Diffusion Tensor ◽  
Internal Gravity Waves ◽  
Energy Cascade ◽  
Turbulence Theory ◽  
Energy Fluxes ◽  
Analytical Treatment ◽  
Turbulent Dissipation ◽  
Inverse Energy Cascade ◽  
The Status ◽  
Direct Energy

Abstract We provide a first-principles analysis of the energy fluxes in the oceanic internal wavefield. The resulting formula is remarkably similar to the renowned phenomenological formula for the turbulent dissipation rate in the ocean which is known as the Finescale Parameterization. The prediction is based on the wave turbulence theory of internal gravity waves and on a new methodology devised for the computation of the associated energy fluxes. In the standard spectral representation of the wave energy density, in the two-dimensional vertical wavenumber – frequency (m – w) domain, the energy fluxes associated with the steady state are found to be directed downscale in both coordinates, closely matching the Finescale-Parameterization formula in functional form and in magnitude. These energy transfers are composed of a ‘local’ and a ‘scale-separated’ contributions; while the former is quantified numerically, the latter is dominated by the Induced Diffusion process and is amenable to analytical treatment. Contrary to previous results indicating an inverse energy cascade from high frequency to low, at odds with observations, our analysis of all non-zero coefficients of the diffusion tensor predicts a direct energy cascade. Moreover, by the same analysis fundamental spectra that had been deemed ‘no-flux’ solutions are reinstated to the status of ‘constant-downscale-flux’ solutions. This is consequential for an understanding of energy fluxes, sources and sinks that fits in the observational paradigm of the Finescale Parameterization, solving at once two long-standing paradoxes that had earned the name of ‘Oceanic Ultraviolet Catastrophe’.

Balanced and unbalanced routes to dissipation in an equilibrated Eady flow

2010 ◽  
Vol 654 ◽  
pp. 35-63 ◽  
Author(s):  
M. JEROEN MOLEMAKER ◽  
JAMES C. MCWILLIAMS ◽  
XAVIER CAPET
Keyword(s):  
General Circulation ◽  
Large Scale ◽  
Energy Cascade ◽  
Vertical Shear ◽  
Boussinesq Model ◽  
Geostrophic Balance ◽  
Numerical Resolution ◽  
Inverse Energy Cascade ◽  
Boundary Dissipation ◽  
Quasigeostrophic Model

The oceanic general circulation is forced at large scales and is unstable to mesoscale eddies. Large-scale currents and eddy flows are approximately in geostrophic balance. Geostrophic dynamics is characterized by an inverse energy cascade except for dissipation near the boundaries. In this paper, we confront the dilemma of how the general circulation may achieve dynamical equilibrium in the presence of continuous large-scale forcing and the absence of boundary dissipation. We do this with a forced horizontal flow with spatially uniform rotation, vertical stratification and vertical shear in a horizontally periodic domain, i.e. a version of Eady's flow carried to turbulent equilibrium. A direct route to interior dissipation is presented that is essentially non-geostrophic in its dynamics, with significant submesoscale frontogenesis, frontal instability and breakdown, and forward kinetic energy cascade to dissipation. To support this conclusion, a series of simulations is made with both quasigeostrophic and Boussinesq models. The quasigeostrophic model is shown as increasingly inefficient in achieving equilibration through viscous dissipation at increasingly higher numerical resolution (hence Reynolds number), whereas the non-geostrophic Boussinesq model equilibrates with only weak dependence on resolution and Rossby number.

scholarly journals The distribution of kinetic energy in the Southern Ocean: a comparison between observations and an eddy resolving general circulation model

1992 ◽  
Vol 338 (1285) ◽  
pp. 251-257 ◽  
Keyword(s):  
Kinetic Energy ◽  
Southern Ocean ◽  
General Circulation Model ◽  
General Circulation ◽  
Circulation Model ◽  
Transient Eddy ◽  
Buoyancy Forcing ◽  
Model Studies ◽  
Eddy Field ◽  
Good Agreement

It is widely believed from model studies that the transient eddy field plays an important role in the dynamics of the Southern Ocean. Accordingly, the distribution and partition of kinetic energy from an eddy resolving general circulation model of the Southern Ocean is compared with existing non-altimetric observations. Good agreement in distribution is found with some of the more recent observations. The amplitudes of the model energies, while for the most part well correlated with observations, are significantly lower than those observed (although observations differ greatly in their estimates). This reduction of energy is in agreement with other recent eddy resolving models, and is partly caused by the lack of correctly varying wind and buoyancy forcing, together with inadequate representation of instability processes. Nevertheless, the correlations suggest that the model results may be used as a proxy for reality in many circumstances.

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