Coherent Structures In Turbulent Flows Research Articles

Statistical inference from atmospheric time series: detecting trends and coherent structures

Abstract. Standard statistical methods involve strong assumptions that are rarely met in real data, whereas resampling methods permit obtaining valid inference without making questionable assumptions about the data generating mechanism. Among these methods, subsampling works under the weakest assumptions, which makes it particularly applicable for atmospheric and climate data analyses. In the paper, two problems are addressed using subsampling: (1) the construction of simultaneous confidence bands for the unknown trend in a time series that can be modeled as a sum of two components: deterministic (trend) and stochastic (stationary process, not necessarily an i.i.d. noise or a linear process), and (2) the construction of confidence intervals for the skewness of a nonlinear time series. Non-zero skewness is attributed to the occurrence of coherent structures in turbulent flows, whereas commonly employed linear time series models imply zero skewness.

Geometric properties of particle trajectories in turbulent flows

We study the statistics of curvature and torsion of Lagrangian trajectories from direct numerical simulations of homogeneous and isotropic turbulence (at e λ ≈280) in order to extract informations on the geometry of small-scale coherent structures in turbulent flows. We find that, as previously observed by Braun et al. (W. Braun, F. De Lillo, and B. Eckhardt, Geometry of particle paths in turbulent flows, J. Turbul. 7 (2006), p. 62) and Xu et al. (H. Xu, N.T. Ouellette, and E. Bodenschatz, Curvature of Lagrangian trajectories in turbulence, Phys. Rev. Lett. 98 (2007), p. 050201), the high curvature statistics is dominated by large-scale flow reversals where velocity magnitude assumes very low values. We show that flow-reversal events are characterized by very short correlation times. We introduce both time filtering and threshold in the minimum velocity amplitude in order to disentangle intense curvature events generated from genuine small-scale vortex structures from simple flow-reversal. We present for the first time measurements of torsion statistics in fully developed turbulent flows. By studying the joint statistics of curvature and torsion, we present further evidences that intense and persistent events are dominated by helical-type trajectories.

三次元角柱周りの乱流の組織的構造

In this study, we clarified a formation process of coherent structures of turbulent flow around a three dimensional rectangular solid. The flow around the rectangular solid with the aspect ratio L/H of 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0 and 5.5, has been computed by the large eddy simulation at Reynolds number of 4 000. The computational results of the distribution of spectrum and Strouhal number correspond well with the flow around a two dimensional cylinder except for variation of peak value. And, in terms of Strouhal number, the result (L/H=1.0) corresponds with experimental result. In large aspect ratios, the visualization results show that a pair of hair pin vortex structures is shed from the vortex formation region alternately and periodically. The rectangular solid has two free ends. So, the aspects of the flow field around the three dimensional solid are different from that around the two dimensional cylinder, especially concerning the vortex formations. And, some characteristics of shear layer and vortex structures in a wake are found to be remarkably different with the aspect ratio. As for some vortices with characteristic aspect ratio, the formation and kinetic mechanisms of some vortices are described in details.

High-resolution numerical simulation of turbulence in natural waterways

We develop an efficient and versatile numerical model for carrying out high-resolution simulations of turbulent flows in natural meandering streams with arbitrarily complex bathymetry. The numerical model solves the 3D, unsteady, incompressible Navier–Stokes and continuity equations in generalized curvilinear coordinates. The method can handle the arbitrary geometrical complexity of natural streams using the sharp-interface curvilinear immersed boundary (CURVIB) method of Ge and Sotiropoulos (2007) [1]. The governing equations are discretized with three-point, central, second-order accurate finite-difference formulas and integrated in time using an efficient, second-order accurate fractional step method. To enable efficient simulations on grids with tens of millions of grid nodes in long and shallow domains typical of natural streams, the algebraic multigrid (AMG) method is used to solve the Poisson equation for the pressure coupled with a matrix-free Krylov solver for the momentum equations. Depending on the desired level of resolution and available computational resources, the numerical model can either simulate, via direct numerical simulation (DNS), large-eddy simulation (LES), or unsteady Reynolds-averaged Navier–Stokes (URANS) modeling. The potential of the model as a powerful tool for simulating energetic coherent structures in turbulent flows in natural river reaches is demonstrated by applying it to carry out LES and URANS in a 50-m long natural meandering stream at resolution sufficiently fine to capture vortex shedding from centimeter-scale roughness elements on the bed. The accuracy of the simulations is demonstrated by comparisons with experimental data and the relative performance of the LES and URANS models is also discussed.

