scholarly journals Nonlinear dynamics of large-scale coherent structures in turbulent free shear layers

2015 ◽  
Vol 787 ◽  
pp. 396-439 ◽  
Author(s):  
Xuesong Wu ◽  
Xiuling Zhuang
Keyword(s):  
Nonlinear Dynamics ◽  
Coherent Structures ◽  
Large Scale ◽  
Shear Layers ◽  
Small Scale ◽  
Evolution System ◽  
Mean Flow ◽  
Free Shear Layers ◽  
The Mean ◽  
Scale Turbulence

Fully developed turbulent free shear layers exhibit a high degree of order, characterized by large-scale coherent structures in the form of spanwise vortex rollers. Extensive experimental investigations show that such organized motions bear remarkable resemblance to instability waves, and their main characteristics, including the length scales, propagation speeds and transverse structures, are reasonably well predicted by linear stability analysis of the mean flow. In this paper, we present a mathematical theory to describe the nonlinear dynamics of coherent structures. The formulation is based on the triple decomposition of the instantaneous flow into a mean field, coherent fluctuations and small-scale turbulence but with the mean-flow distortion induced by nonlinear interactions of coherent fluctuations being treated as part of the organized motion. The system is closed by employing a gradient type of model for the time- and phase-averaged Reynolds stresses of fine-scale turbulence. In the high-Reynolds-number limit, the nonlinear non-equilibrium critical-layer theory for laminar-flow instabilities is adapted to turbulent shear layers by accounting for (1) the enhanced non-parallelism associated with fast spreading of the mean flow, and (2) the influence of small-scale turbulence on coherent structures. The combination of these factors with nonlinearity leads to an interesting evolution system, consisting of coupled amplitude and vorticity equations, in which non-parallelism contributes the so-called translating critical-layer effect. Numerical solutions of the evolution system capture vortex roll-up, which is the hallmark of a turbulent mixing layer, and the predicted amplitude development mimics the qualitative feature of oscillatory saturation that has been observed in a number of experiments. A fair degree of quantitative agreement is obtained with one set of experimental data.

The effects of turbulence on the mean flow past square rods

1983 ◽  
Vol 137 ◽  
pp. 331-345 ◽  
Author(s):  
Y. Nakamura ◽  
Y. Ohya
Keyword(s):  
Growth Rate ◽  
Shear Layer ◽  
Cross Section ◽  
Large Scale ◽  
Small Scale ◽  
Mean Flow ◽  
Flow Past ◽  
The Mean ◽  
Scale Turbulence ◽  
Main Effects

There are two main effects of turbulence on the mean flow past rods of square cross-section aligned with the approaching flow. Small-scale turbulence increases the growth rate of the shear layer, while large-scale turbulence enhances the roll-up of the shear layer. The consequences of these depend on the length of a square rod. The mean base pressure of a square rod varies considerably with turbulence intensity and scale as well as with its length.

Generation mechanism of a hierarchy of vortices in a turbulent boundary layer

2019 ◽  
Vol 865 ◽  
pp. 1085-1109 ◽  
Author(s):  
Yutaro Motoori ◽  
Susumu Goto
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Generation Mechanism ◽  
Small Scale ◽  
Generation Process ◽  
Mean Flow ◽  
The Mean

To understand the generation mechanism of a hierarchy of multiscale vortices in a high-Reynolds-number turbulent boundary layer, we conduct direct numerical simulations and educe the hierarchy of vortices by applying a coarse-graining method to the simulated turbulent velocity field. When the Reynolds number is high enough for the premultiplied energy spectrum of the streamwise velocity component to show the second peak and for the energy spectrum to obey the$-5/3$power law, small-scale vortices, that is, vortices sufficiently smaller than the height from the wall, in the log layer are generated predominantly by the stretching in strain-rate fields at larger scales rather than by the mean-flow stretching. In such a case, the twice-larger scale contributes most to the stretching of smaller-scale vortices. This generation mechanism of small-scale vortices is similar to the one observed in fully developed turbulence in a periodic cube and consistent with the picture of the energy cascade. On the other hand, large-scale vortices, that is, vortices as large as the height, are stretched and amplified directly by the mean flow. We show quantitative evidence of these scale-dependent generation mechanisms of vortices on the basis of numerical analyses of the scale-dependent enstrophy production rate. We also demonstrate concrete examples of the generation process of the hierarchy of multiscale vortices.

