The identification of stream in the straight pipe as a flexible rod has allowed to present the criterion expression for determination of transition of the laminar flow regime to the turbulent as a loss of stability of the rectilinear static structure of translational motion of stream in pipe and its transition to the flexural-vortical dynamic structure of translational motion, just as a flexible rod buckling. The introduced criterion allows to take into account an influencing of the inlet geometry, the pipe length, the flow velocity, and also of any physical factors on stability of the rectilinear flow structure. It is ascertained, that Reynolds number is the number of local hydrodynamic similarity and it is displayed that one is constituent part of the introduced stability criterion. The developed approach to a problem of stability is applicable for a problem solving on internal flow and external streamline.
In pipe, channel and boundary layer flows turbulence first occurs intermittently in space and time: at moderate Reynolds numbers domains of disordered turbulent motion are separated by quiescent laminar regions. Based on direct numerical simulations of pipe flow we here argue that the spatial intermittency has its origin in a nearest neighbor interaction between turbulent regions. We further show that in this regime turbulent flows are intrinsically intermittent with a well defined equilibrium turbulent fraction but without ever assuming a steady pattern. This transition scenario is analogous …
We demonstrate that the space-time statistics of the birth of turbulent spots in boundary layers can be reconstructed qualitatively from the average behavior of macroscopic measures in the transition zone. The conclusion in \cite{vg04} that there exists a connection between the patterns in laminar instability and the birth of turbulent spots is strengthened. We examine why the relationship between instability and transition to turbulence is manifest in some cases and appears to be totally absent in others. Novel cellular automaton type simulations of the transition zone are conducted, and the …
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, non-laminar flow which remains poorly known. We show experimentally that the fluid friction of flash flow is diagnostic of turbulence. We also show that the statistics of flash flow are in keeping with Kolmogorov's phenomenological theory of turbulence (so that, e.g., the energy spectra of both flash flow and turbulent …
We explore the laminar to turbulence transition of round jets at low Reynolds number (Re < 1000) using a novel experimental setup and linear stability theory (LST). The setup has a large domain and a low disturbance environment which increases the critical Re to approximately 500, permitting the appearance of a hitherto unknown puff-like instability (PFI). The instability is identified in the self-similar region of the jet through clean flow visualizations (FV) and further corroborated by particle image velocimetry (PIV) measurements. For 400< Re <700, the flow exhibits PFI embedded in a puff-…
We have confirmed numerically that a subcritical laminar-turbulence transition that belongs to directed percolation (DP) universality class occurs in a purely two-dimensional (2D) simple Navier-Stokes (NS) flow without any walls. The flow is called (extended) Kolmogorov flow which is governed by 2D NS equation in a doubly periodic box with a linear drag and a finite flow rate in the direction in which Galilean invariance is broken. We examine the mechanism of DP class transition focusing on the role of the additional control parameters: the drag coefficient and the flow rate. The drag kills co…
We demonstrate through numerical solutions of the Oldroyd-B model in a two-dimensional Taylor-Couette geometry that the onset of elastic turbulence in a viscoelastic fluid can be controlled by imposed shear-rate modulations. While for slow modulations elastic turbulence is still present, it vanishes for fast modulations and a laminar response with the Taylor-Couette base flow is recovered. We find that the transition from the laminar to the turbulent state is supercritical and occurs at a critical Deborah number. In the state diagram of both control parameters, Weissenberg versus Deborah numbe…
The impact of wall roughness on fully developed laminar pipe flow is investigated numerically. The roughness is comprised of square bars of varying size and pitch. Results show that the inverse relation between the friction factor and the Reynolds number in smooth pipes still persists in rough pipes, regardless of the rib height and pitch. At a given Reynolds number, the friction factor varies quadratically with roughness height and linearly with roughness pitch. We propose a single correlation for the friction factor that successfully collapses the data.
