On the spacing of meandering jets in the strong-stair limit

2021 ◽  
Vol 930 ◽  
Author(s):  
R.K. Scott ◽  
B.H. Burgess ◽  
D.G. Dritschel
Keyword(s):  
Kinetic Energy ◽  
Large Scale ◽  
Complex Structure ◽  
Zonal Jets ◽  
Incomplete Mixing ◽  
Numerical Integrations ◽  
Coherent Vortices ◽  
Perfect Mixing ◽  
The Mean ◽  
Kinetic And Potential Energies

Based on an assumption of strongly inhomogeneous potential vorticity mixing in quasi-geostrophic $\beta$ -plane turbulence, a relation is obtained between the mean spacing of latitudinally meandering zonal jets and the total kinetic energy of the flow. The relation applies to cases where the Rossby deformation length is much smaller than the Rhines scale, in which kinetic energy is concentrated within the jet cores. The relation can be theoretically achieved in the case of perfect mixing between regularly spaced jets with simple meanders, and of negligible kinetic energy in flow structures other than in jets. Incomplete mixing or unevenly spaced jets will result in jets being more widely separated than the estimate, while significant kinetic energy outside the jets will result in jets closer than the estimate. An additional relation, valid under the same assumptions, is obtained between the total kinetic and potential energies. In flows with large-scale dissipation, the two relations provide a means to predict the jet spacing based only on knowledge of the energy input rate of the forcing and dissipation rate, regardless of whether the latter takes the form of frictional or thermal damping. Comparison with direct numerical integrations of the forced system shows broad support for the relations, but differences between the actual and predicted jet spacings arise both from the complex structure of jet meanders and the non-negligible kinetic energy contained in the turbulent background and in coherent vortices lying between the jets.

scholarly journals From Mixing to the Large Scale Circulation: How the Inverse Cascade Is Involved in the Formation of the Subsurface Currents in the Gulf of Guinea

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 147 ◽  
Author(s):  
Fernand Assene ◽  
Yves Morel ◽  
Audrey Delpech ◽  
Micael Aguedjou ◽  
Julien Jouanno ◽  
...  
Keyword(s):  
Large Scale ◽  
Spatial And Temporal Variability ◽  
Gulf Of Guinea ◽  
Equatorial Undercurrent ◽  
Zonal Jets ◽  
Mean Fields ◽  
The Mean ◽  
North And South ◽  
And Diffusion ◽  
Meridional Advection

In this paper, we analyse the results from a numerical model at high resolution. We focus on the formation and maintenance of subsurface equatorial currents in the Gulf of Guinea and we base our analysis on the evolution of potential vorticity (PV). We highlight the link between submesoscale processes (involving mixing, friction and filamentation), mesoscale vortices and the mean currents in the area. In the simulation, eastward currents, the South and North Equatorial Undercurrents (SEUC and NEUC respectively) and the Guinea Undercurrent (GUC), are shown to be linked to the westward currents located equatorward. We show that east of 20° W, both westward and eastward currents are associated with the spreading of PV tongues by mesoscale vortices. The Equatorial Undercurrent (EUC) brings salty waters into the Gulf of Guinea. Mixing diffuses the salty anomaly downward. Meridional advection, mixing and friction are involved in the formation of fluid parcels with PV anomalies in the lower part and below the pycnocline, north and south of the EUC, in the Gulf of Guinea. These parcels gradually merge and vertically align, forming nonlinear anticyclonic vortices that propagate westward, spreading and horizontally mixing their PV content by stirring filamentation and diffusion, up to 20° W. When averaged over time, this creates regions of nearly homogeneous PV within zonal bands between 1.5° and 5° S or N. This mean PV field is associated with westward and eastward zonal jets flanking the EUC with the homogeneous PV tongues corresponding to the westward currents, and the strong PV gradient regions at their edges corresponding to the eastward currents. Mesoscale vortices strongly modulate the mean fields explaining the high spatial and temporal variability of the jets.

scholarly journals Dynamics of Convectively Driven Banded Jets in the Laboratory

2007 ◽  
Vol 64 (11) ◽  
pp. 4031-4052 ◽  
Author(s):  
Peter L. Read ◽  
Yasuhiro H. Yamazaki ◽  
Stephen R. Lewis ◽  
Paul D. Williams ◽  
Robin Wordsworth ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flows ◽  
Large Scale ◽  
Zonal Flow ◽  
Inertial Range ◽  
Instability Criterion ◽  
Rossby Wave Breaking ◽  
Outer Planets ◽  
Zonal Jets ◽  
Geostrophic Turbulence

