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.

scholarly journals A theory for the emergence of coherent structures in beta-plane turbulence

2014 ◽  
Vol 740 ◽  
pp. 312-341 ◽  
Author(s):  
Nikolaos A. Bakas ◽  
Petros J. Ioannou
Keyword(s):  
Turbulent Flows ◽  
Coherent Structures ◽  
Energy Input ◽  
Large Scale ◽  
Order Approximation ◽  
Plane Channel ◽  
Phase Speed ◽  
Homogeneous State ◽  
Zonal Jets ◽  
Beta Plane

AbstractPlanetary turbulent flows are observed to self-organize into large-scale structures such as zonal jets and coherent vortices. One of the simplest models of planetary turbulence is obtained by considering a barotropic flow on a beta-plane channel with turbulence sustained by random stirring. Nonlinear integrations of this model show that as the energy input rate of the forcing is increased, the homogeneity of the flow is broken with the emergence of non-zonal, coherent, westward propagating structures and at larger energy input rates by the emergence of zonal jets. We study the emergence of non-zonal coherent structures using a non-equilibrium statistical theory, stochastic structural stability theory (S3T, previously referred to as SSST). S3T directly models a second-order approximation to the statistical mean turbulent state and allows the identification of statistical turbulent equilibria and study of their stability. Using S3T, the bifurcation properties of the homogeneous state in barotropic beta-plane turbulence are determined. Analytic expressions for the zonal and non-zonal large-scale coherent flows that emerge as a result of structural instability are obtained. Through numerical integrations of the S3T dynamical system, it is found that the unstable structures equilibrate at finite amplitude. Numerical simulations of the nonlinear equations confirm the characteristics (scale, amplitude and phase speed) of the structures predicted by S3T.

scholarly journals Instability wave models for the near-field fluctuations of turbulent jets

2011 ◽  
Vol 689 ◽  
pp. 97-128 ◽  
Author(s):  
K. Gudmundsson ◽  
Tim Colonius
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Microphone Array ◽  
Near Field ◽  
Turbulent Jets ◽  
Instability Wave ◽  
Mean Flow ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Scale Structures

AbstractPrevious work has shown that aspects of the evolution of large-scale structures, particularly in forced and transitional mixing layers and jets, can be described by linear and nonlinear stability theories. However, questions persist as to the choice of the basic (steady) flow field to perturb, and the extent to which disturbances in natural (unforced), initially turbulent jets may be modelled with the theory. For unforced jets, identification is made difficult by the lack of a phase reference that would permit a portion of the signal associated with the instability wave to be isolated from other, uncorrelated fluctuations. In this paper, we investigate the extent to which pressure and velocity fluctuations in subsonic, turbulent round jets can be described aslinearperturbations to the mean flow field. The disturbances are expanded about the experimentally measured jet mean flow field, and evolved using linear parabolized stability equations (PSE) that account, in an approximate way, for the weakly non-parallel jet mean flow field. We utilize data from an extensive microphone array that measures pressure fluctuations just outside the jet shear layer to show that, up to an unknown initial disturbance spectrum, the phase, wavelength, and amplitude envelope of convecting wavepackets agree well with PSE solutions at frequencies and azimuthal wavenumbers that can be accurately measured with the array. We next apply the proper orthogonal decomposition to near-field velocity fluctuations measured with particle image velocimetry, and show that the structure of the most energetic modes is also similar to eigenfunctions from the linear theory. Importantly, the amplitudes of the modes inferred from the velocity fluctuations are in reasonable agreement with those identified from the microphone array. The results therefore suggest that, to predict, with reasonable accuracy, the evolution of the largest-scale structures that comprise the most energetic portion of the turbulent spectrum of natural jets, nonlinear effects need only be indirectly accounted for by considering perturbations to the mean turbulent flow field, while neglecting any non-zero frequency disturbance interactions.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Analysis of Turbulence in the Tip Region of a Waterjet Pump Rotor