Coherent structures and dominant frequencies in a turbulent three-dimensional diffuser

2012 ◽  
Vol 699 ◽  
pp. 320-351 ◽  
Author(s):  
Johan Malm ◽  
Philipp Schlatter ◽  
Dan S. Henningson
Keyword(s):  
Coherent Structures ◽  
Large Scale ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Low Frequency ◽  
Bulk Velocity ◽  
Time Signal ◽  
Mean Flow ◽  
The Mean ◽  
Dominant Frequencies

AbstractDominant frequencies and coherent structures are investigated in a turbulent, three-dimensional and separated diffuser flow at $\mathit{Re}= 10\hspace{0.167em} 000$ (based on bulk velocity and inflow-duct height), where mean flow characteristics were first studied experimentally by Cherry, Elkins and Eaton (Intl J. Heat Fluid Flow, vol. 29, 2008, pp. 803–811) and later numerically by Ohlsson et al. (J. Fluid Mech., vol. 650, 2010, pp. 307–318). Coherent structures are educed by proper orthogonal decomposition (POD) of the flow, which together with time probes located in the flow domain are used to extract frequency information. The present study shows that the flow contains multiple phenomena, well separated in frequency space. Dominant large-scale frequencies in a narrow band $\mathit{St}\equiv fh/ {u}_{b} \in [0. 0092, 0. 014] $ (where $h$ is the inflow-duct height and ${u}_{b} $ is the bulk velocity), yielding time periods ${T}^{\ensuremath{\ast} } = T{u}_{b} / h\in [70, 110] $, are deduced from the time signal probes in the upper separated part of the diffuser. The associated structures identified by the POD are large streaks arising from a sinusoidal oscillating motion in the diffuser. Their individual contributions to the total kinetic energy, dominated by the mean flow, are, however, small. The reason for the oscillating movement in this low-frequency range is concluded to be the confinement of the flow in this particular geometric set-up in combination with the high Reynolds number and the large separated zone on the top diffuser wall. Based on this analysis, it is shown that the bulk of the streamwise root mean square (r.m.s.) value arises due to large-scale motion, which in turn can explain the appearance of two or more peaks in the streamwise r.m.s. value. The weak secondary flow present in the inflow duct is shown to survive into the diffuser, where it experiences an imbalance with respect to the upper expanding corners, thereby giving rise to the asymmetry of the mean separated region in the diffuser.

Aerodynamic sound generation in a pipe

1968 ◽  
Vol 32 (4) ◽  
pp. 765-778 ◽  
Author(s):  
H. G. Davies ◽  
J. E. Ffowcs Williams
Keyword(s):  
Acoustic Waves ◽  
Large Scale ◽  
Sound Field ◽  
Convective Motion ◽  
Energy Output ◽  
Small Scale ◽  
Mean Flow ◽  
Limited Region ◽  
Aerodynamic Sound ◽  
Scale Turbulence

The paper deals with the problem of estimating the sound field generated by a limited region of turbulence in an infinitely long, straight, hard-walled pipe. The field is analysed in a co-ordinate system moving with the assumed uniform mean flow, and the possibility of eddy convection relative to that reference system is considered. Large-scale turbulence is shown to induce plane acoustic waves of intensity proportional to the sixth power of flow velocity. The same is true of small-scale turbulence of low characteristic frequency. In both cases convective effects increase the acoustic output and distribute the bulk of the energy in a mode propagating upstream against the mean flow. Small-scale turbulence of higher frequency excites more modes, the sound increasing with very nearly the eighth power of velocity (U7.7) as soon as the second mode is excited. In the limit, when more than about 20 modes are excited, the energy output is unaffected by the constraint of the pipe walls, increasing with the eighth power of velocity, and being substantially amplified by convective motion.

scholarly journals Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170388 ◽  
Author(s):  
C. J. Cotter ◽  
G. A. Gottwald ◽  
D. D. Holm
Keyword(s):  
Large Scale ◽  
Particle Dynamics ◽  
Homogenization Theory ◽  
Small Scale ◽  
Mean Flow ◽  
Time Dynamics ◽  
Fluid Equations ◽  
Diffusive Limit ◽  
The Mean ◽  
Stochastic Fluid

In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. ( doi:10.1098/rspa.2014.0963 )), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

scholarly journals Statistical State Dynamics of Jet–Wave Coexistence in Barotropic Beta-Plane Turbulence

