scholarly journals The critical layer in pipe flow at high Reynolds number

2008 ◽  
Vol 367 (1888) ◽  
pp. 561-576 ◽  
Author(s):  
D Viswanath
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Shear Flows ◽  
Travelling Wave ◽  
Critical Layer ◽  
Travelling Wave Solutions ◽  
Lower Branch ◽  
Wave Solutions ◽  
High Reynolds

We report the computation of a family of travelling wave solutions of pipe flow up to Re =75 000. As in all lower branch solutions, streaks and rolls feature prominently in these solutions. For large Re , these solutions develop a critical layer away from the wall. Although the solutions are linearly unstable, the two unstable eigenvalues approach 0 as Re →∞ at rates given by Re −0.41 and Re −0.87 ; surprisingly, the solutions become more stable as the flow becomes less viscous. The formation of the critical layer and other aspects of the Re →∞ limit could be universal to lower branch solutions of shear flows. We give implementation details of the GMRES-hookstep and Arnoldi iterations used for computing these solutions and their spectra, while pointing out the new aspects of our method.

Travelling wave states in pipe flow

2016 ◽  
Vol 791 ◽  
pp. 284-328 ◽  
Author(s):  
Ozge Ozcakir ◽  
Saleh Tanveer ◽  
Philip Hall ◽  
Edward A. Overman
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Travelling Wave ◽  
Large Reynolds Number ◽  
Travelling Wave Solutions ◽  
Asymptotic Structure ◽  
Pipe Flows ◽  
Wave Solutions ◽  
Wave States ◽  
Viscous Core

In this paper, we have found two new nonlinear travelling wave solutions in pipe flows. We investigate possible asymptotic structures at large Reynolds number $R$ when wavenumber is independent of $R$ and identify numerically calculated solutions as finite $R$ realizations of a nonlinear viscous core (NVC) state that collapses towards the pipe centre with increasing $R$ at a rate $R^{-1/4}$. We also identify previous numerically calculated states as finite $R$ realizations of a vortex wave interacting (VWI) state with an asymptotic structure similar to the ones in channel flows studied earlier by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). In addition, asymptotics suggests the possibility of a VWI state that collapses towards the pipe centre like $R^{-1/6}$, though this remains to be confirmed numerically.

scholarly journals Exact coherent states and connections to turbulent dynamics in minimal channel flow

2015 ◽  
Vol 782 ◽  
pp. 430-454 ◽  
Author(s):  
Jae Sung Park ◽  
Michael D. Graham
Keyword(s):  
Turbulent Flow ◽  
Coherent States ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Critical Layer ◽  
Asymptotic State ◽  
Travelling Wave Solutions ◽  
Lower Branch ◽  
Mean Velocity ◽  
Wave Solutions

Several new families of nonlinear three-dimensional travelling wave solutions to the Navier–Stokes equation, also known as exact coherent states, are computed for Newtonian plane Poiseuille flow. The symmetries and streak/vortex structures are reported and their possible connections to critical layer dynamics are examined. While some of the solutions clearly display fluctuations that are localized around the critical layer (the surface on which the streamwise velocity matches the wave speed of the solution), for others this connection is not as clear. Dynamical trajectories along unstable directions of the solutions are computed. Over certain ranges of Reynolds number, two solution families are shown to lie on the basin boundary between laminar and turbulent flow. Direct comparison of nonlinear travelling wave solutions to turbulent flow in the same channel is presented. The state-space dynamics of the turbulent flow is organized around one of the newly identified travelling wave families, and in particular the lower-branch solutions of this family are closely approached during transient excursions away from the dominant behaviour. These observations provide a firm dynamical-systems foundation for prior observations that minimal channel turbulence displays time intervals of ‘active’ turbulence punctuated by brief periods of ‘hibernation’ (see, e.g., Xi & Graham, Phys. Rev. Lett., vol. 104, 2010, 218301). The hibernating intervals are approaches to lower-branch nonlinear travelling waves. Representing these solutions on a Prandtl–von Kármán plot illustrates how their bulk flow properties are related to those of Newtonian turbulence as well as the universal asymptotic state called maximum drag reduction (MDR) found in viscoelastic turbulent flow. In particular, the lower- and upper-branch solutions of the family around which the minimal channel dynamics is organized appear to approach the MDR asymptote and the classical Newtonian result respectively, in terms of both bulk velocity and mean velocity profile.

scholarly journals Video: DNS of turbulent pipe flow at high Reynolds number

2021 ◽  
Author(s):  
Alessandro Ceci ◽  
Sergio Pirozzoli ◽  
Joshua Romero ◽  
Massimiliano Fatica ◽  
Roberto Verzicco ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Turbulent Pipe Flow ◽  
High Reynolds

scholarly journals Instabilities in a high-Reynolds-number boundary layer on a film-coated surface

