scholarly journals Transition to turbulence when the Tollmien–Schlichting and bypass routes coexist

2019 ◽  
Vol 880 ◽  
Author(s):  
Stefan Zammert ◽  
Bruno Eckhardt
Keyword(s):  
Initial Conditions ◽  
Travelling Waves ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Transition To Turbulence ◽  
Stable Region ◽  
Bypass Transition ◽  
Parallel Plates ◽  
Tollmien Schlichting

Plane Poiseuille flow, the pressure-driven flow between parallel plates, shows a route to turbulence connected with a linear instability to Tollmien–Schlichting (TS) waves, and another route, the bypass transition, that can be triggered with finite-amplitude perturbation. We use direct numerical simulations to explore the arrangement of the different routes to turbulence among the set of initial conditions. For plates that are a distance $2H$ apart, and in a domain of width $2\unicode[STIX]{x03C0}H$ and length $2\unicode[STIX]{x03C0}H$, the subcritical instability to TS waves sets in at $Re_{c}=5815$ and extends down to $Re_{TS}\approx 4884$. The bypass route becomes available above $Re_{E}=459$ with the appearance of three-dimensional, finite-amplitude travelling waves. Below $Re_{c}$, TS transition appears for a tiny region of initial conditions that grows with increasing Reynolds number. Above $Re_{c}$, the previously stable region becomes unstable via TS waves, but a sharp transition to the bypass route can still be identified. Both routes lead to the same turbulent state in the final stage of the transition, but on different time scales. Similar phenomena can be expected in other flows where two or more routes to turbulence compete.

Passive boundary layer control of oblique disturbances by finite-amplitude streaks

2014 ◽  
Vol 749 ◽  
pp. 1-36 ◽  
Author(s):  
Shahab Shahinfar ◽  
Sohrab S. Sattarzadeh ◽  
Jens H. M. Fransson
Keyword(s):  
High Speed ◽  
Passive Control ◽  
Control Method ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Transition To Turbulence ◽  
Spanwise Direction ◽  
Passive Flow Control ◽  
Tollmien Schlichting ◽  
Streamwise Streaks

AbstractRecent experimental results on the attenuation of two-dimensional Tollmien–Schlichting wave (TSW) disturbances by means of passive miniature vortex generators (MVGs) have shed new light on the possibility of delaying transition to turbulence and hence accomplishing skin-friction drag reduction. A recurrent concern has been whether this passive flow control strategy would work for other types of disturbances than plane TSWs in an experimental configuration where the incoming disturbance is allowed to fully interact with the MVG array. In the present experimental investigation we show that not only TSW disturbances are attenuated, but also three-dimensional single oblique wave (SOW) and pair of oblique waves (POW) disturbances are quenched in the presence of MVGs, and that transition delay can be obtained successfully. For the SOW disturbance an unusual interaction between the wave and the MVGs occurs, leading to a split of the wave with one part travelling with a ‘mirrored’ phase angle with respect to the spanwise direction on one side of the MVG centreline. This gives rise to $\Lambda $-vortices on the centreline, which force a low-speed streak on the centreline, strong enough to overcome the high-speed streak generated by the MVGs themselves. Both these streaky boundary layers seem to act stabilizing on unsteady perturbations. The challenge in a passive control method making use of a non-modal type of disturbances to attenuate modal disturbances lies in generating stable streamwise streaks which do not themselves break down to turbulence.

Finite-amplitude three-dimensional instability of inviscid laminar boundary layers

1995 ◽  
Vol 290 ◽  
pp. 203-212
Author(s):  
Melvin E. Stern
Keyword(s):  
Three Dimensional ◽  
Streamwise Velocity ◽  
Finite Amplitude ◽  
Transition To Turbulence ◽  
Stream Velocity ◽  
Normal Velocity ◽  
Laminar Boundary Layers ◽  
Vertical Thickness ◽  
Layer Flow ◽  
Dimensional Instability