2016 ◽  
Vol 73 (5) ◽  
pp. 2229-2253 ◽  
Author(s):  
Navid C. Constantinou ◽  
Brian F. Farrell ◽  
Petros J. Ioannou
Keyword(s):  
Large Scale ◽  
Cooperative Interaction ◽  
Small Scale ◽  
Mean Flow ◽  
Theoretical Understanding ◽  
Laminar Jet ◽  
Planetary Scale ◽  
Statistical State ◽  
Beta Plane ◽  
Scale Turbulence

Abstract Jets coexist with planetary-scale waves in the turbulence of planetary atmospheres. The coherent component of these structures arises from cooperative interaction between the coherent structures and the incoherent small-scale turbulence in which they are embedded. It follows that theoretical understanding of the dynamics of jets and planetary-scale waves requires adopting the perspective of statistical state dynamics (SSD), which comprises the dynamics of the interaction between coherent and incoherent components in the turbulent state. In this work, the stochastic structural stability theory (S3T) implementation of SSD for barotropic beta-plane turbulence is used to develop a theory for the jet–wave coexistence regime by separating the coherent motions consisting of the zonal jets together with a selection of large-scale waves from the smaller-scale motions that constitute the incoherent component. It is found that mean flow–turbulence interaction gives rise to jets that coexist with large-scale coherent waves in a synergistic manner. Large-scale waves that would exist only as damped modes in the laminar jet are found to be transformed into exponentially growing waves by interaction with the incoherent small-scale turbulence, which results in a change in the mode structure, allowing the mode to tap the energy of the mean jet. This mechanism of destabilization differs fundamentally and serves to augment the more familiar S3T instabilities in which jets and waves arise from homogeneous turbulence with the energy source exclusively from the incoherent eddy field and provides further insight into the cooperative dynamics of the jet–wave coexistence regime in planetary turbulence.

scholarly journals On the impact of swirl on the growth of coherent structures

2014 ◽  
Vol 741 ◽  
pp. 156-199 ◽  
Author(s):  
K. Oberleithner ◽  
C. O. Paschereit ◽  
I. Wygnanski
Keyword(s):  
Stability Analysis ◽  
Coherent Structures ◽  
Large Scale ◽  
Vortex Breakdown ◽  
Shear Mode ◽  
Mean Flow ◽  
Swirling Jet ◽  
The Mean ◽  
The Impact ◽  
Helical Mode

AbstractSpatial linear stability analysis is applied to the mean flow of a turbulent swirling jet at swirl intensities below the onset of vortex breakdown. The aim of this work is to predict the dominant coherent flow structure, their driving instabilities and how they are affected by swirl. At the nozzle exit, the swirling jet promotes shear instabilities and, less unstable, centrifugal instabilities. The latter stabilize shortly downstream of the nozzle, contributing very little to the formation of coherent structures. The shear mode remains unstable throughout generating coherent structures that scale with the axial shear-layer thickness. The most amplified mode in the nearfield is a co-winding double-helical mode rotating slowly in counter-direction to the swirl. This gives rise to the formation of slowly rotating and stationary large-scale coherent structures, which explains the asymmetries in the mean flows often encountered in swirling jet experiments. The co-winding single-helical mode at high rotation rate dominates the farfield of the swirling jet in replacement of the co- and counter-winding bending modes dominating the non-swirling jet. Moreover, swirl is found to significantly affect the streamwise phase velocity of the helical modes rendering this flow as highly dispersive and insensitive to intermodal interactions, which explains the absence of vortex pairing observed in previous investigations. The stability analysis is validated through hot-wire measurements of the flow excited at a single helical mode and of the flow perturbed by a time- and space-discrete pulse. The experimental results confirm the predicted mode selection and corresponding streamwise growth rates and phase velocities.