Abstract The banded organization of clouds and zonal winds in the atmospheres of the outer planets has long fascinated observers. Several recent studies in the theory and idealized modeling of geostrophic turbulence have suggested possible explanations for the emergence of such organized patterns, typically involving highly anisotropic exchanges of kinetic energy and vorticity within the dissipationless inertial ranges of turbulent flows dominated (at least at large scales) by ensembles of propagating Rossby waves. The results from an attempt to reproduce such conditions in the laboratory are presented here. Achievement of a distinct inertial range turns out to require an experiment on the largest feasible scale. Deep, rotating convection on small horizontal scales was induced by gently and continuously spraying dense, salty water onto the free surface of the 13-m-diameter cylindrical tank on the Coriolis platform in Grenoble, France. A “planetary vorticity gradient” or “β effect” was obtained by use of a conically sloping bottom and the whole tank rotated at angular speeds up to 0.15 rad s−1. Over a period of several hours, a highly barotropic, zonally banded large-scale flow pattern was seen to emerge with up to 5–6 narrow, alternating, zonally aligned jets across the tank, indicating the development of an anisotropic field of geostrophic turbulence. Using particle image velocimetry (PIV) techniques, zonal jets are shown to have arisen from nonlinear interactions between barotropic eddies on a scale comparable to either a Rhines or “frictional” wavelength, which scales roughly as (β/Urms)−1/2. This resulted in an anisotropic kinetic energy spectrum with a significantly steeper slope with wavenumber k for the zonal flow than for the nonzonal eddies, which largely follows the classical Kolmogorov k−5/3 inertial range. Potential vorticity fields show evidence of Rossby wave breaking and the presence of a “hyperstaircase” with radius, indicating instantaneous flows that are supercritical with respect to the Rayleigh–Kuo instability criterion and in a state of “barotropic adjustment.” The implications of these results are discussed in light of zonal jets observed in planetary atmospheres and, most recently, in the terrestrial oceans.

scholarly journals Is spontaneous generation of coherent baroclinic flows possible?

2019 ◽  
Vol 862 ◽  
pp. 889-923 ◽  
Author(s):  
Nikolaos A. Bakas ◽  
Petros J. Ioannou
Keyword(s):  
Energy Input ◽  
Large Scale ◽  
Critical Threshold ◽  
Spontaneous Generation ◽  
Large Scale Structures ◽  
Zonal Jets ◽  
Statistical State ◽  
Coherent Vortices ◽  
Geophysical Turbulence ◽  
New Type

Geophysical turbulence is observed to self-organize into large-scale flows such as zonal jets and coherent vortices. Previous studies of barotropic $\unicode[STIX]{x1D6FD}$-plane turbulence have shown that coherent flows emerge from a background of homogeneous turbulence as a bifurcation when the turbulence intensity increases. The emergence of large-scale flows has been attributed to a new type of collective, symmetry-breaking instability of the statistical state dynamics of the turbulent flow. In this work, we extend the analysis to stratified flows and investigate turbulent self-organization in a two-layer fluid without any imposed mean north–south thermal gradient and with turbulence supported by an external random stirring. We use a second-order closure of the statistical state dynamics, that is termed S3T, with an appropriate averaging ansatz that allows the identification of statistical turbulent equilibria and their structural stability. The bifurcation of the statistically homogeneous equilibrium state to inhomogeneous equilibrium states comprising zonal jets and/or large-scale waves when the energy input rate of the excitation passes a critical threshold is analytically studied. Our theory predicts that there is a large bias towards the emergence of barotropic flows. If the scale of excitation is of the order of (or larger than) the deformation radius, the large-scale structures are barotropic. Mixed barotropic–baroclinic states with jets and/or waves arise when the excitation is at scales shorter than the deformation radius with the baroclinic component of the flow being subdominant for low energy input rates and insignificant for higher energy input rates. The predictions of the S3T theory are compared with nonlinear simulations. The theory is found to accurately predict both the critical transition parameters and the scales of the emergent structures but underestimates their amplitude.