1997 ◽  
Vol 353 ◽  
pp. 163-195 ◽  
Author(s):  
S. N. TIMOSHIN
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Film Flow ◽  
Lower Branch ◽  
Interfacial Instabilities ◽  
Layer Potential ◽  
Tollmien Schlichting ◽  
High Reynolds ◽  
Film Viscosity

A high-Reynolds-number asymptotic theory is developed for linear instability waves in a two-dimensional incompressible boundary layer on a flat surface coated with a thin film of a different fluid. The focus in this study is on the influence of the film flow on the lower-branch Tollmien–Schlichting waves, and also on the effect of boundary-layer/potential flow interaction on interfacial instabilities. Accordingly, the film thickness is assumed to be comparable to the thickness of a viscous sublayer in a three-tier asymptotic structure of lower-branch Tollmien–Schlichting disturbances. A fully nonlinear viscous/inviscid interaction formulation is derived, and computational and analytical solutions for small disturbances are obtained for both Tollmien–Schlichting and interfacial instabilities for a range of density and viscosity ratios of the fluids, and for various values of the surface tension coefficient and the Froude number. It is shown that the interfacial instability contains the fastest growing modes and an upper-branch neutral point within the chosen flow regime if the film viscosity is greater than the viscosity of the ambient fluid. For a less viscous film the theory predicts a lower neutral branch of shorter-scale interfacial waves. The film flow is found to have a strong effect on the Tollmien–Schlichting instability, the most dramatic outcome being a powerful destabilization of the flow due to a linear resonance between growing Tollmien–Schlichting and decaying capillary modes. Increased film viscosity also destabilizes Tollmien–Schlichting disturbances, with the maximum growth rate shifted towards shorter waves. Qualitative and quantitative comparisons are made with experimental observations by Ludwieg & Hornung (1989).

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.

scholarly journals The emergence of localized vortex–wave interaction states in plane Couette flow

2013 ◽  
Vol 721 ◽  
pp. 58-85 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall ◽  
Andrew Walton
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Critical Layer ◽  
Navier Stokes ◽  
Turbulent Spots ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractThe recently understood relationship between high-Reynolds-number vortex–wave interaction theory and computationally generated self-sustaining processes provides a possible route to an understanding of some of the underlying structures of fully turbulent flows. Here vortex–wave interaction (VWI) theory is used in the long streamwise wavelength limit to continue the development found at order-one wavelengths by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). The asymptotic description given reduces the Navier–Stokes equations to the so-called boundary-region equations, for which we find equilibrium states describing the change in the VWI as the wavelength of the wave increases from $O(h)$ to $O(Rh)$, where $R$ is the Reynolds number and $2h$ is the depth of the channel. The reduced equations do not include the streamwise pressure gradient of the perturbation or the effect of streamwise diffusion of the wave–vortex states. The solutions we calculate have an asymptotic error proportional to ${R}^{- 2} $ when compared to the full Navier–Stokes equations. The results found correspond to the minimum drag configuration for VWI states and might therefore be of relevance to the control of turbulent flows. The key feature of the new states discussed here is the thickening of the critical layer structure associated with the wave part of the flow to completely fill the channel, so that the roll part of the flow is driven throughout the flow rather than as in Hall & Sherwin as a stress discontinuity across the critical layer. We identify a critical streamwise wavenumber scaling, which, when approached, causes the flow to localize and take on similarities with computationally generated or experimentally observed turbulent spots. In effect, the identification of this critical wavenumber for a given value of the assumed high Reynolds number fixes a minimum box length necessary for the emergence of localized structures. Whereas nonlinear equilibrium states of the Navier–Stokes equations are thought to form a backbone on which turbulent flows hang, our results suggest that the localized states found here might play a related role for turbulent spots.

Experimental study on high Reynolds number pipe flow

2019 ◽  
Vol 2019.68 (0) ◽  
pp. 217
Author(s):  
Kusano Eisuke ◽  
Noriyuki Furuichi ◽  
Wada Yuki ◽  
Yoshiyuki Tsuji
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
High Reynolds

scholarly journals High Reynolds Number Turbulence Model of Rotating Shear Flows

1983 ◽  
Vol 26 (219) ◽  
pp. 1534-1541 ◽  
Author(s):  
Shigeaki MASUDA ◽  
Hide S. KOYAMA ◽  
Ichiro ARIGA
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
High Reynolds Number ◽  
Shear Flows ◽  
High Reynolds ◽  
Rotating Shear Flows
Sign in / Sign up

Export Citation Format

Share Document