2010 ◽  
Author(s):  
Huixuan Wu ◽  
Rinaldo L. Miorini ◽  
Joseph Katz
Keyword(s):  
Energy Flux ◽  
Large Scale ◽  
Multiple Scales ◽  
Tip Clearance ◽  
Mean Flow ◽  
Production Characteristic ◽  
Pump Rotor ◽  
The Mean ◽  
Turbulence Production ◽  
Waterjet Pump

A series of high resolution planar particle image velocimetry measurements performed in a waterjet pump rotor reveal the inner structure of the tip leakage vortex (TLV) which dominates the entire flow field in the tip region. Turbulence generated by interactions among the TLV, the shear layer that develops as the backward leakage flow emerges from the tip clearance as a “wall jet”, the passage flow, and the endwall is highly inhomogeneous and anisotropic. We examine this turbulence in both RANS and LES modelling contexts. Spatially non-uniform distributions of Reynolds stress components are explained in terms of the local mean strain field and associated turbulence production. Characteristic length scales are also inferred from spectral analysis. Spatial filtering of instantaneous data enables the calculation of subgrid scale (SGS) stresses, along with the SGS energy flux (dissipation). The data show that the SGS energy flux differs from the turbulence production rate both in trends and magnitude. The latter is dominated by energy flux from the mean flow to the large scale turbulence, which is resolved in LES, whereas the former is dominated by energy flux from the mean flow to the SGS turbulence. The SGS dissipation rate is also used for calculating the static and dynamic Smagorinsky coefficients, the latter involving filtering at multiple scales; both vary substantially in the tip region, and neither is equal to values obtained in isotropic turbulence.

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 Large-Scale Flow in Micro Electrokinetic Turbulent Mixer

Micromachines ◽  
2020 ◽  
Vol 11 (9) ◽  
pp. 813 ◽  
Author(s):  
Keyi Nan ◽  
Zhongyan Hu ◽  
Wei Zhao ◽  
Kaige Wang ◽  
Jintao Bai ◽  
...  
Keyword(s):  
Flow Field ◽  
Electric Conductivity ◽  
Large Scale ◽  
Three Dimensional ◽  
Mixing Process ◽  
Mean Flow ◽  
Velocity Fluctuations ◽  
Two Fluids ◽  
Large Scale Flow ◽  
Particle Imaging

In the present work, we studied the three-dimensional (3D) mean flow field in a micro electrokinetic (μEK) turbulence based micromixer by micro particle imaging velocimetry (μPIV) with stereoscopic method. A large-scale solenoid-type 3D mean flow field has been observed. The extraordinarily fast mixing process of the μEK turbulent mixer can be primarily attributed to two steps. First, under the strong velocity fluctuations generated by μEK mechanism, the two fluids with different conductivity are highly mixed near the entrance, primarily at the low electric conductivity sides and bias to the bottom wall. Then, the well-mixed fluid in the local region convects to the rest regions of the micromixer by the large-scale solenoid-type 3D mean flow. The mechanism of the large-scale 3D mean flow could be attributed to the unbalanced electroosmotic flows (EOFs) due to the high and low electric conductivity on both the bottom and top surface.

scholarly journals Inferring high-redshift large-scale structure dynamics from the Lyman-α forest

2019 ◽  
Vol 630 ◽  
pp. A151 ◽  
Author(s):  
Natalia Porqueres ◽  
Jens Jasche ◽  
Guilhem Lavaux ◽  
Torsten Enßlin
Keyword(s):  
Large Scale ◽  
High Redshift ◽  
Three Dimensional ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Modal Parameter ◽  
Large Scale Structures ◽  
Quasar Spectra ◽  
Large Scale Flow ◽  
Fully Bayesian

