Nature of laminar-turbulence intermittency in shear flows

Characteristics of Turbulence in the Downstream Region of a Vegetation Patch

In presence of vegetation patches in a channel bed, different flow–morphology interactions in the river will result. The investigation of the nature and intensity of these structures is a crucial part of the research works of river engineering. In this experimental study, the characteristics of turbulence in the non-developed region downstream of a vegetation patch suffering from a gradual fade have been investigated. The changes in turbulent structure were tracked in sequential patterns by reducing the patch size. The model vegetation was selected carefully to simulate the aquatic vegetation patches in natural rivers. Velocity profile, TKE (Turbulent Kinetic Energy), turbulent power spectra and quadrant analysis have been used to investigate the behavior and intensity of the turbulent structures. The results of the velocity profile and TKE indicate that there are three different flow layers in the region downstream of the vegetation patch, including the wake layer, mixing layer and shear layer. When the vegetation patch is wide enough (Dv/Dc > 0.5, termed as the patch width ratio, where Dv is the width of a vegetation patch and Dc is the width of the channel), highly intermittent anisotropic turbulent events appear in the mixing layer at the depth of z/Hv = 0.7~1.1 and distance of x/Hv = 8~12 (where x is streamwise distance from the patch edge, z is vertical distance from channel bed and Hv is the height of a vegetation patch). The results of quadrant analysis show that these structures are associated with the dominance of the outward interactions (Q1). Moreover, these structures accompany large coherent Reynolds shear stresses, anomalies in streamwise velocity, increases in the standard deviation of TKE and increases in intermittent Turbulent Kinetic Energy (TKEi). The intensity and extents of these structures fade with the decrease in the size of a vegetation patch. On the other hand, as the size of the vegetation patch decreases, von Karman vortexes appear in the wake layer and form the dominant flow structures in the downstream region of a vegetation patch.

Spatiotemporal Intermittency in Pulsatile Pipe Flow

Despite its importance in cardiovascular diseases and engineering applications, turbulence in pulsatile pipe flow remains little comprehended. Important advances have been made in the recent years in understanding the transition to turbulence in such flows, but the question remains of how turbulence behaves once triggered. In this paper, we explore the spatiotemporal intermittency of turbulence in pulsatile pipe flows at fixed Reynolds and Womersley numbers (Re=2400, Wo=8) and different pulsation amplitudes. Direct numerical simulations (DNS) were performed according to two strategies. First, we performed DNS starting from a statistically steady pipe flow. Second, we performed DNS starting from the laminar Sexl–Womersley flow and disturbed with the optimal helical perturbation according to a non-modal stability analysis. Our results show that the optimal perturbation is unable to sustain turbulence after the first pulsation period. Spatiotemporally intermittent turbulence only survives for multiple periods if puffs are triggered. We find that puffs in pulsatile pipe flow do not only take advantage of the self-sustaining lift-up mechanism, but also of the intermittent stability of the mean velocity profile.

Intermittency and Critical Scaling in Annular Couette Flow

The onset of turbulence in subcritical shear flows is one of the most puzzling manifestations of critical phenomena in fluid dynamics. The present study focuses on the Couette flow inside an infinitely long annular geometry where the inner rod moves with constant velocity and entrains fluid, by means of direct numerical simulation. Although for a radius ratio close to unity the system is similar to plane Couette flow, a qualitatively novel regime is identified for small radius ratio, featuring no oblique bands. An analysis of finite-size effects is carried out based on an artificial increase of the perimeter. Statistics of the turbulent fraction and of the laminar gap distributions are shown both with and without such confinement effects. For the wider domains, they display a cross-over from exponential to algebraic scaling. The data suggest that the onset of the original regime is consistent with the dynamics of one-dimensional directed percolation at onset, yet with additional frustration due to azimuthal confinement effects.

Inflow boundary conditions determine T-mixer efficiency

We report on a comprehensive experimental–computational study of a simple T-shaped mixer for Reynolds numbers up to 4000.

Relaminarization by Steady Modification of the Streamwise Velocity Profile in a Pipe

We show that a rather simple, steady modification of the streamwise velocity profile in a pipe can lead to a complete collapse of turbulence and the flow fully relaminarizes. Two different devices, a stationary obstacle (inset) and a device which injects fluid through an annular gap close to the wall, are used to control the flow. Both devices modify the streamwise velocity profile such that the flow in the center of the pipe is decelerated and the flow in the near wall region is accelerated. We present measurements with stereoscopic particle image velocimetry to investigate and capture the development of the relaminarizing flow downstream these devices and the specific circumstances responsible for relaminarization. We find total relaminarization up to Reynolds numbers of 6000, where the skin friction in the far downstream distance is reduced by a factor of 3.4 due to relaminarization. In a smooth straight pipe the flow remains completely laminar downstream of the control. Furthermore, we show that transient (temporary) relaminarization in a spatially confined region right downstream the devices occurs also at much higher Reynolds numbers, accompanied by a significant local skin friction drag reduction. The underlying physical mechanism of relaminarization is attributed to a weakening of the near-wall turbulence production cycle.

Laws of Resistance in Transitional Pipe Flows

As everyone knows who has opened a kitchen faucet, pipe flow is laminar at low flow velocities and turbulent at high flow velocities. At intermediate velocities, there is a transition wherein plugs of laminar flow alternate along the pipe with "flashes" of a type of fluctuating, nonlaminar flow that remains poorly understood. In the 19th century, Osborne Reynolds sought to connect these states of flow with quantitative "laws of resistance," whereby the fluid friction is determined as a function of the Reynolds number. While he succeeded for laminar and turbulent flows, the laws for transitional flows eluded him and remain unknown to this day. By properly distinguishing between laminar plugs and flashes in the transitional regime, we show experimentally and numerically that the law of resistance for laminar plugs corresponds to the laminar law and the law of resistance for flashes is identical to that of turbulence.

Streamwise decay of localized states in channel flow

Channel flow, the pressure driven flow between parallel plates, has exact coherent structures that show various degrees of localization. For states which are localized in streamwise direction but extended in spanwise direction, we show that they are exponentially localized, with decay constants that are different on the upstream and downstream sides. We extend the analysis of Brand and Gibson [J. Fluid Mech. 750, R1 (2014)]JFLSA70022-112010.1017/jfm.2014.285 for stationary states to the case of advected structures that is needed here, and derive expressions for the decay in terms of eigenvalues and eigenfunctions of certain second order differential equations. The results are in very good agreement with observations on exact coherent structures of different transversal wavelengths.

Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states

In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is "extensive" in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.

Study of the instability of the Poiseuille flow using a thermodynamic formalism

The stability of the plane Poiseuille flow is analyzed using a thermodynamic formalism by considering the deterministic Navier-Stokes equation with Gaussian random initial data. A unique critical Reynolds number, Rec ≈ 2,332, at which the probability of observing puffs in the solution changes from 0 to 1, is numerically demonstrated to exist in the thermodynamic limit and is found to be independent of the noise amplitude. Using the puff density as the macrostate variable, the free energy of such a system is computed and analyzed. The puff density approaches zero as the critical Reynolds number is approached from above, signaling a continuous transition despite the fact that the bifurcation is subcritical for a finite-sized system. An action function is found for the probability of observing puffs in a small subregion of the flow, and this action function depends only on the Reynolds number. The strategy used here should be applicable to a wide range of other problems exhibiting subcritical instabilities.