An inviscid laminar boundary layer flow Û(ŷ) with vertical thickness λy, and free stream velocity U is disturbed at time $\tcirc$ = 0 by a normal velocity $\vcirc$ and by a spanwise velocity ŵ([xcirc ],ŷ, $\zcirc$, 0) of finite amplitude αU, with spanwise ($\zcirc$) scale λz, and streamwise ([xcirc ]) scale λx = λz/α; the streamwise velocity û([xcirc ],ŷ,$\zcirc$,$\tcirc$) is initially undisturbed. A long wave λy/λz → 0) expansion of the Euler equations for fixed α and time scale $\tcirc$s = U−1λz/α results in a hyperbolic equation for Lagrangian displacements ŷ. Within the interval $\tcirc$ > $\tcirc$s of asymptotic validity, finite parcel displacements (O(λy)) with finite (O(U)) û fluctuations occur, independent of α no matter how small; the basic flow Û is therefore said to be unstable to streaky (λx [Gt ] λz) spanwise perturbations. The temporal development of the ('spot’) region in the (x,z) plane wherein inflected û profiles appear is computed and qualitatively related to observations of ‘breakdown’ and transition to turbulence in the flow over a flat plate. The maximum $\vcirc$([xcirc ],ŷ,$\zcirc$,$\tcirc$) increases monotonically to infinity as $\tcirc$ → $\tcirc$s.

The effect of rigid rotation on the finite-amplitude stability of pipe flow at high Reynolds number

1984 ◽  
Vol 148 ◽  
pp. 193-205 ◽  
Author(s):  
T. R. Akylas ◽  
J.-P. Demurger
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Neutral Stability ◽  
Axisymmetric Mode ◽  
High Reynolds

A theoretical study is made of the stability of pipe flow with superimposed rigid rotation to finite-amplitude disturbances at high Reynolds number. The non-axisymmetric mode that requires the least amount of rotation for linear instability is considered. An amplitude expansion is developed close to the corresponding neutral stability curve; the appropriate Landau constant is calculated. It is demonstrated that the flow exhibits nonlinear subcritical instability, the nonlinear effects being particularly strong owing to the large magnitude of the Landau constant. These findings support the view that a small amount of extraneous rotation could play a significant role in the transition to turbulence of pipe flow.

On certain aspects of three-dimensional instability of parallel flows

1983 ◽  
Vol 385 (1788) ◽  
pp. 53-84 ◽  
Keyword(s):  
Three Dimensional ◽  
Periodic Variation ◽  
Finite Amplitude ◽  
Basic Flow ◽  
Spanwise Direction ◽  
Equilibrium Solutions ◽  
Wave Disturbances ◽  
Parallel Flows ◽  
Tollmien Schlichting ◽  
Dimensional Instability

The effect of small imperfections in shear flows on the development of finite-amplitude three-dimensional disturbances in the flow is examined. A model problem is studied, one in which the basic flow is plane Poiseuille flow in a channel and the small imperfection in the form of spanwise periodic variation of the basic flow is introduced from the channel boundaries. It is shown that this has a positive effect on the growth of larger Tollmien-Schlichting wave disturbances, which are in the form of standing waves in the spanwise direction. Equations for the amplitudes of these disturbances, based on Stuart-Watson-Eckhaus theory, are derived and over a range of Reynolds number, the regions in the wavenumber plane over which equilibrium solutions are possible are identified. The possibility of three-dimensional disturbances that are oscillatory in the streamwise direction but that may be growing exponentially in a spanwise direction is examined.

scholarly journals Modelling single- and tandem-bubble dynamics between two parallel plates for biomedical applications

2013 ◽  
Vol 716 ◽  
pp. 137-170 ◽  
Author(s):  
C.-T. Hsiao ◽  
J.-K. Choi ◽  
S. Singh ◽  
G. L. Chahine ◽  
T. A. Hay ◽  
...  
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Bubble Dynamics ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Design Tool ◽  
Parallel Plates ◽  
Jet Formation ◽  
Viscous Boundary Layer ◽  
Element Method