Relaxation of Spatially Advancing Coherent Structures in a Turbulent Curved Channel Flow

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Koji Matsubara ◽  
Tomoya Ohishi ◽  
Keisuke Shida ◽  
Takahiro Miura
Keyword(s):  
Small Scale ◽  
Computational Domain ◽  
Mean Flow ◽  
Curved Channel ◽  
Concave Wall ◽  
Convex Wall ◽  
Mean Pressure ◽  
Coherent Vortex ◽  
The Mean ◽  
Scale Turbulence

A direct numerical simulation is made for the incompressible turbulent flow in the 180 deg curved channel with a long straight portion connected to its exit port. An examination is made for how the organized coherent vortex grows and decays in the curved channel: the radius ratio of 0.92, the aspect ratio of 7.2, and the succeeding straight section length of 75 times the channel half width. The 1552 × 91 × 128 ( = 18,427,136) grids are allocated to the computational domain. The frictional-velocity-based Reynolds number is kept at 150 to resolve the long domain including curved and straight regions. In contrast to that the coherent vortex grows along the concave wall, the vortex remains strong in the convex-wall side after the curvature accompanying a tail of the small-scale turbulence near the convex wall. The dissimilarity between the onset and disappearing of the coherent vortex essentially comes from the mean pressure gradient, which aids or averts the near-wall fluid oppositely between the curvature inlet and the exit. The mean flow is decelerated near the inlet of the convex wall to destabilize the flow and to trigger the onset of the coherent vortex. Contrary, the mean flow is accelerated near the exit of the convex wall to weaken the coherent vortex, and is decelerated near the exit of the concave wall to enhance the turbulence. Therefore, the turbulence enhancement and attenuation occurs oppositely between the inlet and exit of the curvature, and the coherent vortex draws a wake in the convex-side rather than the concave-side where it starts.

Measurements of Velocity Wave Forms in the Dog Aorta

1976 ◽  
Vol 98 (2) ◽  
pp. 297-304 ◽  
Author(s):  
K. M. Kiser ◽  
H. L. Falsetti ◽  
K. H. Yu ◽  
M. R. Resitarits ◽  
G. P. Francis ◽  
...  
Keyword(s):  
Reverse Flow ◽  
Small Scale ◽  
Mean Flow ◽  
Developed Turbulence ◽  
Before And After ◽  
Wave Forms ◽  
The Mean ◽  
Scale Turbulence ◽  
Hot Film ◽  
The Waves

Hot film needle and catheter probes were used to measure the velocity waves in the dog aorta between the aortic valve and the iliac bifurcation. The forms of the waves were found to be of two types, those in which there was a reverse flow, following systole, everywhere along the centerline of the aorta and those for which there was no flow reversal in the regions below the diaphragm. Energy spectra were measured before and after the administration of a cardiac stimulant. Except for a shift to higher frequencies, no significant change in the form of the spectra was observed. Characteristic times developed for the mean flow and the decay of a fully developed turbulence suggest that it is difficult to sustain small scale turbulence which might be initiated during peak systole.

scholarly journals Structure and Spacing of Jets in Barotropic Turbulence

2007 ◽  
Vol 64 (10) ◽  
pp. 3652-3665 ◽  
Author(s):  
Brian F. Farrell ◽  
Petros J. Ioannou
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Small Scale ◽  
Mean Flow ◽  
Structure Amplitude ◽  
Large Spatial Scale ◽  
Zonal Jets ◽  
Development Processes ◽  
Scale Turbulence ◽  
Jet Structure

Abstract Turbulent flows are often observed to be organized into large-spatial-scale jets such as the familiar zonal jets in the upper levels of the Jovian atmosphere. These relatively steady large-scale jets are not forced coherently but are maintained by the much smaller spatial- and temporal-scale turbulence with which they coexist. The turbulence maintaining the jets may arise from exogenous sources such as small-scale convection or from endogenous sources such as eddy generation associated with baroclinic development processes within the jet itself. Recently a comprehensive theory for the interaction of jets with turbulence has been developed called stochastic structural stability theory (SSST). In this work SSST is used to study the formation of multiple jets in barotropic turbulence in order to understand the physical mechanism producing and maintaining these jets and, specifically, to predict the jet amplitude, structure, and spacing. These jets are shown to be maintained by the continuous spectrum of shear waves and to be organized into stable attracting states in the mutually adjusted mean flow and turbulence fields. The jet structure, amplitude, and spacing and the turbulence level required for emergence of jets can be inferred from these equilibria. For weak but supercritical turbulence levels the jet scale is determined by the most unstable mode of the SSST system and the amplitude of the jets at equilibrium is determined by the balance between eddy forcing and mean flow dissipation. At stronger turbulence levels the jet amplitude saturates with jet spacing and amplitude satisfying the Rayleigh–Kuo stability condition that implies the Rhines scale. Equilibrium jets obtained with the SSST system are in remarkable agreement with equilibrium jets obtained in simulations of fully developed β-plane turbulence.

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