Particle Image Velocimetry Measurements of In-Cylinder Flow in a Four-Stroke Utility Engine and Correlation With Combustion Measurements

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Karen E. Bevan ◽  
Jaal B. Ghandhi
Keyword(s):  
Kinetic Energy ◽  
Horizontal Plane ◽  
Large Scale ◽  
Particle Image ◽  
Vertical Plane ◽  
Combustion Performance ◽  
Combustion Duration ◽  
Image Velocimetry ◽  
The Mean ◽  
High Pass

Large-scale flows in internal combustion engines directly affect combustion duration and emission production. The effect of intake port geometry on combustion performance was studied in a four-stroke spark-ignition utility engine. Three intake port geometries were investigated at three port orientations. In-cylinder flows in orthogonal planes were measured using particle image velocimetry (PIV). The PIV data were processed to calculate the large-scale mean vorticity and mean high-pass filtered velocity. Combustion performance data were separately acquired at two load conditions at a fixed equivalence ratio, and compared with the PIV data. The cumulative distribution functions of the flow parameters did not show significant port-to-port differences in either measurement plane. The mean vorticity and high-pass filtered velocity did exhibit differences due to port orientation in the horizontal plane, but not in the vertical plane. The 0 deg ports (tangential orientation) consistently produced the highest values of large-scale mean vorticity and mean high-pass filtered velocity in the horizontal plane. The kinetic energy present at ignition was also calculated to characterize the flow. The ensemble-averaged values of the mean large-scale vorticity, high-pass filtered velocity, and kinetic energy were compared to the combustion duration. The vertical-plane vorticity and high-pass filtered velocity did not correlate with combustion performance. The horizontal-plane vorticity and high-pass filtered velocity were found to exhibit modest correlation at the fixed torque condition, and somewhat lower correlation at the wide open throttle condition. The correlation between kinetic energy and combustion duration was poor. The best correlation of flow field structure with engine performance was achieved for ports at the 0 deg port orientation. Ports at this orientation generated coherent, large-scale swirl.

The role of coherent vortices near the turbulent/non-turbulent interface in a planar jet

2011 ◽  
Vol 369 (1937) ◽  
pp. 738-753 ◽  
Author(s):  
Carlos Bettencourt da Silva ◽  
Ricardo José Nunes dos Reis
Keyword(s):  
Numerical Simulation ◽  
Large Scale ◽  
Vortical Structures ◽  
Micro Scale ◽  
Planar Jet ◽  
Coherent Vortices ◽  
The Mean ◽  
Turbulent Plane ◽  
Plane Jet

The role of coherent vortices near the turbulent/non-turbulent (T/NT) interface in a turbulent plane jet is analysed by a direct numerical simulation (DNS). The coherent vortices near the jet edge consist of large-scale vortical structures (LSVSs) maintained by the mean shear and intense vorticity structures (IVSs) created by the background fluctuating turbulence field. The radius of the LSVS is equal to the Taylor micro-scale R lsvs ≈ λ , while the radius of the IVS is of the order of the Kolmogorov micro-scale R ivs ∼ η . The LSVSs are responsible for the observed vorticity jump at the T/NT interface, being of the order of the Taylor micro-scale. The coherent vortices in the proximity of the T/NT interface are preferentially aligned with the tangent to the T/NT interface and are responsible for the viscous dissipation of kinetic energy near the T/NT interface and to the characteristic shape of the enstrophy viscous diffusion observed at that location.

scholarly journals Anisotropic turbulence and zonal jets in rotating flows with a β-effect

2006 ◽  
Vol 13 (1) ◽  
pp. 83-98 ◽  
Author(s):  
B. Galperin ◽  
S. Sukoriansky ◽  
N. Dikovskaya ◽  
P. L. Read ◽  
Y. H. Yamazaki ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Turbulent Flows ◽  
Large Scale ◽  
Scaling Laws ◽  
Physical Nature ◽  
Small Scale ◽  
Oceanic Circulation ◽  
Kinetic Energy Spectrum ◽  
Zonal Jets

Abstract. Numerical studies of small-scale forced, two-dimensional turbulent flows on the surface of a rotating sphere have revealed strong large-scale anisotropization that culminates in the emergence of quasi-steady sets of alternating zonal jets, or zonation. The kinetic energy spectrum of such flows also becomes strongly anisotropic. For the zonal modes, a steep spectral distribution, E(n)=CZ (Ω/R)2 n-5, is established, where CZ=O(1) is a non-dimensional coefficient, Ω is the angular velocity, and R is the radius of the sphere, respectively. For other, non-zonal modes, the classical, Kolmogorov-Batchelor-Kraichnan, spectral law is preserved. This flow regime, referred to as a zonostrophic regime, appears to have wide applicability to large-scale planetary and terrestrial circulations as long as those are characterized by strong rotation, vertically stable stratification and small Burger numbers. The well-known manifestations of this regime are the banded disks of the outer planets of our Solar System. Relatively less known examples are systems of narrow, subsurface, alternating zonal jets throughout all major oceans discovered in state-of-the-art, eddy-permitting simulations of the general oceanic circulation. Furthermore, laboratory experiments recently conducted using the Coriolis turntable have basically confirmed that the lateral gradient of ''planetary vorticity'' (emulated via the topographic β-effect) is the primary cause of the zonation and that the latter is entwined with the development of the strongly anisotropic kinetic energy spectrum that tends to attain the same zonal and non-zonal distributions, −5 and , respectively, in both the slope and the magnitude, as the corresponding spectra in other environmental conditions. The non-dimensional coefficient CZ in the −5 spectral law appears to be invariant, , in a variety of simulated and natural flows. This paper provides a brief review of the zonostrophic regime. The review includes the discussion of the physical nature, basic mechanisms, scaling laws and universality of this regime. A parameter range conducive to its establishment is identified, and collation of laboratory and naturally occurring flows is presented through which the zonostrophic regime manifests itself in the real world.