Turbulence in the flow of fluid through a pipe can be suppressed by buoyancy forces. As the suppression of turbulence leads to severe heat transfer deterioration, this is an important and undesirable phenomenon in both heating and cooling applications. Vertical flow is often considered, as the axial buoyancy force can help drive the flow. With heating measured by the buoyancy parameter $C$, our DNS show that shear-driven turbulence may either be completely laminarised or transitions to a relatively quiescent convection-driven state. Buoyancy forces cause a flattening of the base flow profile, …
Turbulence in fluids is an ubiquitous phenomenon, characterized by spontaneous transition of a smooth, laminar flow to rapidly changing, chaotic dynamics. In 1883, Reynolds experimentally demonstrated that, in an initially laminar flow of water, turbulent motions emerge without any measurable external disturbance. To this day, turbulence remains a major unresolved phenomenon in fluid mechanics; in particular, there is a lack of a mathematical model where turbulent dynamics emerge naturally from a laminar flow. Recently, we proposed a new theory of turbulence in gases, according to which turbul…
In this note we advocate the notion of variety as juxtaposed to the notion of complexity. Laminar flows are complex, turbulence is various. When the gradients reach a critical point, laminar flows are subjected to instabilities and transitions, sometime soft, sometime dramatic, and the final result is the variety. Turbulent flows in nature are fascinating, and loosely speaking we could say that a system is complex when differences are suffered, is various when diversities are enjoyed and exploited as opportunities.
Turbulent-laminar intermittency, typically in the form of bands and spots, is a ubiquitous feature of the route to turbulence in wall-bounded shear flows. Here we study the idealised shear between stress-free boundaries driven by a sinusoidal body force and demonstrate quantitative agreement between turbulence in this flow and that found in the interior of plane Couette flow -- the region excluding the boundary layers. Exploiting the absence of boundary layers, we construct a model flow that uses only four Fourier modes in the shear direction and yet robustly captures the range of spatiotempor…
The effect of slip surfaces on the laminar-turbulent separatrix of plane Poiseuille flow is studied by direct numerical simulation. Turbulence lifetimes, the likelihood that turbulence is sustained, is investigated for transitional flows with various slip lengths. Slip surfaces decrease the likelihood of sustained turbulence compared to the no-slip case, and likelihood is further decreased as slip length is increased. A deterministic analysis of the effects of slip surfaces on transition to turbulence is performed using nonlinear traveling wave solutions to the Navier-Stokes equations, also kn…
We study the turbulence transition of plane Couette flow in large domains where localised perturbations are observed to generate growing turbulent spots. Extending previous studies on the boundary between laminar and turbulent dynamics we determine invariant structures intermediate between laminar and turbulent flow. In wide but short domains we find states that are localised in spanwise direction, and in wide and long domains the states are also localised in downstream direction. These localised states act as critical nuclei for the transition to turbulence in spatially extended domains.
Suspended particles can alter the properties of fluids and in particular also affect the transition from laminar to turbulent flow. In the present experimental study, we investigate the impact of neutrally buoyant, spherical inertial particles on transition to turbulence in a pipe flow. At low particle concentrations, like in single phase Newtonian fluids, turbulence only sets in when triggered by sufficiently large perturbations and, as characteristic for this transition localized turbulent regions (puffs) co-exist with laminar flow. In agreement with earlier studies this transition point ini…
Plane Couette flow, the flow between two parallel planes moving in opposite directions, is an example of wall-bounded flow experiencing a transition to turbulence with an ordered coexistence of turbulent and laminar domains in some range of Reynolds numbers [R_g,R_t]. When the aspect-ratio is sufficiently large, this coexistence occurs in the form of alternately turbulent and laminar oblique bands. As R goes up trough the upper threshold R_t, the bands disappear progressively to leave room to a uniform regime of featureless turbulence. This continuous transition is studied here by means of und…
The velocity and friction properties of laminar pipe flow of a viscoelastic solution are bounded by the corresponding values for two Newtonian fluids, namely, the solvent and a fluid with a viscosity identical to the total viscosity of the solution. The lower friction factor for the flow of the solution when compared to the latter is tracked to an increased strain rate needed to enhance viscous dissipation. Lastly, we show analytically that the effective viscosity varies similarly to the radial diagonal component of the conformation tensor as observed numerically in turbulent flows, and give a…
