Hydrodynamic Stability and Turbulence: Beyond Transients to a Self‐Sustaining Process

Waleffe, Fabian

doi:10.1002/sapm1995953319

Cited by 166 publications

(179 citation statements)

References 39 publications

Supporting

Mentioning

169

Contrasting

Order By: Relevance

“…Further inspection of the dynamics of each of the attached eddies revealed that the streaks and quasi-streamwise vortical structures form a self-sustaining process [41,55,65] exactly the same as the one shown in figure 3 with a turn-over time scale of Tu τ /λ z 2 [54]. The streaks are amplified from quasi-streamwise vortices via a coherent lift-up effect [26,30,35]; they then undergo rapid oscillation via secondary instability and/or transient growth on top of the streaks [39,40,42,55]; the quasi-streamwise vortical structures are nonlinearly regenerated [41,54,55]. The time scale of the self-sustaining process corresponds well to that of the 'bursting' in the logarithmic region, indicating that the bursting is naturally embedded in the self-sustaining process [54].…”

Section: Relation To Townsend's Attached Eddiesmentioning

confidence: 76%

“…In addition to the existence of the robust coherent lift-up effect discussed in §2, it was also shown that large-scale coherent streaks can undergo secondary instabilities at sufficiently large amplitudes [39,40], suggesting that a 'coherent' self-sustaining process similar to the buffer-layer one [41,42] might be at work also at larger scales in turbulent flows. To prove that such a type of process actually exists, however, it should be verified that motions of a given scale of interest are not sustained by larger-or smaller-scale motions.…”

Section: Self-sustaining Process At Large Scalementioning

confidence: 87%

“…The streak is significantly amplified by the coherent lift-up effect from the quasi-streamwise vortical structures ( figure 4 c,d). The amplified streak subsequently undergoes 'rapid' streamwise meandering motions, reminiscent of streak instability or non-normal amplification of a sinuous mode on top of the streaks (figure 4e) [39,40,42,55]. This eventually results in the breakdown of the streaks and regeneration of new quasi-streamwise vortical structures 4 (figure 4f ).…”

Section: Self-sustaining Process At Large Scalementioning

confidence: 99%

See 2 more Smart Citations

Self-sustaining processes at all scales in wall-bounded turbulent shear flows

Cossu

Hwang

2017

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

We collect and discuss the results of our recent studies which show evidence of the existence of a whole family of self-sustaining motions in wall-bounded turbulent shear flows with scales ranging from those of buffer-layer streaks to those of large-scale and very-large-scale motions in the outer layer. The statistical and dynamical features of this family of self-sustaining motions, which are associated with streaks and quasi-streamwise vortices, are consistent with those of Townsend’s attached eddies. Motions at each relevant scale are able to sustain themselves in the absence of forcing from larger- or smaller-scale motions by extracting energy from the mean flow via a coherent lift-up effect. The coherent self-sustaining process is embedded in a set of invariant solutions of the filtered Navier–Stokes equations which take into full account the Reynolds stresses associated with the residual smaller-scale motions. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

show abstract

Section: Relation To Townsend's Attached Eddiesmentioning

confidence: 76%

Section: Self-sustaining Process At Large Scalementioning

confidence: 87%

Section: Self-sustaining Process At Large Scalementioning

confidence: 99%

See 1 more Smart Citation

Self-sustaining processes at all scales in wall-bounded turbulent shear flows

Cossu

Hwang

2017

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…The kinetic energy is splitted into its three components (E u , E v and E w ) additional phenomenon of internal gravity waves, it is possible that new forms of ECS could exist strictly for Ri b > 0. These would have different underpinning dynamics to that in unstratified flows (known variously as the self-sustaining process (SSP) - Waleffe (1995Waleffe ( , 1997 or Vortex-Wave-Interaction (VWI) -Hall & Smith (1991); Hall & Sherwin (2010)) and therefore would be of considerable interest. The investigation was started by reproducing Schneider et al's (2008) unstratified edge state calculation for (Re, Ri b , L x , L z ) = (400, 0, 4π, 2π).…”

Section: Identifying Ecs: Edge Trackingmentioning

confidence: 99%

Exact coherent structures in stably stratified plane Couette flow

Olvera

Kerswell

2017

J. Fluid Mech.

View full text Add to dashboard Cite

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. The existence of exact coherent structures in stably-stratified plane Couette flow (gravity perpendicular to the plates) is investigated over Reynolds-Richardson number (ReRi b ) space for a fluid of unit Prandtl number (P r = 1) using a combination of numerical and asymptotic techniques. Two states are repeatedly discovered using edge-tracking -EQ7 and EQ7-1 in the nomenclature of Gibson & Brand (2014) -and found to connect with 2-dimensional convective roll solutions when tracked to negative Ri b (the RayleighBenard problem with shear). Both these states and Nagata's (1990) original exact solution feel the presence of stable stratification when Ri b = O(Re −2 ) or equivalently when the Rayleigh number Ra := −Ri b Re 2 P r = O(1). This is confirmed via a stratified extension of the Vortex-Wave-Interaction (VWI) theory of Hall & Sherwin (2010). If the stratification is increased further, EQ7 is found to progressively spanwise and crossstream localise until a second regime is entered at Ri b = O(Re −2/3 ). This corresponds to a stratified version of the Boundary Reduced Equation (BRE) regime of Deguchi, Hall & Walton (2013). Increasing the stratification further, appears to lead to a third, ultimate regime where Ri b = O(1) in which the flow fully localises in all three directions at the minimal Kolmogorov scale which then corresponds to the Osmidov scale. Implications for the laminar-turbulent boundary in the (Re-Ri b ) plane are briefly discussed.

show abstract

“…For channel flows, Waleffe and co-workers, guided by the early ideas of Benney and colleagues, looked into the possibility that the Navier-Stokes equations might support wave systems occurring as instabilities of streamwise vortex flows but sufficiently large to drive the vortex flows; see for example Waleffe (1995Waleffe ( , 1997Waleffe ( , 1998Waleffe ( , 2001Waleffe ( , 2003, Wang et al (2007). The approach used was to find fully nonlinear solutions of the Navier-Stokes equations using various fictitious forces to identify equilibrium states and then continue them when the forcing was switched off.…”

Section: Introductionmentioning

confidence: 99%

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

2013

View full text Add to dashboard Cite

The 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 theory, which we now refer to as VWI, is used in the long streamwise wavelength limit to continue the development found at order one wavelengths by Hall and Sherwin (2010). 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 and Sherwin (2010) as a stress discontinuity across the critical layer. We identify a critical streamwise wavenumber scaling which when approached causes the flow to localise 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.

show abstract

Hydrodynamic Stability and Turbulence: Beyond Transients to a Self‐Sustaining Process

Cited by 166 publications

References 39 publications

Self-sustaining processes at all scales in wall-bounded turbulent shear flows

Self-sustaining processes at all scales in wall-bounded turbulent shear flows

Exact coherent structures in stably stratified plane Couette flow

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

Contact Info

Product

Resources

About