Fast Large-Eddy Simulation of Low Reynolds Number Flows over a NACA0025

Fast Large-Eddy Simulation of Low Reynolds Number Flows over a NACA0025

Detached eddy simulation of flow around two wall-mounted cubes in tandem

We investigate the performance of unsteady Reynolds-averaged Navier–Stokes (URANS) computation and various versions of detached eddy simulation (DES) in resolving coherent structures in turbulent flow around two cubes mounted in tandem on a flat plate at Reynolds number ( Re) of 22,000 and for a thin incoming boundary layer. Calculations are carried out using four different coherent structure resolving turbulence models: (1) URANS with the Spalart–Allmaras model; (2) the standard DES [Spalart, P.R., Jou, W.H., Strelets, M., Allmaras, S.R., 1997. Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In: Liu, C., Liu, Z., (Eds.), Advances in DNS/LES. Greyden Press, Columbus, OH]; (3) the Delayed DES (DDES); and (4) the DES with a low- Re modification (DES-LR) [Spalart, P., Deck, S., Shur, M., Squires, K., Strelets, M., Travin, A., 2006. A new version of detached eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn. 20 (3), 181–195]. The grid sensitivity of the computed solutions is examined by carrying out simulations on two successively refined grids. The computed results for all cases are compared with the experimental measurements of Martinuzzi and Havel [Martinuzzi, R., Havel, B., 2000. Turbulent flow around two interfering surface-mounted cubic obstacles in tandem arrangement. ASME J. Fluids Eng. 122, 24–31] for two different cube spacings. All turbulence models reproduce essentially identical separation of the approach thin boundary layer and yield an unsteady horseshoe vortex system consisting of multiple vortices in the leading edge region of the upstream cube. Significant discrepancies between the URANS and all DES solutions are observed, however, in other regions of interest such as the shear layers emanating from the cubes, the inter-cube gap and the downstream wake. Regardless of the grid refinement, URANS fails to capture key features of the mean flow, including the second horseshoe vortex in the upstream junction and recirculating flow on the top surface of the downstream cube for the large cube spacing, and underestimates significantly turbulence statistics in most regions of the flow for both cases. On the coarse mesh, all three DES approaches appear to yield very similar results and fail to reproduce the second horseshoe vortex. The standard DES and DDES solutions obtained on the fine meshes are essentially identical and both suffer from premature switching to unresolved DNS, due to the mis-interpretation of grid refinement as wall proximity, which leads to spurious vortices in the inter-cube region. Numerical solutions show that the low- Re modification (DES-LR) is critical prerequisite in DES on the ambiguously fine – not fine enough for full LES – mesh to prevent excessive nonlinear drop of the subgrid eddy viscosity in low cell- Re regions like in the inter-obstacle gap. Mean flow quantities and turbulence statistics obtained with DES-LR on the fine mesh are in good overall agreement with the measurements in most regions of interest for both cases.

Visualisation of statistically periodic coherent structures in turbulent flows using a phase-locked averaging method

Coherent structures are the focus of many flow investigations, although their contribution to turbulent mixing is not well understood. When occurring together with high intense turbulent mixing, these structures require statistical methods for visualisation and analysis of simulation results obtained using high-resolution numerical schemes, such as LES or DES. The method of 'phase-locked' averaging separates transient processes with a given frequency. This paper reveals an online formulation for the phase-locked averaging technique at a certain frequency to be set by the user. The method is demonstrated for two realistic flow configurations, an isothermal double-concentric combustor flow and a jet-in-crossflow situation.

Hydrodynamics of a forced riffle pool in a gravel bed river: 2. Scale and structure of coherent turbulent events

In the companion article, we present mean velocity and turbulence intensity statistics at a range of discharges in a forced riffle pool unit and show that the distributions of mean velocity and turbulence are characteristic of nonuniform flows. The objectives of this paper are to describe the spatial and temporal variability of the structure of turbulence in the forced riffle pool unit and to examine turbulence generation mechanisms and the links between the scales of macrobed forms and coherent turbulent flow structures. Our results show that while larger‐scale structures develop outside of the thalweg, the scales of coherent turbulent flow structures decrease with velocity and discharge in the forced riffle pool. Flow separation is shown to be an important factor, with full separation occurring in lateral shear zones and intermittent separation near the bed in the pool head. These zones generate new turbulence that disrupts a number of coherent turbulent flow structures that are typical of uniform flows. Coherent turbulent flow structures do not appear to be the source of morphological scaling in the forced riffle pool.

