Lower branch coherent states in plane Couette flow have an asymptotic structure that consists of O(1) streaks, $O(R^{-1})$ streamwise rolls and a weak sinusoidal wave that develops a critical layer, for large Reynolds number $R$. Higher harmonics become negligible. These unstable lower branch states appear to have a single unstable eigenvalue at all Reynolds numbers. These results suggests that the lower branch coherent states control transition to turbulence and that they may be promising targets for new turbulence prevention strategies.
We investigate the flow evolution of a linear and a branched wormlike micellar solution with matched rheology in a Taylor-Couette (TC) cell using a combination of particle-tracking velocimetry, birefringence, and turbidity measurements. Both solutions exhibit a stress plateau within a range of shear rates. Under startup of a steady shear rate flow within the stress plateau, both linear and branched samples exhibit strong transient shear thinning flow profiles. However, while the flow of the linear solution evolves to a banded structure at longer times, the flow of the branched solution transit…
We study the morphology of Eulerian vortical structures and their interaction with density interfaces in increasingly turbulent stably-stratified shear layers. We analyse the three-dimensional, simultaneous velocity and density fields obtained in the stratified inclined duct laboratory experiment. We track, across 15 datasets, the evolution of coherent structures from pre-turbulent Holmboe waves, through intermittent turbulence, to full turbulence and mixing. We use the Rortex--Shear decomposition of the vorticity field into a pure rotational part (the rortex vector), and a non-rotational part…
The cascade of energy in turbulent flows, i.e., the transfer of kinetic energy from large to small flow scales or vice versa (backward cascade), is the cornerstone of most theories and models of turbulence since the 1940s. Yet, understanding the spatial organisation of kinetic energy transfer remains an outstanding challenge in fluid mechanics. Here, we unveil the three-dimensional structure of the energy cascade across the shear-dominated scales using numerical data of homogeneous shear turbulence. We show that the characteristic flow structure associated with the energy transfer is a vortex …
Exact coherent states of a linearly stable, plane parallel shear flow confined between stationary stress-free walls and driven by a sinusoidal body force (a flow first introduced by F. Waleffe, Phys. Fluids 9, 883 (1997)) are computed using equations obtained from a large Reynolds-number asymptotic reduction of the Navier-Stokes equations. The reduced equations employ a decomposition into streamwise-averaged (mean) and streamwise-varying (fluctuation) components and are characterized by an effective order one Reynolds number in the mean equations along with a formally higher-order diffusive re…
We consider turbulence in a stratified 'Kolmogorov' flow, driven by horizontal shear in the form of sinusoidal body forcing in the presence of an imposed background linear stable stratification in the third direction. This flow configuration allows the controlled investigation of the formation of coherent structures, which here organise the flow into horizontal layers by inclining the background shear as the strength of the stratifica- tion is increased. By numerically converging exact steady states from direct numerical simulations of chaotic flow, we show, for the first time, a robust connec…
Recent field experiments conducted in the near-wake (up to 0.5 rotor diameters downwind of the rotor) of a 2.5 MW wind turbine using snow-based super-large-scale particle image velocimetery (SLPIV) (Hong et al., Nature Comm., vol. 5, 2014, no. 4216) were successful in visualizing tip vortex cores as areas devoid of snowflakes. The so-visualized snow voids, however, suggested tip vortex cores of complex shape consisting of circular cores with distinct elongated comet-like tails. We employ large-eddy simulation (LES) to elucidate the structure and dynamics of the complex tip vortices identified …
Unstable equilibrium solutions in a homogeneous shear flow with sinuous symmetry are numerically found in large-eddy simulations (LES) with no kinetic viscosity. The small-scale properties are determined by the mixing length scale $l_S$ used to define eddy viscosity, and the large-scale motion is induced by the mean shear at the integral scale, which is limited by the spanwise box dimension $L_z$. The fraction $ R_S= L_z/l_S$, which plays the role of a Reynolds number, is used as a numerical continuation parameter. It is shown that equilibrium solutions appear by a saddle-node bifurcation as $…
Nonhelical shear dynamos are studied with a particular focus on the possibility of coherent dynamo action. The primary results -- serving as a follow up to the results of Squire & Bhattacharjee [arXiv:1506.04109 (2015)] -- pertain to the "magnetic shear-current effect" as a viable mechanism to drive large-scale magnetic field generation. This effect raises the interesting possibility that the saturated state of the small-scale dynamo could drive large-scale dynamo action, and is likely to be important in the unstratified regions of accretion disk turbulence. In this paper, the effect is studie…