Accurate prediction of the transition from laminar flow to turbulence remains an unresolved challenge despite its importance for understanding a variety of environmental, biological, and industrial phenomena. Well over a century of concerted effort has aimed toward a quantitative, mechanistic explanation of Osborne Reynolds' seminal observation of transition to turbulence in pipe flow, typically occurring when the ratio of inertial and viscous fluid dynamic forces -- the eponymous Reynolds number -- is approximately 2000. These studies have been confounded by subsequent observations that the R…
The nonlinear robustness of laminar plane Couette flow is considered under the action of in-phase spanwise wall oscillations by computing properties of the edge of chaos, i.e., the boundary of its basin of attraction. Three measures are used to quantify the chosen control strategy on laminar-to-turbulent transition: the kinetic energy of edge states (local attractors on the edge of chaos), the form of the minimal seed (least energetic perturbation on the edge of chaos), and the laminarization probability (the probability that a random perturbation from the laminar flow of given kinetic energy …
We report frictional drag reduction and a complete flow re-laminarization of elastic turbulence (ET) at vanishing inertia in a viscoelastic channel flow past an obstacle. We show that intensity of observed elastic waves and wall-normal vorticity correlate well with the measured drag above the ET onset. Moreover, we find that the elastic wave frequency grows with Weissenberg number, and at sufficiently high frequency it causes decay of the elastic waves, resulting in ET attenuation and drag reduction. Thus, this allows us to substantiate a physical mechanism, involving interaction of elastic wa…
Recent experiments indicated that polymers can reduce the turbulent drag beyond the asymptotic limit known as the MDR, leading to a laminar flow. In this Letter, we show through direct numerical simulations that, when the MDR is exceeded, the flow can remain in a laminar-like regime for a very long period without being truly laminar. During this period called pseudo-laminar state, a transient behavior is observed as a consequence of a small rate of polymer energy injected into the flow. Later on, flow instabilities develop across the channel, finally triggering elastoinertial turbulence.
The fluctuations of turbulence intensity in a pipe flow around the critical Reynolds number is difficult to study but important because they are related to turbulent-laminar transitions. We here propose a rare-event sampling method to study such fluctuations in order to measure the time-scale of the transition efficiently. The method is composed of two parts: (i) the measurement of typical fluctuations (the bulk part of an accumulative probability function) and (ii) the measurement of rare fluctuations (the tail part of the probability function) by employing dynamics where a feedback control o…
Tidal turbines are deployed in sites which have elevated levels of free stream turbulence (FST). Accounting for elevated FST on their operation become vital from a design standpoint. Detailed experimental measurements of the dynamic near-wake of a tidal turbine model in elevated FST environments is presented; an active grid turbulence generator developed by our group was used to seed in the elevated FST and evaluate the influence of turbulence intensity (Ti) and inflow integral length scale (L) on the near-wake of the turbine. Three inflow conditions are tested: a quasi-laminar flow with Ti ~ …
Lower-branch traveling waves and equilibria computed in pipe flow and other shear flows appear intermediate between turbulent and laminar motions. We take a step towards connecting these lower-branch solutions to transition by deriving a numerical method for finding certain special disturbances of the laminar flow in a short pipe. These special disturbances cause the disturbed velocity field to approach the lower-branch solution by evolving along its stable manifold. If the disturbance were slightly smaller, the flow would relaminarize, and if slightly larger, it would transition to a turbulen…
An iterface structure between turbulence and laminar flow is investigated in two-dimensional channel flow. This spatially localized structure not only sustains itself, but also converts laminar state into turbulence actively. In other words, this coherent structure has a functionality to generate inhomogeneity by its inner dynamics. The dynamics of this functional coherent structure is isolated using the filtered simulation, and a physical perspective of its dynamics is summarized in a phenomenological model called an "ejection-jet" cycle, which includes multiscale interaction process.