Influence of wavy surfaces on coherent structures in a turbulent flow

We describe how outer flow turbulence phenomena depend on the interaction with the wall. We investigate coherent structures in turbulent flows over different wavy surfaces and specify the influence of the different surface geometries on the coherent structures. The most important contribution to the turbulent momentum transport is attributed to these structures, therefore this flow configuration is of large engineering interest. In order to achieve a homogeneous and inhomogeneous reference flow situation two different types of surface geometries are considered: (1) three sinusoidal bottom wall profiles with different amplitude-to-wavelength ratios of α = 2a/Λ = 0.2 (Λ = 30 mm), α = 0.2 (Λ = 15 mm), and α = 0.1 (Λ = 30 mm); and (2) a profile consisting of two superimposed sinusoidal waves with α = 0.1 (Λ = 30 mm). Measurements are carried out in a wide water channel facility (aspect ratio 12:1). Digital particle image velocimetry (PIV) is performed to examine the spatial variation of the streamwise, spanwise and wall-normal velocity components in three measurement planes. Measurements are performed at a Reynolds number of 11,200, defined with the half channel height h and the bulk velocity U B. We apply the method of snapshots and perform a proper orthogonal decomposition (POD) of the streamwise, spanwise, and wall-normal velocity components to extract the most dominant flow structures. The structure of the most dominant eigenmode is related to counter-rotating, streamwise-oriented vortices. A qualitative comparison of the eigenfunctions for different sinusoidal wall profiles shows similar structures and comparable characteristic spanwise scales Λ z = 1.5 H in the spanwise direction for each mode. The scale is observed to be slightly smaller for α = 0.2 (Λ = 15 mm) and slightly larger for α = 0.2 (Λ = 30 mm). This scaling for the flow over the basic wave geometries indicates that the size of the largest structures is neither directly linked to the solid wave amplitude, nor to the wavelength. The characteristic spanwise scale of the dominant eigenmode for the developed flow over the surface consisting of two superimposed waves reduces to 0.85 H. However, a scale in the order of 1.3 H is identified for the second mode. The eigenvalue spectra for the superimposed waves is much broader, more modes contribute to the energy-containing range. The turbulent flow with increased complexity of the bottom surface is characterized by an increased number of dominant large-scale structures with different spanwise scales.

Local models of small-scale dynamo action

Coherent structures in turbulent flows consisting of vorticity filaments may generate small-scale magnetic fields by means of dynamo action with a mechanism similar to that known as the Herzenberg dynamo. In order to analyse the consequences of this assumption for the properties of t he resulting magnetic field, we have performed numerical simulations for a Herzenberg-like model system with a prescribed flow, and determined the critical magnetic Reynolds number Hz for the dynamo. The critical value is of the order of a few hundred and is to be compared wit h the local magnetic Reynolds number for a pair of vortex filaments, calculated as a function of the Reynolds number of the flow by means of a scaling argument following Kolmogorov theory. This gives us fairly stringent conditions on the magnetic Prandtl number. Pr M has to be large, of the order of a few hundred. The resulting magnetic field has a scale comparable with the diameter of the vorticity tubes and is thus of small scale, compared to the integral scale of the flow

Localized disturbances in parallel shear flows

The development of localized disturbances in parallel shear flows is reviewed. The inviscid case is considered, first for a general velocity profile and then in the special case of plane Couette flow so as to bring out the key asymptotic results in an explicit form. In this context, the distinctive differences between the wave-packet associated with the asymptotic behavior of eigenmodes and the non-dispersive (inviscid) continuous spectrum is highlighted. The largest growth is found for three-dimensional disturbances and occurs in the normal vorticity component. It is due to an algebraic instability associated with the lift-up effect. Comparison is also made between the analytical results and some numerical calculations. Next the viscous case is treated, where the complete solution to the initial value problem is presented for bounded flows using eigenfunction expansions. The asymptotic, wave-packet type behaviour is analyzed using the method of steepest descent and kinematic wave theory. For short times, on the other hand, transient growth can be large, particularly for three-dimensional disturbances. This growth is associated with cancelation of non-orthogonal modes and is the viscous equivalent of the algebraic instability. The maximum transient growth possible to obtain from this mechanism is also presented, the so called optimal growth. Lastly the application of the dynamics of three dimensional disturbances in modeling of coherent structures in turbulent flows is discussed.