This paper examines the mechanisms of coherent structure interactions in spatially evolving turbulent free shear layers at different values of the velocity ratio parameter λ=$(U_1-U_2)/(U_1+U_2)$, where $U_1$ and $U_2 (\leq U_1)$ are the free stream velocities on either side of the layer. The study employs the point-vortex (or vortex-gas) model presented in part I (arXiv:1509.00603) which predicts spreading rates that are in the close neighborhood of results from most high Reynolds number experiments and 3D simulations. The present (2D) simulations show that the well-known steep-growth merger …
A shear flow of liquid metal (Galinstan) is driven in an annular channel by counter-rotating traveling magnetic fields imposed at the endcaps. When the traveling velocities are large, the flow is turbulent and its azimuthal component displays random reversals. Power spectra of the velocity field exhibit a $1/f^α$ power law on several decades and are related to power-law probability distributions $P(τ)\simτ^{-β}$ of the waiting times between successive reversals. This $1/f$ type spectrum is observed only when the Reynolds number is large enough. In addition, the exponents $α$ and $β$ are contro…
This article discusses the description of wall-bounded turbulence as a deterministic high-dimensional dynamical system of interacting coherent structures, defined as eddies with enough internal dynamics to behave relatively autonomously from any remaining incoherent part of the flow. The guiding principle is that randomness is not a property, but a methodological choice of what to ignore in the flow, and that a complete understanding of turbulence, including the possibility of control, requires that it be kept to a minimum. After briefly reviewing the underlying low-order statistics of flows a…
We examine how known unstable equilibria of the Navier-Stokes equations in plane Couette flow adapt to the presence of an imposed stable density difference between the two boundaries for varying values of the Prandtl number $Pr$, the ratio of viscosity to density diffusivity, and fixed moderate Reynolds number, $Re=400$. In the two asymptotic limits $Pr \to 0$ and $Pr \to \infty$, it is found that such solutions exist at arbitrarily high bulk stratification but for different physical reasons. In the $Pr \to 0$ limit, density variations away from a constant stable density gradient become vanish…
Richtmyer-Meshkov instability (RMI) plays an important role in many areas of science and engineering, from supernovae and fusion to scramjets and nano-fabrication. Classical Richtmyer-Meshkov instability is induced by a steady shock and impulsive acceleration, whereas in realistic environments the acceleration is usually variable. We focus on RMI induced by acceleration with power-law time-dependence and apply group theory to solve the long-standing problem. For early-time dynamics, we find the dependence of the growth-rate on the initial conditions and show that it is independent of the accel…
We study aqueous xanthan solutions at shear rates up to about 105 s-1. At these shear rates, the salt-free solutions show a second Newtonian branch. Depending on the xanthan concentration, we find two different regimes with scaling laws well-known for the zero viscosity of dilute and semidilute particle solutions: The crossover concentration is considerably higher than in the first Newtonian branch, which can be related to the orientation of the polyelectrolytes. In the second regime, the normal stress differences increase with an exponent of about 1, indicating that the polymer solution behav…
The role of instability in the growth of a 2D, temporally evolving, `turbulent' free shear layer is analyzed using vortex-gas simulations that condense all dynamics into the kinematics of the Biot-Savart relation. The initial evolution of perturbations in a constant-vorticity layer is found to be in accurate agreement with the linear stability theory of Rayleigh. There is then a stage of non-universal evolution of coherent structures that is closely approximated not by Rayleigh stability theory, but by the Karman-Rubach-Lamb linear instability of monopoles, until the neighboring coherent struc…
We present a numerical investigation of three-dimensional, short-wavelength linear instabilities in Kelvin-Helmholtz (KH) vortices in homogeneous and stratified environments. The base flow, generated using two-dimensional numerical simulations, is characterized by the Reynolds number and the Richardson number defined based on the initial one-dimensional velocity and buoyancy profiles. The local stability equations are then solved on closed streamlines in the vortical base flow, which is assumed quasi-steady. For the unstratified case, the elliptic instability at the vortex core dominates at ea…
We study the development of coherent structures in local simulations of the magnetorotational instability in accretion discs in regimes of on-off intermittency. In a previous paper [Chian et al., Phys. Rev. Lett. 104, 254102 (2010)], we have shown that the laminar and bursty states due to the on-off spatiotemporal intermittency in a one-dimensional model of nonlinear waves correspond, respectively, to nonattracting coherent structures with higher and lower degrees of amplitude-phase synchronization. In this paper we extend these results to a three-dimensional model of magnetized Keplerian shea…
