The effects of global flow rotation and curvature on the subcritical transition to turbulence in shear flows are examined. The relevant time-scales of the problem are identified by a decomposition of the flow into a laminar and a deviation from laminar parts, which is performed for rotating plane Couette and Taylor-Couette flows. The usefulness and relevance of this procedure are discussed at the same time. By comparing the self-sustaining process time-scale to the time-scales previously identified, an interpretation is brought to light for the behavior of the transition Reynolds number with the rotation number and relative gap width in the whole neighborhood (in parameter space) of the non-rotating plane Couette flow covered by the available data.
Transition to turbulence in straight pipes occurs in spite of the linear stability of the laminar Hagen--Poiseuille flow if the amplitude of flow perturbations as well as the Reynolds number exceed a minimum threshold (subcritical transition). As the pipe curvature increases centrifugal effects become important, modifying the basic flow as well as the most unstable linear modes. If the curvature (tube-to-coiling diameter $d/D$) is sufficiently large a Hopf bifurcation (supercritical instability) is encountered before turbulence can be excited (subcritical instability). We trace the instability…
The possibility of subcritical behaviour in the geostrophic turbulence regime of rapidly rotating thermally driven convection is explored. In this regime a non-local inverse energy transfer may compete with the more traditional and local direct cascade. We show that, even for control parameters for which no inverse cascade has previously been observed, a subcritical transition towards a large-scale vortex state can occur when the system is initialized with a vortex dipole of finite amplitude. This new example of bistability in a turbulent flow, which may not be specific to rotating convection,…
We present a new experimental set-up that creates a shear flow with zero mean advection velocity achieved by counterbalancing the nonzero streamwise pressure gradient by moving boundaries, which generates plane Couette-Poiseuille flow. We carry out the first experimental results in the transitional regime for this flow. Using flow visualization we characterize the subcritical transition to turbulence in Couette-Poiseuille flow and show the existence of turbulent spots generated by a permanent perturbation. Due to the zero mean advection velocity of the base profile, these turbulent structures …
We demonstrate that the nonlinear optimisation of a finite-amplitude disturbance over a freely evolving and possibly even turbulent flow, can successfully identify subcritical dynamo branches as well as the structure and amplitude of their critical perturbations. As this approach does not require prior knowledge of the magnetic field amplification mechanisms, it opens a new avenue for systematically probing subcritical dynamo flows.
Drag reduction and subcritical turbulence in controlled pipe flows
Politecnico di Milano（米兰理工大学）；Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille（里尔大学、法国国家科学研究中心、法国航空发展局、巴黎国立高等工艺学院、里尔中央理工学院）；Massachusetts Institute of Technology（麻省理工学院）
In wall-bounded flows, the laminar regime remain linearly stable up to large values of the Reynolds number while competing with nonlinear turbulent solutions issued from finite amplitude perturbations. The transition to turbulence of plane channel flow (plane Poiseuille flow) is more specifically considered via numerical simulations. Previous conflicting observations are reconciled by noting that the two-dimensional directed percolation scenario expected for the decay of turbulence may be interrupted by a symmetry-breaking bifurcation favoring localized turbulent bands. At the other end of the…
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…
This work studies the effects of skin-friction drag reduction in a turbulent flow over a curved wall, with a view to understanding the relationship between the reduction of friction and changes to the total aerodynamic drag. Direct numerical simulations (DNS) are carried out for an incompressible turbulent flow in a channel where one wall has a small bump; two bump geometries are considered, that produce mildly separated and attached flows. Friction drag reduction is achieved by applying streamwise-travelling waves of spanwise velocity (StTW). The local friction reduction produced by the StTW …
Direct numerical simulations (DNS) of particle-laden turbulent flow in straight, mildly curved and strongly bent pipes are performed in which the solid phase is modelled as small heavy spherical particles. A total of seven populations of dilute particles with different Stokes numbers, one-way coupled with their carrier phase, are simulated. The objective is to examine the effect of the curvature on micro-particle transport and accumulation. It is shown that even a slight non-zero curvature in the flow configuration strongly impact the particle concentration map such that the concentration of i…
The subcritical transition to turbulence, as occurs in pipe flow, is believed to generically be a phase transition in the directed percolation universality class. At its heart is a balance between the decay rate and proliferation rate of localized turbulent structures, called puffs in pipe flow. Here we propose the first-ever dynamical mechanism for puff proliferation -- the process by which a puff splits into two. In the first stage of our mechanism, a puff expands into a slug. In the second stage, a laminar gap is formed within the turbulent core. The notion of a split-edge state, mediating …
