Session H38: Flow Instability: Transition

Is there universal predator-prey dynamics at the laminar-turbulent phase transition?

Direct numerical simulation of pipe flow shows that transitional turbulence is dominated by two collective modes: a longitudinal mode for small-scale turbulent fluctuations whose anisotropy induces an emergent large-scale azimuthal mode (so-called zonal flow) that inhibits anisotropic Reynolds stress [1]. ~This activation-inhibition interaction leads to stochastic predator-prey-like dynamics, from which it follows that the transition to turbulence belongs to the directed percolation universality class [1]. ~~Here we show how predator-prey dynamics arises by deriving phenomenologically an effective field theory of the transition from a coarse-graining of the Reynolds equation. ~The rigorous mapping between the conserved currents in Rayleigh-Benard convection (RBC), Taylor-Couette and pipe flows [2] suggests that the zonal flow-turbulence scenario might occur in these systems, consistent with observations of zonal flows in two-dimensional RBC [3], and bursts of transitional turbulence in Couette flow that follow the critical scalings of directed percolation [4]. ~ [1] H.-Y. Shih et al., Nat. Phys. 12, 245 (2016). [2] B. Eckhardt et al., EPL 78, 24001 (2007). [3] D. Goluskin et al., J. Fluid Mech. 759, 360 (2014). [4] G. Lemoult et al., Nat. Phys. 12, 254 (2016).   

Flow structure in self-sustaining and intermittently turbulent reciprocating channel flow

The leading order terms in the Reynolds-averaged momentum equation are studied to better understand the underlying mechanism of transition to turbulence in reciprocating channel flow. The balance of the leading order terms confirms that fully-developed turbulence first emerges at the early phases in the decelerating portion of the cycle. The underlying mechanism of this transition appears to be the emergence of an internal layer that first develops during the late phases of the accelerating portion of the cycle. In the absence of this internal layer, the flow remains transitional over the entire cycle. The turbulent structure associated with the internal layer is investigated using different flow structure identification schemes. In particular, the Q-R criteria and the triple decomposition of the strain rate tensor.​   

Transitions to Turbulence in an Electromagnetically-Driven 2D Fluid

We present an experimental and numerical analysis of the transition to turbulence for a quasi-two-dimensional liquid. Our system is a Kolmogorov-like flow, realized as a Lorentz-forced thin fluid layer, which exhibits shearing-induced vortex pattern formation. The system dynamics are quantified using particle image velocimetry to create time-resolved velocity fields. We focus on the series of bifurcations leading to spatiotemporally chaotic behavior and quantitatively compare these results with simulations of an identical system to adjust system-specific parameters in accordance with first-principle modifications to the Navier-Stokes equations.   

Experiments on Laminar to Turbulence Transition and Relaminarization in Pulsatile Flows

Biological flows display laminar-turbulence-laminar transitions due to the cyclic nature of a beating heart. Addressing the question of how turbulence appears, decays and is suppressed in the cardiovascular system, particularly in the large arteries, is challenging due to flow unsteadiness, very complicated geometry and flow-wall interaction. In the present work we have designed and tested a facility to simulate unsteady pulsatile flows and the onset of transition under varying Reynolds and Womersley numbers. A moving piston is used to generate a flow pulsation and control the velocity amplitude. Time-Resolved Particle Image Velocimetry (TR-PIV) techniques were used to acquire velocity data on the plane of a CW laser illumination. Two different decompositions were applied to analyze the non-stationary and non-linear time-dependent data, the Empirical Mode Decomposition (EMD) and the Trend Removal Method (TRM). Two flow regimes were found, one in which the pulsatile flow exhibits phase-locked turbulence which is associated with the stabilizing effects of longitudinal straining during acceleration and a second where transition occurs very close to the wall while the core remains laminar.   

Routes to turbulence in the rotating disk boundary-layer of a rotor-stator cavity

The rotating disk is an important classical problem, due to the similarities between the 3D boundary layers on a disk and a swept aircraft wing. It is nowadays admitted that a direct transition to turbulence may exist through a steep-fronted nonlinear global mode located at the boundary between the locally connectively and absolutely unstable regions (Pier 2003; Viaud et al. 2008, 2011; Imayama et al. 2014 and others). However, recent studies (Healey 2010; Harris et al. 2012; Imayama et al. 2013) suggest that there may be an alternative route starting at lower critical Reynolds number, based on convective travelling waves but this scenario is still not fully validated and proven. To better characterize such transition, direct numerical simulations are performed in a closed cylindrical rotor-stator cavity (without hub) up to $Re=O(10^5)$. All boundaries are no slip and for the stable region around the rotation axis prevents the disturbances coming from the very unstable stator boundary to disturb the rotor boundary layer. Different transition scenarii to turbulence are investigated when the rotor boundary layer is forced at different positions and forcing amplitude. The associated dynamics of coherent structures in various flow regions are also investigated when increasing $Re$.   