Seasonal and diurnal variations of coherent structures over a deciduous forest

Coherent structures in turbulent flow above a midlatitude deciduous forest are identified using a wavelet analysis technique. Coupling between motions above the canopy (z/h=1.5, whereh is canopy height) and within the canopy (z/h=0.6) are studied using composite velocity and temperature fields constructed from 85 hours of data. Data are classified into winter and summer cases, for both convective and stable conditions. Vertical velocity fluctuations are in phase at both observation levels. Horizontal motions associated with the structures within the canopy lead those above the canopy, and linear analysis indicates that the horizontal motions deep in the canopy should lead the vertical motions by 90°. On average, coherent structures are responsible for only about 40% of overall turbulent heat and momentum fluxes, much less than previously reported. However, our large data set reveals that this flux fraction comes from a wide distribution that includes much higher fractions in its upper extremes. The separation distanceLs between adjacent coherent structures, 6–10h, is comparable to that obtained in previous observations over short canopies and in the laboratory. Changes in separation between the summer and winter (leafless) conditions are consistent withLs being determined by a local horizontal wind shear scale.

Characteristic of coherent structure of turbulent flow in straight-eandering open channel

Characteristic of coherent structure of turbulent flow in straight-eandering open channel is investigated using flow visualization techniques and two-components laser-Doppler anemometry. Flow visualization indicates that characteristic coherent st ructures are informed near the bottom wall, side wall and water surface with channel meandering. It is clear that vortical structure on the bottom wall incline toward concave wall at the meandering portion. Velocity measurements indicate the presence of remarkable disproportion of the transverse profiles of mean velocity (-U, W), turbulent intensity (u′, w′) and Reynolds stress (-uw) at meandering portion. It seems that these coherent structures contribute to remarkable disproportion of the turbulent structure.

Lyapunov exponents and the dimension of periodic incompressible Navier—Stokes flows: numerical measurements

In this paper we study the quasi-stationary turbulent state developed by an incompressible flow submitted to a constant periodic force. The turbulent state is described by its Lyapunov exponents and Lyapunov dimension. Our aim is to investigate in particular if the dimension is, as several lines of argument seem to indicate, given in one way or another by the number of ‘turbulent’ modes present in the flow.The exponents may be viewed as the asymptotic limits of local exponents, which are the divergence rates between the actual state of the fluid and nearby states. These local exponents fluctuate as the fluid suffers chaotic changes: they are systematically larger during bursts of excitation at large scale. In one case, we find that the flow oscillates repeatedly, on a very long timescale, between two distinct turbulent states, which have distinct local Lyapunov spectra and also distinct energy spectra. At the moderate resolutions studied here (642, 1282 and 163), we find that the dimension of the attractor in flows with standard dissipation is bounded above by the number of degrees of freedom contained in the large scales, i.e. at wavenumbers smaller than that of the injection wavenumber kf. We also consider two-dimensional flows with artificial terms (hyperviscosity), which concentrate small-scale dissipation in a narrow band of wavenumbers, and allow the formation of an inertial range. The dimension in these flows is no longer bounded by the number of large scales; it grows with, but remains significantly smaller than, the number of modes contained in the inertial range. It is conjectured that this is due to the presence of coherent structures in the flow, and that at higher resolutions also, the presence of coherent structures in turbulent flows will lead to an effective attractor dimension significantly lower than the estimations based on self-similar Kolmogorov theories.

THE ROLE OF COHERENT STRUCTURES IN TURBULENT FLOW

THE ROLE OF COHERENT STRUCTURES IN TURBULENT FLOW

On helicity fluctuations in turbulence

The role that helicity fluctuations play in relationship to small-scale intermittency and coherent structures in turbulent flows is examined from a theoretical standpoint. It has been argued recently that regions of large turbulent activity are associated with regions of small local helicity and, hence, that such a correlation exists. In this paper, it will be proven that fluctuations in the local helicity are not Galilean invariant and, consequently, it is possible to have completely different local helicity fluctuations for a given fluctuating velocity field and its associated turbulence statistics. It is thus highly doubtful that local helicity fluctuations can be of any fundamental value in correlating small-scale intermittency or coherent structures.