The swirling secondary flow in curved pipes is studied in three-space dimensions using a weakly compressible Smoothed Particle Hydrodynamics (WCSPH) formulation coupled to new non-reflecting outflow boundary conditions. A large-eddy simulation (LES) model for turbulence is benchmarked with existing experimental data. After validation of the present model against experimental results for a 90 grades pipe bend, a detailed numerical study aimed at reproducing experimental flow measurements for a wide range of Reynolds numbers has been performed for different pipe geometries, including U pipe bend…
For channel flow at subcritical Reynolds numbers ($Re<5772$), a laminar-to-turbulent transition can emerge due to a large transient amplification in the kinetic energy of small perturbations, resulting in an increase in drag at the walls. The objectives of the present study are three-fold: (1) to study the nonlinear effects on transient energy growth, (2) to design a feedback control strategy to prevent this subcritical transition, and (3) to examine the control mechanisms that enable transition suppression. We investigate transient energy growth of linear optimal disturbance in plane Poiseuil…
Abrupt transitions to the state of thermoacoustic instability (TAI) in gas turbine combustors are a significant challenge plaguing the development of next-generation low-emission aircraft and power generation engines. In this paper, we present the observation of abrupt transition in three disparate turbulent thermoacoustic systems: an annular combustor, a swirl-stabilized combustor, and a preheated bluff-body stabilized combustor. Using a low-order stochastic thermoacoustic model, we show that the reported abrupt transitions occur when an initially stable, supercritical limit cycle becomes uns…
The transition to turbulence in Taylor-Couette flow often occurs via a sequence of supercritical bifurcations to progressively more complex, yet stable, flows. We describe a subcritical laminar-turbulent transition in the counter-rotating regime mediated by an unstable intermediate state in a system with an axial aspect ratio of $Γ=5.26$ and a radius ratio of $η=0.905$. In this regime, flow visualization experiments and numerical simulations indicate the intermediate state corresponds to an aperiodic flow featuring interpenetrating spirals. Furthermore, the reverse transition out of turbulence…
The transition to turbulence in a precessing cylindrical vessel is experimentally investigated. Our measurements are performed for a { nearly-resonant} configuration with an initially laminar flow dominated by an inertial mode with azimuthal wave number $m=1$ superimposed on a solid body rotation. By increasing the precession ratio, we observe a transition from the laminar to a non-linear regime, which then breakdowns to turbulence for larger precession ratio. Our measurements show that the transition to turbulence is subcritical, with a discontinuity of the wall-pressure and the power consump…
In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude perturbations can lead to sustained turbulence. We explore the general problem of characterizing how and when the transition from near-laminar states to sustained turbulence occurs; a model of the interchange instability being used as a concrete example. These questions are fundamentally nonlinear, and the answers must go beyond the linear transient amplificatio…
Isolated patches of turbulence in transitional straight pipes are sustained by a strong instability at their upstream front, where the production of turbulent kinetic energy (TKE) is up to five times higher than in the core. Direct numerical simulations presented in this paper show no evidence of such strong fronts if the pipe is bent. We examine the temporal and spatial evolution of puffs and slugs in a toroidal pipe with pipe-to-torus diameter ratio $δ= D/d = 0.01$ at several subcritical Reynolds numbers. Results show that the upstream overshoot of TKE production is at most one-and-a-half ti…
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…
This paper aims at extending the code verification methodology to high-order accurate scheme implementations on curved wall-bounded domains as well as for realistic turbulent flows such as the flat plate boundary layer modelled by the Reynolds-averaged Navier-Stokes (RANS) equations. Two new manufactured solutions (MSs) are introduced with demonstrated ability to verify the treatment of slip and no-slip boundary conditions in high-order frameworks on curved domains. These MSs serve as well to discuss the impact of the method of computation of boundary normals on the order of accuracy (OOA) of …
When subcritical shear flows transition to turbulence, laminar and turbulent flow often coexists in space, giving rise to turbulent-laminar patterns. Most prominent are regular stripe patterns with large-scale periodicity and oblique orientation. Oblique stripes are a robust phenomenon, observed in experiments and flow simulations, yet their origin remains unclear. We demonstrate the existence of an invariant equilibrium solution of the fully nonlinear 3D Navier-Stokes equations that resembles the oblique pattern of turbulent-laminar stripes in plane Couette flow. We uncover the origin of the …
Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a spatial modulation of the turbulent flow, due to a linear instability. We sample over many realizations the linear response of the fluctuating turbulent field to a temporal impulse, in the regime where the turbulent flow is stable, just before the onset of the instability. The dispersion relation is constructed from the ensemble-averaged relaxation rates. As the…