Laminar-turbulent intermittency is intrinsic to the transitional regime of a wide range of fluid flows including pipe, channel, boundary layer and Couette flow. In the latter turbulent spots can grow and form continuous stripes, yet in the stripe-normal direction they remain interspersed by laminar fluid. We carry out direct numerical simulations in a long narrow domain and observe that individual turbulent stripes are transient. In agreement with recent observations in pipe flow we find that turbulence becomes sustained at a distinct critical point once the spatial proliferation outweighs the…
Intermittent turbulent-laminar patterns characterize the transition to turbulence in pipe, plane Couette and plane channel flows. The time evolution of turbulent-laminar bands in plane channel flow is studied via direct numerical simulations using the parallel pseudospectral code ChannelFlow in a narrow computational domain tilted by $24^{\circ}$ with respect to the streamwise direction. Mutual interactions between bands are studied through their propagation velocities. Energy profiles show that the flow surrounding isolated turbulent bands returns to the laminar base flow over large distances…
In this visualisation, the transition from laminar to turbulent flow is characterised by the intermittent ejection of wall fluid into the outer stream. The normalised thickness of the viscous flow layer reaches an asymptotic value but the physical thickness drops exponentially after transition. The critical transition pipe Reynolds number can be obtained simply by equating it with the asymptotic value of the normalised thickness of viscous flow layer. Key words: Transition, critical stability Reynolds number, critical transition Reynolds number, non-Newtonian pipe flow
Transition to turbulence dramatically alters the properties of fluid flows. In most canonical shear flows, the laminar flow is linearly stable and a finite-amplitude perturbation is necessary to trigger transition. Controlling transition to turbulence is achieved via the broadening or narrowing of the basin of attraction of the laminar flow. In this paper, a novel methodology to assess the robustness of the laminar flow and the efficiency of control strategies is introduced. It relies on the statistical sampling of the phase space neighborhood around the laminar flow in order to assess the tra…
Wall-bounded flows experience a transition to turbulence characterized by the coexistence of laminar and turbulent domains in some range of Reynolds number R, the natural control parameter. This transitional regime takes place between an upper threshold Rt above which turbulence is uniform (featureless) and a lower threshold Rg below which any form of turbulence decays, possibly at the end of overlong chaotic transients. The most emblematic cases of flow along flat plates transiting to/from turbulence according to this scenario are reviewed. The coexistence is generally in the form of bands, a…
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…
The volatile transition from quiescent laminar to strongly fluctuating turbulent dynamics in shear flows remains only poorly understood despite its practical importance and more than a century of intense research. The theoretical understanding of the transition process has been complicated by the lack of a linear instability mechanism and additionally by a catastrophic collapse of turbulence which can occur after extremely long lifetimes. Turbulence close to onset is investigated experimentally in three different geometries: pipe, duct and channel flow. The reverse transition from turbulent to…
Superfluid helium is an intimate mixture of a viscous normal fluid, with continuous vorticity, and an inviscid superfluid, where vorticity is constrained to thin, stable topological defects. One mechanism to generate turbulence in this system is through the application of a heat flux, so called thermal counterflow. Of particular interest is how turbulence in the superfluid responds to both a laminar and turbulent normal fluid in the presence of walls. We model superfluid vortex lines as reconnecting space curves with fixed circulation, and consider both laminar (Poiseuille) and turbulent norma…
In shear flows turbulence first occurs in the form of localized structures (puffs/spots) surrounded by laminar fluid. We here investigate such spatially intermittent flows in a pipe experiment showing that turbulent puffs have a well defined interaction distance, which sets the minimum spacing of puffs as well as the maximum observable turbulent fraction. Two methodologies are employed here. Starting from a laminar flow puffs can be created by locally injecting a jet of fluid through the pipe wall. When the perturbation is applied periodically at low frequencies, as expected, a regular sequenc…
We study Kolmogorov flow on a three dimensional, periodic domain with aspect ratios fixed to unity. Using an energy method, we give a concise proof of the linear stability of the laminar flow profile. Since turbulent motion is observed for high enough Reynolds numbers, we expect the domain of attraction of the laminar flow to be bounded by the stable manifolds of simple invariant solutions. We show one such edge state to be an equilibrium with a spatial structure reminiscent of that found in plane Couette flow, with stream wise rolls on the largest spatial scales. When tracking the edge state,…
Turbulent-laminar banded patterns in plane Poiseuille flow are studied via direct numerical simulations in a tilted and translating computational domain using a parallel version of the pseudospectral code Channelflow. 3D visualizations via the streamwise vorticity of an instantaneous and a time-averaged pattern are presented, as well as 2D visualizations of the average velocity field and the turbulent kinetic energy. Simulations for Reynolds numbers descending from 2300 to 700 show the gradual development from uniform turbulence to a pattern with wavelength 20 half-gaps near Re=1900, to a patt…
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…