scholarly journals S3T Stability of the Homogeneous State of Barotropic Beta-Plane Turbulence

2015 ◽  
Vol 72 (5) ◽  
pp. 1689-1712 ◽  
Author(s):  
Nikolaos A. Bakas ◽  
Navid C. Constantinou ◽  
Petros J. Ioannou
Keyword(s):  
Large Scale ◽  
Modulational Instability ◽  
Homogeneous State ◽  
Mean Flow ◽  
Large Scale Structures ◽  
Zonal Jets ◽  
Statistical Framework ◽  
Beta Plane ◽  
The Mean ◽  
Large Scale Flow

Abstract Zonal jets and nonzonal large-scale flows are often present in forced–dissipative barotropic turbulence on a beta plane. The dynamics underlying the formation of both zonal and nonzonal coherent structures is investigated in this work within the statistical framework of stochastic structural stability theory (S3T). Previous S3T studies have shown that the homogeneous turbulent state undergoes a bifurcation at a critical parameter and becomes inhomogeneous with the emergence of zonal and/or large-scale nonzonal flows and that these statistical predictions of S3T are reflected in direct numerical simulations. In this paper, the dynamics underlying the S3T statistical instability of the homogeneous state as a function of parameters is studied. It is shown that, for weak planetary vorticity gradient β, both zonal jets and nonzonal large-scale structures form from upgradient momentum fluxes due to shearing of the eddies by the emerging infinitesimal flow. For large β, the dynamics of the S3T instability differs for zonal and nonzonal flows but in both the destabilizing vorticity fluxes decrease with increasing β. Shearing of the eddies by the mean flow continues to be the mechanism for the emergence of zonal jets while nonzonal large-scale flows emerge from resonant and near-resonant triad interactions between the large-scale flow and the stochastically forced eddies. The relation between the formation of large-scale structure through modulational instability and the S3T instability of the homogeneous state is also investigated and it is shown that the modulational instability results are subsumed by the S3T results.

On the asymptotic behaviour of large-scale turbulence in homogeneous shear flow

2009 ◽  
Vol 637 ◽  
pp. 213-239 ◽  
Author(s):  
JUAN C. ISAZA ◽  
LANCE R. COLLINS
Keyword(s):  
Kinetic Energy ◽  
Shear Flow ◽  
Dissipation Rate ◽  
Large Scale ◽  
Turbulent Energy ◽  
Time Behaviour ◽  
Initial Value ◽  
Shear Parameter ◽  
Long Time ◽  
The Mean

The asymptotic behaviour of large-scale velocity statistics in an homogeneous turbulent shear flow is investigated using direct numerical simulations (DNS) of the incompressible Navier–Stokes equations on a 5123 grid, and with viscous rapid distortion theory (RDT). We use a novel pseudo-spectral algorithm that allows us to set the initial value of the shear parameter in the range 3–30 without the shortcomings of previous numerical approaches. We find there is an explicit dependence of the early-time behaviour on the initial value of the shear parameter. Moreover, the long-time asymptotes of large-scale quantities such as the ratio of the turbulent kinetic energy production rate over dissipation rate, the Reynolds stress anisotropic tensor and the shear parameter itself depend sensitively on the initial value of the shear parameter over the range of Reynolds number we could achieve (26 ≤ Rλ ≤ 63) with the stringent resolution requirements that were satisfied. To gain further insight into the matter, we analyse the full viscous RDT. While inviscid RDT has received a great deal of attention, viscous RDT has not been fully analysed. Our motivation for considering viscous RDT is so that the energy dissipation rate enters the problem, enabling the shear parameter to be defined. We show asymptotic expansions for the short-time behaviour and numerically evaluate the integrals to determine the long-time prediction of viscous RDT. The results are in quantitative agreement with DNS for short times; however, at long times viscous RDT predicts the turbulent energy decays to zero. Through an analysis of the pressure–strain terms, we show that the nonlinear ‘slow’ terms are essential for rearranging turbulent energy from the streamwise direction to the mean shear direction, and this sustains the indefinite growth of the kinetic energy at long times. In effect, the nonlinear pressure–strain correlation maintains the three-dimensionality of the turbulence, countering the tendency of the mean shear to project the turbulence onto the two-dimensional plane of the mean-flow streamlines. We postulate that the predictions of viscous RDT at long times could be improved by introducing a model for the ‘slow’ pressure–strain term, along the lines of the Rotta model.