As a first step towards the asymptotic description of coherent structures in compressible shear flows, we present a description of nonlinear equilibrium solutions of the Navier--Stokes equations in the compressible asymptotic suction boundary layer (ASBL). The free-stream Mach number is assumed to be $< 0.8$ so that the flow is in the subsonic regime and we assume a perfect gas. We extend the large-Reynolds number free-stream coherent structure theory of \cite{deguchi_hall_2014a} for incompressible ASBL flow to describe a nonlinear interaction in a thin layer situated just below the free-strea…
Localised turbulent structures such as puffs or oblique stripes are building blocks of the intermittency regimes in subcritical wall-bounded shear flows. These turbulent structures are investigated in incompressible pressure-driven annular pipe flow using direct numerical simulations in long domains. For low enough radius ratio $η$, these coherent structures have a dynamics comparable to that of puffs in cylindrical pipe flow. For $η$ larger than 0.5, they take the shape of helical stripes inclined with respect to the axial direction. The transition from puffs to stripes is analysed statistica…
We propose a novel non-linear manifold learning from snapshot data and demonstrate its superiority over Proper Orthogonal Decomposition (POD) for shedding-dominated shear flows. Key enablers are isometric feature mapping, Isomap (Tenenbaum et al., 2000), as encoder and K-nearest neighbours (KNN) algorithm as decoder. The proposed technique is applied to numerical and experimental datasets including the fluidic pinball, a swirling jet, and the wake behind a couple of tandem cylinders. Analyzing the fluidic pinball, the manifold is able to describe the pitchfork bifurcation and the chaotic regim…
Coherent structures play an important role in the near-field of shear flows such as round jets. In the following the near-field of a round jet is numerically investigated , this for different initial conditions. Two configurations are considered one with a fully developed turbulence at the inlet, the other with an under developed turbulence. Calculations are carried out with a k-epsilon turbulence model but different sets of values for the constants inducing different level of diffusion within the flow. Finally, the results show that the presence of coherent structures in the near-field depend…
The asymptotic suction boundary layer (ASBL) is a parallel shear flow that becomes turbulent in a bypass transition in parameter regions where the laminar profile is stable. We here add a temperature gradient perpendicular to the plate and explore the interaction between convection and shear in determining the transition. We find that the laminar state becomes unstable in a subcritical bifurcation and that the critical Rayleigh number and wavenumber depend strongly on the Prandtl number. We also track several secondary bifurcations and identify states that are localized in two directions, show…
The vectoral wind structure of daytime atmospheric boundary layer (ABL) turbulence is strongly dependent on the balance between shear-driven turbulence production of horizontal fluctuations (driven by winds at the mesoscale), and buoyancy-driven turbulence production of vertical velocity fluctuations (driven by solar heating), characterized by the global instability state parameter $-z_i/L > 0$. In the fully shear-driven neutral limit $-z_i/L \rightarrow 0$, the surface layer is dominated by coherent streamwise-elongated concentrations of negative streamwise fluctuating velocity (low-speed str…
We briefly review the recent advances in the rheology of entangled polymers and identify emerging research trends and outstanding challenges, especially with respect to branched polymers. Emphasis is placed on the role of well-characterized model systems, as well as the synergy of synthesis-characterization, rheometry and modeling/simulations. The theoretical framework for understanding the observed linear and nonlinear rheological phenomena is the tube model which is critically assessed in view of its successes and shortcomings, whereas alternative approaches are briefly discussed. Finally, i…
Hairpin vortices are widely studied as an important structural aspect of wall turbulence. The present work describes, for the first time, nonlinear traveling wave solutions to the Navier--Stokes equations in the channel flow geometry -- exact coherent states (ECS) -- that display hairpin-like vortex structure. This solution family comes into existence at a saddle-node bifurcation at Reynolds number Re=666. At the bifurcation, the solution has a highly symmetric quasistreamwise vortex structure similar to that reported for previously studied ECS. With increasing distance from the bifurcation, h…
In shear flows at transitional Reynolds numbers, localized patches of turbulence, known as puffs, coexist with the laminar flow. Recently, Avila et al., Phys. Rev. Let. 110, 224502 (2013) discovered two spatially localized relative periodic solutions for pipe flow, which appeared in a saddle-node bifurcation at low speeds. Combining slicing methods for continuous symmetry reduction with Poincaré sections for the first time in a shear flow setting, we compute and visualize the unstable manifold of the lower-branch solution and show that it contains a heteroclinic connection to the upper branch …
Leveling of MHD turbulence imbalance in shear flows
Abastumani Astrophysical Observatory（阿巴斯图马尼天体物理观测站）；Department of Physics, Faculty of Exact and Natural Sciences, Tbilisi State University（第比利斯国立大学精确与自然科学学院物理系）；Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿-罗斯多夫亥姆霍兹中心）；M. Nodia Institute of Geophysics（M.诺迪亚地球物理研究所）
