Spectral Energy Fluxes in Geostrophic Turbulence: Implications for Ocean Energetics

2007 ◽  
Vol 37 (3) ◽  
pp. 673-688 ◽  
Author(s):  
Robert B. Scott ◽  
Brian K. Arbic
Keyword(s):  
Kinetic Energy ◽  
Energy Cascade ◽  
Altimeter Data ◽  
Spectral Energy ◽  
Model Parameters ◽  
Baroclinic Mode ◽  
Mean Flow ◽  
Energy Fluxes ◽  
Inverse Cascade ◽  
Geostrophic Turbulence

Abstract The energy pathways in geostrophic turbulence are explored using a two-layer, flat-bottom, f-plane, quasigeostrophic model forced by an imposed, horizontally homogenous, baroclinically unstable mean flow and damped by bottom Ekman friction. A systematic presentation of the spectral energy fluxes, the mean flow forcing, and dissipation terms allows for a comprehensive understanding of the sources and sinks for baroclinic and barotropic energy as a function of length scale. The key new result is a robust inverse cascade of kinetic energy for both the baroclinic mode and the upper layer. This is consistent with recent observations of satellite altimeter data over the South Pacific Ocean. The well-known forward cascade of baroclinic potential and total energy was found to be very robust. Decomposing the spectral fluxes into contributions from different terms provided further insight. The inverse baroclinic kinetic energy cascade is driven mostly by an efficient interaction between the baroclinic velocity and the barotropic vorticity, the latter playing a crucial catalytic role. This cascade can be further enhanced by the baroclinic mode self-interaction, which is only present with nonuniform stratification (unequal layer depths). When model parameters are set such that modeled eddies compare favorably with observations, the inverse baroclinic kinetic energy cascade is actually much stronger than the well-known inverse cascade in the barotropic mode. The upper-layer kinetic energy cascade was found to dominate the lower-layer cascade over a wide range of parameters, suggesting that the surface cascade and time mean density stratification may be sufficient for estimating the depth-integrated cascade from ocean observations. This may find useful application in inferring the kinetic to gravitational potential energy conversion rate from satellite measurements.

scholarly journals Cascade Inequalities for Forced–Dissipated Geostrophic Turbulence

2007 ◽  
Vol 37 (6) ◽  
pp. 1470-1487 ◽  
Author(s):  
Brian K. Arbic ◽  
Glenn R. Flierl ◽  
Robert B. Scott
Keyword(s):  
Kinetic Energy ◽  
Bottom Friction ◽  
Decay Rates ◽  
Symmetric System ◽  
Small Scale ◽  
Kinetic Energy Density ◽  
Spatial Average ◽  
Mean Flow ◽  
Inverse Cascade ◽  
Geostrophic Turbulence

Abstract Analysis of spectral kinetic energy fluxes in satellite altimetry data has demonstrated that an inverse cascade of kinetic energy is ubiquitous in the ocean. In geostrophic turbulence models, a fully developed inverse cascade results in barotropic eddies with large horizontal scales. However, midocean eddies contain substantial energy in the baroclinic mode and in compact horizontal scales (scales comparable to the deformation radius Ld). This paper examines the possibility that relatively strong bottom friction prevents the oceanic cascade from becoming fully developed. The importance of the vertical structure of friction is demonstrated by contrasting numerical simulations of two-layer quasigeostrophic turbulence forced by a baroclinically unstable mean flow and damped by bottom Ekman friction with turbulence damped by vertically symmetric Ekman friction (equal decay rates in the two layers). “Cascade inequalities” derived from the energy and enstrophy equations are used to interpret the numerical results. In the symmetric system, the inequality formally requires a cascade to large-scale barotropic flow, independent of the stratification. The inequality is less strict when friction is in the bottom layer only, especially when stratification is surface intensified. Accordingly, model runs with surface-intensified stratification and relatively strong bottom friction retain substantial small-scale baroclinic energy. Altimetric data show that the symmetric inequality is violated in the low- and midlatitude ocean, again suggesting the potential impact of the “bottomness” of friction on eddies. Inequalities developed for multilayer turbulence suggest that high baroclinic modes in the mean shear also enhance small-scale baroclinic eddy energy. The inequalities motivate a new interpretation of barotropization in weakly damped turbulence. In that limit the barotropic mode dominates the spatial average of kinetic energy density because large values of barotropic density are found throughout the model domain, consistent with the barotropic cascade to large horizontal scales, while baroclinic density is spatially localized.

scholarly journals Characteristics, Energetics, and Origins of Agulhas Current Meanders and Their Limited Influence on Ring Shedding

