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 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.

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.

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).

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.

scholarly journals Near Wake Development Behind Marine Propeller Model in Presence of Freestream Turbulence

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Bennitt L. Hermsen ◽  
Matthew Bornemeier ◽  
Luksa Luznik
Keyword(s):  
Kinetic Energy ◽  
Three Dimensional ◽  
Small Scale ◽  
Shear Stresses ◽  
Marine Propeller ◽  
Freestream Turbulence ◽  
Mean Flow ◽  
Near Wake ◽  
External Turbulence ◽  
Inflow Conditions

Abstract Three-dimensional particle image velocimetry (PIV) experiments were conducted in the immediate near wake and up to seven diameters downstream of a three-bladed marine propeller model operating in two different inflow conditions: one with imposed freestream turbulence with intensity of 7% and streamwise integral length scale comparable to propeller geometry, and the second experiment with a quiescent inflow conditions as a reference. The resulting Reynolds number based on propeller chord and relative velocity is Re0.7R = 4.7 × 105. All components of radial transport of mean flow kinetic energy are analyzed and the largest contributor to the fluxes is found to be correlated to Reynolds shear stresses, resulting in radially outward flux in the wake. Two regions of the near wake are distinguishable with downstream extent dependent on the level of external turbulence. In the first region, immediately behind the propeller, shed tip vortices are very coherent and undergo grouping and roll-up around each other and the second region where the vortex merger process is complete and characterized by breakdown of vortices into small-scale turbulence. The latter region was found to occur earlier in the experiment with external turbulence. Conditional statistics of velocity fluctuations were employed and they show that outward interactions and sweep events contribute the most to the transfer of mean flow kinetic energy from the inner wake to the freestream.

Analyzing the Kinetic Energy budget of submesoscale-permitting ensemble simulations

2021 ◽  
Author(s):  
Quentin Jamet ◽  
William K. Dewar ◽  
Thierry Penduff ◽  
Julien Le Sommer ◽  
Stephanie Leroux ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Surface Pressure ◽  
Rate Of Change ◽  
Small Scale ◽  
Mean Flow ◽  
Time Step ◽  
Ocean Turbulence ◽  
Ensemble Simulations ◽  
Short Period ◽  
Ensemble Mean

<p>Ensemble simulations are becoming more and more popular in oceanography. Among other advantages, this modeling strategy elevates the number of dimensions available to apply statistics, and then offer new opportunities to disentangle small scale ocean turbulence from the larger scale (ensemble mean) flow, as well as their interactions. In such a framework, ocean turbulence is usually defined as the ensemble spread, reflecting the intrinsic variability that spontaneously emerges from the ocean, while the larger scale flow is defined as the ensemble mean, and whose variability is controlled by the forcing. Here, we aim at leveraging results of recently produced, submesoscale-permitting (1/60<sup>o</sup>) ensemble simulations of a forced ocean model configuration of the western Mediterranean Sea (MEDWEST60, 20 members) to diagnose the role played by ocean turbulence in the Kinetic Energy (KE) budget of these simulations. We develop for this purpose offline tools to compute such budget based on the NEMO modeling platform, which we aim at presenting.</p><p><br>These offline tools are part of the CDFTOOLS, a FORTRAN based package developed to export the NEMO code into an offline version of it for post-processing. Our contributions have been to include the momentum budget of the code into this package, on which kinetic energy builds upon. We first evaluate the accuracy of these offline computations against online estimates over a short period of time. At the model time step, this accuracy reaches  up to 10<sup>-3</sup> -10<sup>-4</sup> for time rate of change, advection and pressure work, and 10<sup>-1</sup> for vertical dissipation. The surface pressure correction associated with the time-splitting scheme has proven difficult to implement offline, due to 1/ sub-domain boundaries instabilities in the computation of the barotropic mode, and 2/ replication of the interpolation scheme used in NEMO for atmospheric forcing fields (atmospheric surface pressure, evaporation, precipitations, runoff). The use of one hour model outputs is found to degrade the accuracy of the offline estimates by up to one order of magnitude locally. We then present and discuss preliminary applications of these diagnostics to the MEDWEST60 ensemble simulation model outputs (hourly averages).</p>

Inverse cascade in simulated MHD turbulence driven by small scale source of magnetic helicity

2016 ◽  
Vol 52 (1) ◽  
pp. 261-268
Author(s):  
R. Stepanov ◽  
◽  
V. Titov ◽  
◽  
Keyword(s):  
Magnetic Helicity ◽  
Small Scale ◽  
Mhd Turbulence ◽  
Inverse Cascade

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.

scholarly journals Pulsations of blue supergiants before and after helium core ignition

2013 ◽  
Vol 9 (S301) ◽  
pp. 321-324
Author(s):  
Jakub Ostrowski ◽  
Jadwiga Daszyńska-Daszkiewicz
Keyword(s):  
Energy Density ◽  
Kinetic Energy ◽  
Kinetic Energy Density ◽  
Low Degree ◽  
Before And After

AbstractWe present results of pulsation analyses of B-type supergiant models with masses of 14 – 18 M⊙, considering evolutionary stages before and after helium core ignition. Using a non-adiabatic pulsation code, we compute instability domains for low-degree modes. For selected models in these two evolutionary phases, we compare properties of pulsation modes. Significant differences are found in oscillation spectra and the kinetic energy density of pulsation modes.

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