One of the major science goals over the coming decade is to test fundamental physics with probes of the cosmic large-scale structure out to high redshift. Here we present a fully Bayesian approach to infer the three-dimensional cosmic matter distribution and its dynamics at z >  2 from observations of the Lyman-α forest. We demonstrate that the method recovers the unbiased mass distribution and the correct matter power spectrum at all scales. Our method infers the three-dimensional density field from a set of one-dimensional spectra, interpolating the information between the lines of sight. We show that our algorithm provides unbiased mass profiles of clusters, becoming an alternative for estimating cluster masses complementary to weak lensing or X-ray observations. The algorithm employs a Hamiltonian Monte Carlo method to generate realizations of initial and evolved density fields and the three-dimensional large-scale flow, revealing the cosmic dynamics at high redshift. The method correctly handles multi-modal parameter distributions, which allow constraining the physics of the intergalactic medium with high accuracy. We performed several tests using realistic simulated quasar spectra to test and validate our method. Our results show that detailed and physically plausible inference of three-dimensional large-scale structures at high redshift has become feasible.

scholarly journals WKB theory for rapid distortion of inhomogeneous turbulence

1999 ◽  
Vol 390 ◽  
pp. 325-348 ◽  
Author(s):  
S. NAZARENKO ◽  
N. K.-R. KEVLAHAN ◽  
B. DUBRULLE
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Two Dimensional ◽  
Turbulent Spot ◽  
Mean Flow ◽  
Mean Velocity ◽  
Inhomogeneous Turbulence ◽  
Large Scale Vortex ◽  
The Mean ◽  
Mean Strain

A WKB method is used to extend RDT (rapid distortion theory) to initially inhomogeneous turbulence and unsteady mean flows. The WKB equations describe turbulence wavepackets which are transported by the mean velocity and have wavenumbers which evolve due to the mean strain. The turbulence also modifies the mean flow and generates large-scale vorticity via the averaged Reynolds stress tensor. The theory is applied to Taylor's four-roller flow in order to explain the experimentally observed reduction in the mean strain. The strain reduction occurs due to the formation of a large-scale vortex quadrupole structure from the turbulent spot confined by the four rollers. Both turbulence inhomogeneity and three-dimensionality are shown to be important for this effect. If the initially isotropic turbulence is either homogeneous in space or two-dimensional, it has no effect on the large-scale strain. Furthermore, the turbulent kinetic energy is conserved in the two-dimensional case, which has important consequences for the theory of two-dimensional turbulence. The analytical and numerical results presented here are in good qualitative agreement with experiment.

Flow Instabilities in Gas Turbine Chute Seals

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
Joshua T. M. Horwood ◽  
Fabian P. Hualca ◽  
Mike Wilson ◽  
James A. Scobie ◽  
Carl M. Sangan ◽  
...  
Keyword(s):  
Large Scale ◽  
Computational Study ◽  
Leading Edge ◽  
Large Scale Structures ◽  
Strong Shear ◽  
Time Marching ◽  
Flow Through ◽  
Scale Structures ◽  
Large Scale Flow ◽  
Secondary Flow Field

Abstract The ingress of hot annulus gas into stator–rotor cavities is an important topic to engine designers. Rim-seals reduce the pressurized purge required to protect highly stressed components. This paper describes an experimental and computational study of flow through a turbine chute seal. The computations—which include a 360 deg domain—were undertaken using dlrtrace's time-marching solver. The experiments used a low Reynolds number turbine rig operating with an engine-representative flow structure. The simulations provide an excellent prediction of cavity pressure and swirl, and good overall agreement of sealing effectiveness when compared to experiment. Computation of flow within the chute seal showed strong shear gradients which influence the pressure distribution and secondary-flow field near the blade leading edge. High levels of shear across the rim-seal promote the formation of large-scale structures at the wheel-space periphery; the number and speed of which were measured experimentally and captured, qualitatively and quantitatively, by computations. A comparison of computational domains ranging from 30 deg to 360 deg indicates that steady features of the flow are largely unaffected by sector size. However, differences in large-scale flow structures were pronounced with a 60 deg sector and suggest that modeling an even number of blades in small sector simulations should be avoided.

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