Reported in the paper are results of unsteady three-dimensional direct numerical simulations of laminar and turbulent, lean hydrogen-air, complex-chemistry flames propagating in forced turbulence in a box. To explore the eventual influence of thermo-diffusive instability of laminar flames on turbulent burning velocity, (i) a critical length scale Λn that bounds regimes of unstable and stable laminar combustion is numerically determined by gradually decreasing the width Λ of computational domain until a stable laminar flame is obtained and (ii) simulations of turbulent flames are performed by v…
A stationary cylindrical vessel containing a rotating plate near the bottle surface is partially filled with liquid. With the bottom rotating, the shape of the liquid surface would become polygon-like. This polygon vortex phenomenon is an ideal system to demonstrate the Laminar-Turbulent transition process. Within the framework of equilibrium statistical mechanics, a profound comparison with Landau's phase transition theory was applied in the symmetry-breaking aspect to derive the evolution equation of this system phenomenologically. A comparison between theoretical prediction and experimental…
Pulsating flows through tubular geometries are laminar provided that velocities are moderate. This in particular is also believed to apply to cardiovascular flows where inertial forces are typically too low to sustain turbulence. On the other hand flow instabilities and fluctuating shear stresses are held responsible for a variety of cardiovascular diseases. Here we report a nonlinear instability mechanism for pulsating pipe flow that gives rise to bursts of turbulence at low flow rates. Geometrical distortions of small, yet finite amplitude are found to excite a state consisting of helical vo…
Aquatic animals have developed effective strategies to reduce their body drag over a long period of time. In this work, the influence of the scales of fish on the laminar-to-turbulent transition in the boundary layer is investigated. Arrays of biomimetic fish scales in typical overlapping arrangements are placed on a flat plate in a low-turbulence laminar water channel. Transition to turbulence is triggered by controlled excitation of a Tollmien-Schlichting (TS) wave. It was found that the TS wave can be attenuated with scales on the plate which generate streamwise streaks. As a consequence, t…
Superfluid flow around an oscillating microsphere is investigated at temperatures down to 25 mK. Stable laminar flow below a critical velocity and turbulence at large drives are found to be separated below 0.5 K by an intermediate range of driving forces where the flow is unstable, intermittently switching between laminar and turbulent phases. We have recorded time series of this switching phenomenon and have made a statistical analysis of the switching probability. The mean lifetime of the turbulent phases grows with increasing drive and becomes infinite at a critical value. Stability of the …
The phenomenon of relaminarization is observed in many flow situations, including that of an initially turbulent boundary layer subjected to strong favourable pressure gradients. Available turbulence models have hitherto been unsuccessful in correctly predicting boundary layer parameters for such flows. Narasimha and Sreenivasan \cite{narasimha1973relaminarization} proposed a quasi-laminar theory (QLT) based on a two-layer model to explain the later stages of relaminarization. This theory showed good agreement with the experimental data available, which at the time was at relatively low $Re$. …
Energy and Sustainability Research Institute Groningen, Faculty of Science and Engineering, University of Groningen（格罗宁根能源与可持续发展研究所，科学与工程学院，格罗宁根大学）；Groningen Institute for Evolutionary Life Sciences, University of Groningen（格罗宁根进化生命科学研究所，格罗宁根大学）
The transition to turbulence in pipe flow does not follow the scenario familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even when the flow speed is high enough and the perturbation sufficiently strong such that turbulent flow is established, it can return to the laminar state without any indication of the imminent decay. In this parameter range, the lifetimes of perturbations show a sensitive dependence on initial conditions and an exponential distribution. The turbulence seems to be…
We study the Lagrangian dynamics of semi-flexible macromolecules in laminar as well as in homogeneous and isotropic turbulent flows by means of analytically solvable stochastic models and direct numerical simulations. The statistics of the bending angle is qualitatively different in laminar and turbulent flows and exhibits a strong dependence on the topology of the velocity field. In particular, in two-dimensional turbulence, particles are either found in a fully extended or in a fully folded configuration; in three dimensions, the predominant configuration is the fully extended one.
In this work, the laminar decaying inlet swirl flow in a straight micro-pipe with wall slip is solved analytically and the solution verified numerically. Based on a fully developed parabolic axial velocity profiles, the swirl velocity equation is solved by the separation of variable technique. The solution is expressed as a function of the flow Reynolds number, the axial distance within the micro-pipe from the inlet, the wall slip and the inlet swirl velocity profile. The effects of the parameters on the swirl velocity distribution and the swirl decay are analyzed along the flow. Addition of a…
Over the past decade, the edge of chaos has proven to be a fruitful starting point for investigations of shear flows when the laminar base flow is linearly stable. Numerous computational studies of shear flows demonstrated the existence of states that separate laminar and turbulent regions of the state space. In addition, some studies determined invariant solutions that reside on this edge. In this paper, we study the unstable manifold of one such solution with the aid of continuous symmetry-reduction, which we formulate here for the first time for the simultaneous quotiening of axial and azim…