scholarly journals From Mixing to the Large Scale Circulation: How the Inverse Cascade Is Involved in the Formation of the Subsurface Currents in the Gulf of Guinea.

2021 ◽  
Author(s):  
Fernand Assene ◽  
Yves Morel ◽  
Audrey Delpech ◽  
Micael Aguedjou ◽  
Julien Jouanno ◽  
...  
Keyword(s):  
Large Scale ◽  
Spatial And Temporal Variability ◽  
Gulf Of Guinea ◽  
Equatorial Undercurrent ◽  
Zonal Jets ◽  
Mean Fields ◽  
The Mean ◽  
North And South ◽  
And Diffusion ◽  
Meridional Advection

<p>We analyse the results from a numerical model at high resolution. We focus on the formation and maintenance of subsurface equatorial currents in the Gulf of Guinea and we base our analysis on the evolution of potential vorticity (PV). We highlight the link between submesoscale processes (involving mixing, friction and filamentation), mesoscale vortices and the mean currents in the area. In the simulation, eastward currents, the South and North Equatorial Undercurrents (SEUC and NEUC respectively) and the Guinea Undercurrent (GUC), are shown to be linked to the westward currents located equatorward. We show that east of 20<sup>◦</sup>W, both westward and eastward currents are associated with the spreading of PV tongues by mesoscale vortices. The Equatorial Undercurrent (EUC) brings salty waters into the Gulf of Guinea. Mixing diffuses the salty anomaly downward. Meridional advection, mixing and friction are involved in the formation of fluid parcel swith PV anomalies in the lower part and below the pycnocline, north and south of the EUC, in the Gulf of Guinea. These parcels gradually merge and vertically align, forming nonlinear anticyclonic vortices that propagate westward, spreading and horizontally mixing their PV content by stirring filamentation and diffusion, up to 20<sup>◦</sup>W. When averaged over time, this creates regions of nearly homogeneous PV within zonal bands between 1.5<sup>◦</sup> and 5<sup>◦</sup>S or N. This mean PV field is associated with westward and eastward zonal jets flanking the EUC with the homogeneous PV tongues corresponding to the westward currents, and the strong PV gradient regions at their edges corresponding to the eastward currents. Mesoscale vortices strongly modulate the mean fields explaining the high spatial and temporal variability of the jets.</p>

Investigation of the influence of miniature vortex generators on the large-scale motions of a turbulent boundary layer

2021 ◽  
Vol 932 ◽  
Author(s):  
C.I. Chan ◽  
R.C. Chin
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Velocity Fluctuation ◽  
High Speed ◽  
Large Scale ◽  
Vortex Generators ◽  
Mean Flow ◽  
Low Speed ◽  
The Mean

Well resolved large-eddy simulation data are used to study the physical modulation effects of miniature vortex generators (MVGs) in a moderate Reynolds number zero pressure gradient turbulent boundary layer. Large-scale counter-rotating primary vortex pairs (PVPs) imposed by the MVG contribute to the formation of streamwise streaks by transporting high momentum fluids from the outer regions of the boundary layer towards the wall, giving rise to high-speed regions centred at the PVP. Consequently, low-speed regions are formed along the outer flank of the PVP, resulting in a pronounced alternating high- and low-speed flow pattern. The PVP also relates to regions with skin friction modification, where a local skin friction reduction of up to 15 % is obtained at the low-speed region, but the opposite situation is observed over the high-speed region. The MVG-induced flow feature is further investigated by spectral analysis of the triple decomposition velocity fluctuation. Pre-multiplied energy spectra of the streamwise MVG-induced velocity fluctuation reveal that the large-scale induced modes scale with the spanwise wavelength and the length of the MVG, but the energy peak is eventually repositioned to the size of the near-wall streaks in the streamwise direction. Analysis of the triple decomposition of the kinetic energy transport equations revealed the significance of the mean flow gradient in generating kinetic energy which sustains the secondary motion. There is also an energy transfer between the turbulent and MVG-induced kinetic energy independent of the mean flow.

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