AbstractCarefully timed tandem microbubbles have been shown to produce directional and targeted membrane poration of individual cells in microfluidic systems, which could be of use in ultrasound-mediated drug and gene delivery. This study aims at contributing to the understanding of the mechanisms at play in such an interaction. The dynamics of single and tandem microbubbles between two parallel plates is studied numerically and analytically. Comparisons are then made between the numerical results and the available experimental results. Numerically, assuming a potential flow, a three-dimensional boundary element method (BEM) is used to describe complex bubble deformations, jet formation, and bubble splitting. Analytically, compressibility and viscous boundary layer effects along the channel walls, neglected in the BEM model, are considered while shape of the bubble is not considered. Comparisons show that energy losses modify the bubble dynamics when the two approaches use identical initial conditions. The initial conditions in the boundary element method can be adjusted to recover the bubble period and maximum bubble volume when in an infinite medium. Using the same conditions enables the method to recover the full dynamics of single and tandem bubbles, including large deformations and fast re-entering jet formation. This method can be used as a design tool for future tandem-bubble sonoporation experiments.

scholarly journals Doubly localized states in plane Couette flow

2014 ◽  
Vol 758 ◽  
pp. 1-4 ◽  
Author(s):  
Bruno Eckhardt
Keyword(s):  
Couette Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Linear Instability ◽  
Localized States ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Plane Couette Flow ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

AbstractMuch of our understanding of the transition to turbulence in flows without a linear instability came with the discovery and characterization of fully three-dimensional solutions to the Navier–Stokes equation. The first examples in plane Couette flow were periodic in both spanwise and streamwise directions, and could explain the transitions in small domains only. The presence of localized turbulent spots in larger domains, the spatiotemporal decoherence on larger scales and the ability to trigger turbulence with pointwise perturbations require solutions that are localized in both directions, like the one presented by Brand & Gibson (J. Fluid Mech., vol. 750, 2014, R3). They describe a steady solution of the Navier–Stokes equations and characterize in unprecedented detail, including an analytic computation of its localization properties. The study opens up new ways to describe localized turbulent patches.

scholarly journals The critical point of the transition to turbulence in pipe flow

2018 ◽  
Vol 839 ◽  
pp. 76-94 ◽  
Author(s):  
Vasudevan Mukund ◽  
Björn Hof
Keyword(s):  
Steady State ◽  
Critical Point ◽  
Pipe Flow ◽  
Initial Conditions ◽  
Flow Patterns ◽  
Finite Amplitude ◽  
Decay Rates ◽  
Transition To Turbulence ◽  
Intermittent Flow ◽  
Spatio Temporal

In pipes, turbulence sets in despite the linear stability of the laminar Hagen–Poiseuille flow. The Reynolds number ($Re$) for which turbulence first appears in a given experiment – the ‘natural transition point’ – depends on imperfections of the set-up, or, more precisely, on the magnitude of finite amplitude perturbations. At onset, turbulence typically only occupies a certain fraction of the flow, and this fraction equally is found to differ from experiment to experiment. Despite these findings, Reynolds proposed that after sufficiently long times, flows may settle to steady conditions: below a critical velocity, flows should (regardless of initial conditions) always return to laminar, while above this velocity, eddying motion should persist. As will be shown, even in pipes several thousand diameters long, the spatio-temporal intermittent flow patterns observed at the end of the pipe strongly depend on the initial conditions, and there is no indication that different flow patterns would eventually settle to a (statistical) steady state. Exploiting the fact that turbulent puffs do not age (i.e. they are memoryless), we continuously recreate the puff sequence exiting the pipe at the pipe entrance, and in doing so introduce periodic boundary conditions for the puff pattern. This procedure allows us to study the evolution of the flow patterns for arbitrary long times, and we find that after times in excess of $10^{7}$ advective time units, indeed a statistical steady state is reached. Although the resulting flows remain spatio-temporally intermittent, puff splitting and decay rates eventually reach a balance, so that the turbulent fraction fluctuates around a well-defined level which only depends on $Re$. In accordance with Reynolds’ proposition, we find that at lower $Re$ (here 2020), flows eventually always resume to laminar, while for higher $Re$ (${\geqslant}2060$), turbulence persists. The critical point for pipe flow hence falls in the interval of $2020<Re<2060$, which is in very good agreement with the recently proposed value of $Re_{c}=2040$. The latter estimate was based on single-puff statistics and entirely neglected puff interactions. Unlike in typical contact processes where such interactions strongly affect the percolation threshold, in pipe flow, the critical point is only marginally influenced. Interactions, on the other hand, are responsible for the approach to the statistical steady state. As shown, they strongly affect the resulting flow patterns, where they cause ‘puff clustering’, and these regions of large puff densities are observed to travel across the puff pattern in a wave-like fashion.