Coherent structures in the asymptotic suction boundary layer over a heated plate

The asymptotic suction boundary layer over a heated plate [S. Zammert et al. arXiv:1605.06956] is a good point of entry to study the dynamics of thermal boundary layers by means of dynamical systems theory. We analyze the stability of this flow in dependence on the Reynolds, Rayleigh and Prandtl numbers and identify the bifurcating secondary solutions. It turns out that in contrast to the Rayleigh-B\'enard problem the base flow becomes unstable in a subcritical bifurcation. In the subcritcal range the secondary solutions are the starting point for a bifurcation cascade that creates a chaotic attractor. As in other subcritical flow, a boundary crisis bifurcation turns this attractor into a chaotic saddle causing transient chaotic motion in the subcritical range. We also calculate mean turbulent profiles and their scaling with the Rayleigh and Prandtl number. It turned out that the turbulent flow in the system is characterized by large-scale coherent structures which extend surprisingly far above the plate.   

Canonical Nonlinear Viscous Core Solution in pipe and elliptical geometry

In an earlier paper (Ozcakir et. al.(2016)), two new nonlinear traveling wave solutions were found with collapsing structure towards the center of the pipe as Reynolds number $R \rightarrow \infty$, which were called Nonlinear Viscous Core (NVC) states. Asymptotic scaling arguments suggested that the NVC state collapse rate scales as $R^{-1/4}$ where axial, radial and azimuthal velocity perturbations from Hagen-Poiseuille flow scale as $R^{-1/2}$, $R^{-3/4}$ and $R^{-3/4}$ respectively, while $(1-c)=O(R^{-1/2})$ where $c$ is the traveling wave speed. The theoretical scaling results were roughly consistent with full Navier-Stokes numerical computations in the range $10^{5} [Preview Abstract]

Patterns of the turbulent Taylor-Couette flow

We are interested in the study of the transition to turbulence in the Taylor-Couette flow, the flow between two independently rotating coaxial cylinders. Once the geometry is fixed, the flow is controlled by the inner and outer Reynolds numbers and present a large variety of flow regimes. In counter-rotation, the transition is characterized by a succession of more or less turbulent flow regimes: intermittency with turbulent spots, spiral turbulence, featureless turbulence. For larger values of the inner Reynolds number, turbulent Taylor roll re-emerge from the featureless turbulence and remain for very large values of the Reynolds numbers. Bifurcations between different turbulent rolls states are even observed in the ultimate turbulence regime. Nevertheless the transition from the featureless turbulence to the turbulent rolls still requires a detailed study and the mechanism which causes and sustains turbulent spots or turbulent spirals remains unknown. In this study we present new experimental information on the organization of the flow for the different regimes with turbulence. The experiments are conducted in a Taylor-Couette flow with $\eta = 0.8$. Stereo-Particle Image Velocimetry measurements and visualizations of the different flow regimes are realized and discussed.   

Perturbing turbulence beyond collapse

Wall-bounded turbulent flows are considered to be in principle stable against perturbations and persist as long as the Reynolds number is sufficiently high. We show for the example of pipe flow that a specific perturbation of the turbulent flow field disrupts the genesis of new turbulence at the wall. This leads to an immediate collapse of the turbulent flow and causes complete relaminarisation further downstream. The annihilation of turbulence is effected by a steady manipulation of the streamwise velocity component only, greatly simplifying control efforts which usually require knowledge of the highly complex three dimensional and time dependent velocity fields. We present several different control schemes from laboratory experiments which achieve the required perturbation of the flow for total relaminarisation. Transient growth, a linear amplification mechanism measuring the efficiency of eddies in redistributing shear that quantifies the maximum perturbation energy amplification achievable over a finite time in a linearized framework, is shown to set a clear-cut threshold below which turbulence is impeded in its formation and thus permanently annihilated.   

Stability and sensitivity analysis of experimental data for passive control of a turbulent wake

When the linear stability analysis is applied to the mean flow field past a bluff body, a quasi-marginally stable mode is identified, with a frequency very close to the real vortex shedding one. A formally consistent approach to justify this kind of analysis is based on a triple decomposition of the flow variables[1]. With this formalism, the adjoint-based sensitivity analysis can be extended to investigate passive controls of high-Reynolds-number wakes (e.g.[2]). The objective of the present work is to predict the effect of a small control cylinder on the vortex shedding frequency in a turbulent wake with an analysis which solely relies on PIV measurements available for the considered flow. The key ingredient of the numerical analysis is an ad-hoc tuned model for the mean flow field, built using an original procedure which includes all the experimental information available on the flow. This analysis is here applied to the wake flow past a thick porous plate at Reynolds numbers in the range between Re$=6.7\times10^3$ and Re=$5.3\times10^4$. It is shown that the derived control map agrees reasonably well with the equivalent map obtained experimentally. [1]Viola,F.,Iungo,G.V.,Camarri,S.,Gallaire,F.,J.FluidMech.750(R1),2014 [2]Meliga,P.,Pujals,G.,Serre,E.,Phys.Fluids24(061701),2012