On the helical nature of three-dimensional coherent structures in turbulent flows

Available experimental data on three-dimensional coherent structures in various turbulent flows are used to demonstrate the helical nature of these structures.

Instantaneous Two-Dimensional Gas Concentration Measurements by Light Scattering

A light-scatteri ng technique which makes it possible to map out the instantaneous concentration field at 104 points in a thin sheet intersecting a nonreacting turbulent flow is described. The concentration is inferred from the intensity of the Lorenz/Mie scattered radiation from a seeded flow. The signal is detected by a computer- controlled, low-light-level TV camera and the resulting data have the advantage of being both quantitative and visually interpretable. The technique can be modified to obtain temporal as well as spatial information. In addition, the use of other scattering mechanisms for similar measurements is discussed. ITH the realization of the importance of coherent structures in turbulent flows, there has been an increased interest in experimental means of obtaining in- formation on the nature of these structures. The use of multipoint probes, conditional sampling techniques, and flow visualization has provided much new data. The picture is still incomplete, however, since most simultaneous multipoint measurements have been limited to a relatively small number of points, usually along a single line. Also, flow visualization, which provides a large amount of information, is generally only qualitative. In order to provide a large number of simultaneous, quantitative measurements, a nonintrusive light-scattering technique has been developed which makes it possible to measure gas concentration at 10,000 points within a plane intersecting a nonreacting turbulent flow. The technique used is an extension of one first developed by Rosensweig1 and later employed by several other researchers. A thorough review of the method has been given by Becker.2 The technique is based on the fact that, if a gas is seeded with light-scattering particles having dimensions so small that there is negligible slip between trie particles and the surrounding gas, each unit mass of the seeded gas will be marked by ap- proximately the same number of aerosols in the course of its motion. (The size of the particles is sufficiently large so that there is negligible Brownian diffusion of particles due to molecular agitation. A precise estimate of how well the particles follow the fluid motion is given later.) If the seeded gas mixes with a second unseeded gas, the number of scat- tering particles in each unit volume of the mixture will be reduced and the scattered radiation will be proportionall y less. Early experiments of this type used a bright lamp to illuminate a smoke-laden flow. Later, Shaughnessy and Morton3 found that using a laser as the illumination source improved the signal/noise ratio. By a system of lenses and slits, the scattering from a small volume of seeded gas was collected and focused onto a photomultiplie r tube (PMT). The PMT output was then shown to be proportional to the seeded gas concentration, and it was possible to measure average concentration, concentration fluctuations, and power spectra at a single point. Our experiments invoke the same principle but, rather than measuring the time evolution of the

Jet noise spectra at low Reynolds number

The current interest in coherent structures in turbulent flows and their possible influence on acoustic radiation is the impetus for a detailed examination of the acoustic field surrounding a turbulent jet at low Reynolds numbers. In this study the acoustic characteristics are examined over a Reynolds number range of 16 000 to 148 000 at a constant Mach number of 0.52. This is accomplished using a series of geometrically similar nozzles ranging in size from 1.3 to 12.2 mm. The remarkable conclusion is that the spectral content changes significantly below a Reynolds number of about 1 × 105. The shift in peak frequency with increasing emission angle (the so‐called reverse Doppler shift) characteristic of high Reynolds number jets is not observed. In fact, the spectra are observed to peak at a Helmholtz number, fd/ɑ0, of about 0.08, independent of emission angle. This result is discussed in light of recent findings concerning the role of initial shear layer instabilities on the subsequent development of turbulent flow. [Work supported by AFOSR.]

Premixed turbulent flame blowoff velocity correlation based on coherent structures in turbulent flows

A correlation for the blowoff velocity of premixed turbulent flames stabilized by bluff bodies is developed using a simple model for coherent structures in turbulent flows. The correlation shows the correct trends for variations in equivalence ratio, free stream pressure and temperature, flameholder characteristic size, and turbulent Reynolds number, and good agreement with published experimental data is obtained.