2015 ◽  
Vol 45 (9) ◽  
pp. 2294-2314 ◽  
Author(s):  
Shane Elipot ◽  
Lisa M. Beal
Keyword(s):  
Kinetic Energy ◽  
Single Mode ◽  
Cyclonic Circulation ◽  
Recent Analysis ◽  
Altimeter Data ◽  
Western Boundary ◽  
Mean Flow ◽  
Current Time ◽  
Agulhas Current ◽  
The Mean

AbstractThe Agulhas Current intermittently undergoes dramatic offshore excursions from its mean path because of the downstream passage of mesoscale solitary meanders or Natal pulses. New observations and analyses are presented of the variability of the current and its meanders using mooring observations from the Agulhas Current Time-Series Experiment (ACT) near 34°S. Using a new rotary EOF method, mesoscale meanders and smaller-scale meanders are differentiated and each captured in a single mode of variance. During mesoscale meanders, an onshore cyclonic circulation and an offshore anticyclonic circulation act together to displace the jet offshore, leading to sudden and strong positive conversion of kinetic energy from the mean flow to the meander via nonlinear interactions. Smaller meanders are principally represented by a single cyclonic circulation spanning the entire jet that acts to displace the jet without extracting kinetic energy from the mean flow. Synthesizing in situ observations with altimeter data leads to an account of the number of mesoscale meanders at 34°S: 1.6 yr−1 on average, in agreement with a recent analysis by Rouault and Penven (2011) and significantly less than previously understood. The links between meanders and the arrival of Mozambique Channel eddies or Madagascar dipoles at the western boundary upstream are found to be robust in the 20-yr altimeter record. Yet, only a small fraction of anomalies arriving at the western boundary result in meanders, and of those, two-thirds can be related to ring shedding. Most Agulhas rings are shed independently of meanders.

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.

The evolution of a uniformly sheared thermally stratified turbulent flow

1997 ◽  
Vol 334 ◽  
pp. 61-86 ◽  
Author(s):  
PAUL PICCIRILLO ◽  
CHARLES W. VAN ATTA
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Richardson Number ◽  
Initial Conditions ◽  
Velocity Shear ◽  
Spectral Energy ◽  
Small Scale ◽  
Mean Flow ◽  
Mean Velocity ◽  
Small Scales

Experiments were carried out in a new type of stratified flow facility to study the evolution of turbulence in a mean flow possessing both uniform stable stratification and uniform mean shear.The new facility is a thermally stratified wind tunnel consisting of ten independent supply layers, each with its own blower and heaters, and is capable of producing arbitrary temperature and velocity profiles in the test section. In the experiments, four different sized turbulence-generating grids were used to study the effect of different initial conditions. All three components of the velocity were measured, along with the temperature. Root-mean-square quantities and correlations were measured, along with their corresponding power and cross-spectra.As the gradient Richardson number Ri = N2/(dU/dz)2 was increased, the downstream spatial evolution of the turbulent kinetic energy changed from increasing, to stationary, to decreasing. The stationary value of the Richardson number, Ricr, was found to be an increasing function of the dimensionless shear parameter Sq2/∈ (where S = dU/dz is the mean velocity shear, q2 is the turbulent kinetic energy, and ∈ is the viscous dissipation).The turbulence was found to be highly anisotropic, both at the small scales and at the large scales, and anisotropy was found to increase with increasing Ri. The evolution of the velocity power spectra for Ri [les ] Ricr, in which the energy of the large scales increases while the energy in the small scales decreases, suggests that the small-scale anisotropy is caused, or at least amplified, by buoyancy forces which reduce the amount of spectral energy transfer from large to small scales. For the largest values of Ri, countergradient buoyancy flux occurred for the small scales of the turbulence, an effect noted earlier in the numerical results of Holt et al. (1992), Gerz et al. (1989), and Gerz & Schumann (1991).

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 Direct Evidence of an Oceanic Inverse Kinetic Energy Cascade from Satellite Altimetry

2005 ◽  
Vol 35 (9) ◽  
pp. 1650-1666 ◽  
Author(s):  
Robert B. Scott ◽  
Faming Wang
Keyword(s):  
Kinetic Energy ◽  
Energy Flux ◽  
Direct Evidence ◽  
Inertial Range ◽  
Turbulence Theory ◽  
Kinetic Energy Density ◽  
Geostrophic Flow ◽  
Inverse Cascade ◽  
Barotropic Mode ◽  
Geostrophic Turbulence