scholarly journals Boundary layer stabilization using free-stream vortices

2014 ◽  
Vol 764 ◽  
Author(s):  
L. Siconolfi ◽  
S. Camarri ◽  
J. H. M. Fransson
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Control Method ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Transition To Turbulence ◽  
Free Stream Turbulence ◽  
Passive Flow Control ◽  
Tollmien Schlichting ◽  
Transition Delay

AbstractIn this numerical investigation we explore the possibility of applying free-stream vortices as a passive flow control method for delaying the transition to turbulence. The work is motivated by previous experimental studies demonstrating that stable streamwise boundary layer (BL) streaks can attenuate both two- and three-dimensional disturbances inside the BL, leading to transition delay, with the implication of reducing skin-friction drag. To date, successful control has been obtained using physical BL modulators mounted on the surface in order to generate stable streaks. However, surface mounted BL modulators are doomed to failure when the BL is subject to free-stream turbulence (FST), since a destructive interaction between the two is inevitable. In order to tackle free-stream disturbances, such as FST, a smooth surface is desired, which has motivated us to seek new methods to induce streamwise streaks inside the BL. A first step, in a systematic order, is taken in the present paper to prove the control idea of generating free-stream vortices for the attenuation of ordinary Tollmien–Schlichting waves inside the BL. In this proof-of-concept study we show that, by applying a spanwise array of counter-rotating free-stream vortices, inducing streamwise BL streaks further downstream, it is possible to alter the BL stability characteristics to such a degree that transition delay may be accomplished. For the demonstration we use direct numerical simulations along with stability analysis.

Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems

2005 ◽  
Vol 12 (5) ◽  
pp. 056317 ◽  
Author(s):  
A. R. Miles ◽  
B. Blue ◽  
M. J. Edwards ◽  
J. A. Greenough ◽  
J. F. Hansen ◽  
...  
Keyword(s):  
Blast Wave ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Transition To Turbulence ◽  
Driven Systems

Boundary-layer transition by interaction of discrete and continuous modes

2008 ◽  
Vol 604 ◽  
pp. 199-233 ◽  
Author(s):  
YANG LIU ◽  
TAMER A. ZAKI ◽  
PAUL A. DURBIN
Keyword(s):  
Boundary Layer ◽  
Finite Amplitude ◽  
Secondary Instability ◽  
Boundary Layer Transition ◽  
Length Scale ◽  
Bypass Transition ◽  
Continuous Mode ◽  
Layer Transition ◽  
Boundary Layer Turbulence ◽  
Tollmien Schlichting

The natural and bypass routes to boundary-layer turbulence have traditionally been studied independently. In certain flow regimes, both transition mechanisms might coexist, and, if so, can interact. A nonlinear interaction of discrete and continuous Orr-Sommerfeld modes, which are at the origin of orderly and bypass transition, respectively, is found. It causes breakdown to turbulence, even though neither mode alone is sufficient. Direct numerical simulations of the interaction shows that breakdown occurs through a pattern of Λ-structures, similar to the secondary instability of Tollmien–Schlichting waves. However, the streaks produced by the Orr-Sommerfeld continuous mode set the spanwise length scale, which is much smaller than that of the secondary instability of Tollmien–Schlichting waves. Floquet analysis explains some of the features seen in the simulations as a competition between destabilizing and stabilizing interactions between finite-amplitude distortions.

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