The proliferation of turbulence in subcritical wall-bounded shear flows involves spatially localised coherent structures. Turbulent spots correspond to finite-time nonlinear responses to pointwise disturbances and are regarded as seeds of turbulence during transition. The rapid spatial decay of the turbulent fluctuations away from a spot is accompanied by large-scale flows with a robust structuration. The far field velocity field of these spots is investigated numerically using spectral methods in large domains in four different flow scenarios (plane Couette, plane Poiseuille, Couette-Poiseuil…
The link to the online abstract of this manuscript, accepted in Phys. Rev. Fluids, is https://journals.aps.org/prfluids/accepted/32074S4aH8b1c608e19768b42571f9001086a3f44. A subcritical route to turbulence via purely quasi-two-dimensional mechanisms, for a quasi-two-dimensional system composed of an isolated exponential boundary layer, is numerically investigated. Exponential boundary layers are highly stable, and are expected to form on the walls of liquid metal coolant ducts within magnetic confinement fusion reactors. Subcritical transitions were detected only at weakly subcritical Reynolds…
Planetary cores consist of liquid metals (low Prandtl number $Pr$) that convect as the core cools. Here we study nonlinear convection in a rotating (low Ekman number $Ek$) planetary core using a fully 3D direct numerical simulation. Near the critical thermal forcing (Rayleigh number $Ra$), convection onsets as thermal Rossby waves, but as the $Ra$ increases, this state is superceded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are smoothly connected. As the planetary core rotates faster, the smooth transition is…
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA（美国加州理工学院工程与应用科学系）
We apply Fourier neural operators (FNOs), a state-of-the-art operator learning technique, to forecast the temporal evolution of experimentally measured velocity fields. FNOs are a recently developed machine learning method capable of approximating solution operators to systems of partial differential equations through data alone. The learned FNO solution operator can be evaluated in milliseconds, potentially enabling faster-than-real-time modeling for predictive flow control in physical systems. Here we use FNOs to predict how physical fluid flows evolve in time, training with particle image v…
The Dynamic Mode Decomposition (DMD) is a Koopman-based algorithm that straightforwardly isolates individual mechanisms from the compound morphology of direct measurement. However, many may be perplexed by the messages the DMD structures carry. This work investigates the modal implications of the DMD/Koopman modes through the prototypical subcritical free-shear flow over a square prism. It selected and analysed the fluid mechanics and phenomenology of the ten most dominant modes. The results showed that the reduced-order description is morphologically accurate and physically insightful. Mode 1…
Transition to the ultimate regime of turbulent convection in stratified inclined duct flow
University of Twente（特温特大学）；Imperial College（帝国理工学院）；University of Rome ‘Tor Vergata’（罗马托维加塔大学）；Gran Sasso Science Institute（格兰萨索科学研究所）；Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）
The dynamics, structure and stability of zonal jets in planetary flows are still poorly understood, especially in terms of coupling with the small-scale turbulent flow. Here, we use an experimental approach to address the questions of zonal jets formation and long-term evolution. A strong and uniform topographic $β$-effect is obtained inside a water-filled rotating tank thanks to the paraboloidal fluid free upper surface combined with a specifically designed bottom plate. A small-scale turbulent forcing is performed by circulating water through the base of the tank. Time-resolving PIV measurem…
Direct Numerical Simulation of turbulent Taylor-Couette flow
本文描述了完全湍流状态下Taylor-Couette流动的直接数值模拟（DNS）。数值方法扩展了Quadrio和Luchini（Eur. J. Mech. B / Fluids，v.21，pp.413--427，2002），并且基于使用混合空间离散化（均匀方向上的谱方案，以及径向方向上的四阶、紧凑显式有限差分方案）的并行计算机代码。本文首次用DNS方法模拟了湍流状态下的Taylor-Couette流动。统计量的计算，以补充现有的实验信息，以期比较它的平面，压力驱动的湍流在相同的雷诺数值。平面流和曲壁流之间的流量统计差异的主要来源是由于曲率效应产生的大规模旋转结构的存在。
Imperial College London（帝国理工学院）；The Alan Turing Institute（艾伦·图灵研究所）；Delft University of Technology（代尔夫特理工大学）
The dynamics of a turbulent flow tend to occupy only a portion of the phase space at a statistically stationary regime. From a dynamical systems point of view, this portion is the attractor. The knowledge of the turbulent attractor is useful for two purposes, at least: (i) We can gain physical insight into turbulence (what is the shape and geometry of the attractor?), and (ii) it provides the minimal number of degrees of freedom to accurately describe the turbulent dynamics. Autoencoders enable the computation of an optimal latent space, which is a low-order representation of the dynamics. If …
This is the second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number $\textbf{Re}$. In this work, we show that there is constant $0 < c_0 \ll 1$, independent of $\textbf{Re}$, such that sufficiently regular disturbances of size $ε\lesssim \textbf{Re}^{-2/3-δ}$ for any $δ> 0$ exist at least until $t = c_0ε^{-1}$ and in general evolve to be $O(c_0)$ due to the lift-up effect. Further, after times $t \gtrsim \textbf{Re}^{1/3}$, the streamwise dependence of the solution is rapidly diminishe…