Abstract Sea surface height measurements from satellites reveal the turbulent properties of the South Pacific Ocean surface geostrophic circulation, both supporting and challenging different aspects of geostrophic turbulence theory. A near-universal shape of the spectral kinetic energy flux is found and provides direct evidence of a source of kinetic energy near to or smaller than the deformation radius, consistent with linear instability theory. The spectral kinetic energy flux also reveals a net inverse cascade (i.e., a cascade to larger spatial scale), consistent with two-dimensional turbulence phenomenology. However, stratified geostrophic turbulence theory predicts an inverse cascade for the barotropic mode only; energy in the large-scale baroclinic modes undergoes a direct cascade toward the first-mode deformation scale. Thus if the surface geostrophic flow is predominately the first baroclinic mode, as expected for oceanic stratification profiles, then the observed inverse cascade contradicts geostrophic turbulence theory. The latter interpretation is argued for. Furthermore, and consistent with this interpretation, the inverse cascade arrest scale does not follow the Rhines arrest scale, as one would expect for the barotropic mode. A tentative revision of theory is proposed that would resolve the conflicts; however, further observations and idealized modeling experiments are needed to confirm, or refute, the revision. It is noted that no inertial range was found for the inverse cascade range of the spectrum, implying inertial range scaling, such as the established K−5/3 slope in the spectral kinetic energy density plot, is not applicable to the surface geostrophic flow.

The Latitudinal Dependence of Atmospheric Jet Scales and Macroturbulent Energy Cascades

2015 ◽  
Vol 72 (10) ◽  
pp. 3891-3907 ◽  
Author(s):  
Rei Chemke ◽  
Yohai Kaspi
Keyword(s):  
Kinetic Energy ◽  
Eddy Kinetic Energy ◽  
Mean Flow ◽  
Rotation Rates ◽  
Inverse Cascade ◽  
Energy Cascades ◽  
Zonal Wavenumber ◽  
Wide Range ◽  
Scale Down ◽  
Baroclinic Zone

Abstract The latitudinal width of atmospheric eddy-driven jets and scales of macroturbulence are examined latitude by latitude over a wide range of rotation rates using a high-resolution idealized GCM. It is found that for each latitude, through all rotation rates, the jet spacing scales with the Rhines scale. These simulations show the presence of a “supercriticality latitude” within the baroclinic zone, where poleward (equatorward) of this latitude, the Rhines scale is larger (smaller) than the Rossby deformation radius. Poleward of this latitude, a classic geostrophic turbulence picture appears with a − spectral slope of inverse cascade from the deformation radius up to the Rhines scale. A shallower slope than the −3 slope of enstrophy cascade is found from the deformation radius down to the viscosity scale as a result of the broad input of baroclinic eddy kinetic energy. At these latitudes, eddy–eddy interactions transfer barotropic eddy kinetic energy from the input scales of baroclinic eddy kinetic energy up to the jet scale and down to smaller scales. For the Earth case, this latitude is outside the baroclinic zone and therefore an inverse cascade does not appear. Equatorward of the supercriticality latitude, the − slope of inverse cascade vanishes, eddy–mean flow interactions play an important role in the balance, and the spectrum follows a −3 slope from the Rhines scale down to smaller scales, similar to what is observed on Earth. Moreover, the length scale of the energy-containing zonal wavenumber is equal to (larger than) the jet scale poleward (equatorward) of the supercriticality latitude.

Mesoscale to Submesoscale Transition in the California Current System. Part III: Energy Balance and Flux

2008 ◽  
Vol 38 (10) ◽  
pp. 2256-2269 ◽  
Author(s):  
X. Capet ◽  
J. C. McWilliams ◽  
M. J. Molemaker ◽  
A. F. Shchepetkin
Keyword(s):  
Kinetic Energy ◽  
Current System ◽  
California Current ◽  
Essential Elements ◽  
Force Balance ◽  
Spectral Energy ◽  
Surface Boundary ◽  
Surface Boundary Layer ◽  
California Current System ◽  
Geostrophic Turbulence

Abstract This is the last of a suite of three papers about the transition that occurs in numerical simulations for an idealized equilibrium, subtropical, eastern-boundary upwelling current system similar to the California Current. The transition is mainly explained by the emergence of ubiquitous submesoscale density fronts and ageostrophic circulations about them in the weakly stratified surface boundary layer. Here the high-resolution simulations are further analyzed from the perspective of the kinetic energy (KE) spectrum shape and spectral energy fluxes in the mesoscale-to-submesoscale range in the upper ocean. For wavenumbers greater than the mesoscale energy peak, there is a submesoscale power-law regime in the spectrum with an exponent close to −2. In the KE balance an important conversion from potential to kinetic energy takes place at all wavenumbers in both mesoscale and submesoscale ranges; this conversion is the energetic counterpart of the vertical restratification flux and frontogenesis discussed in the earlier papers. A significant forward cascade of KE occurs in the submesoscale range en route to dissipation at even smaller scales. This is contrary to the inverse energy cascade of geostrophic turbulence and it is, in fact, fundamentally associated with the horizontally divergent (i.e., ageostrophic) velocity component. The submesoscale dynamical processes of frontogenesis, frontal instability, and breakdown of diagnostic force balance are all essential elements of the energy cycle of potential energy conversion and forward KE cascade.

On Quadratic Bottom Drag, Geostrophic Turbulence, and Oceanic Mesoscale Eddies

2008 ◽  
Vol 38 (1) ◽  
pp. 84-103 ◽  
Author(s):  
Brian K. Arbic ◽  
Robert B. Scott
Keyword(s):  
Mesoscale Eddy ◽  
Wave Drag ◽  
Ocean Model ◽  
Strength Parameter ◽  
Altimeter Data ◽  
Mean Flow ◽  
Quadratic Drag ◽  
Linear Drag ◽  
Geostrophic Turbulence ◽  
Satellite Altimeter Data

Abstract Many investigators have idealized the oceanic mesoscale eddy field with numerical simulations of geostrophic turbulence forced by a horizontally homogeneous, baroclinically unstable mean flow. To date such studies have employed linear bottom Ekman friction (hereinafter, linear drag). This paper presents simulations of two-layer baroclinically unstable geostrophic turbulence damped by quadratic bottom drag, which is generally thought to be more realistic. The goals of the paper are 1) to describe the behavior of quadratically damped turbulence as drag strength changes, using previously reported behaviors of linearly damped turbulence as a point of comparison, and 2) to compare the eddy energies, baroclinicities, and horizontal scales in both quadratic and linear drag simulations with observations and to discuss the constraints these comparisons place on the form and strength of bottom drag in the ocean. In both quadratic and linear drag simulations, large barotropic eddies develop with weak damping, large equivalent barotropic eddies develop with strong damping, and the comparison in goal 2 above is closest when the nondimensional friction strength parameter is of order 1. Typical values of the quadratic drag coefficient (cd ∼ 0.0025) and of boundary layer depths (Hb ∼ 50 m) imply that the quadratic friction strength parameter cdLd/Hb, where Ld is the deformation radius, may indeed be of order 1 in the ocean. Model eddies are realistic over a wider range of friction strengths when drag is quadratic, because of a reduced sensitivity to friction strength in that case. The quadratic parameter is independent of the mean shear, in contrast to the linear parameter. Plots of eddy length scales, computed from satellite altimeter data, versus mean shear and versus rough estimates of the friction strength parameters suggest that both linear and quadratic bottom drag may be active in the ocean. Topographic wave drag contains terms that are linear in the bottom flow, thus providing some justification for the use of linear bottom drag in models.

scholarly journals Surface Geostrophic Circulation of the Mediterranean Sea Derived from Drifter and Satellite Altimeter Data

2012 ◽  
Vol 42 (6) ◽  
pp. 973-990 ◽  
Author(s):  
Pierre-Marie Poulain ◽  
Milena Menna ◽  
Elena Mauri
Keyword(s):  
Kinetic Energy ◽  
Mediterranean Sea ◽  
Surface Waters ◽  
Energy Levels ◽  
Altimeter Data ◽  
Mean Flow ◽  
Satellite Altimeter ◽  
The Mean ◽  
Surface Geostrophic Circulation ◽  
Satellite Altimeter Data

Abstract Drifter observations and satellite-derived sea surface height data are used to quantitatively study the surface geostrophic circulation of the entire Mediterranean Sea for the period spanning 1992–2010. After removal of the wind-driven components from the drifter velocities and low-pass filtering in bins of 1° × 1° × 1 week, maps of surface geostrophic circulation (mean flow and kinetic energy levels) are produced using the drifter and/or satellite data. The mean currents and kinetic energy levels derived from the drifter data appear stronger/higher with respect to those obtained from satellite altimeter data. The maps of mean circulation estimated from the drifter data and from a combination of drifter and altimeter data are, however, qualitatively similar. In the western basin they show the main pathways of the surface waters flowing eastward from the Strait of Gibraltar to the Sicily Channel and the current transporting waters back westward along the Italian, French, and Spanish coasts. Intermittent and long-lived subbasin-scale eddies and gyres abound in the Tyrrhenian and Algerian Seas. In the eastern basin, the surface waters are transported eastward by several currents but recirculate in numerous eddies and gyres before reaching the northward coastal current off Israel, Lebanon, and Syria and veering westward off Turkey. In the Ionian Sea, the mean geostrophic velocity maps were also produced separately for the two extended seasons and for multiyear periods. Significant variations are confirmed, with seasonal reversals of the currents in the south and changes of the circulation from anticyclonic (prior to 1 July 2007) to cyclonic and back to anticyclonic after 31 December 2005.

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