The Significance of Simple Invariant Solutions in Turbulent Flows

Kawahara, Genta; Uhlmann, Markus; Veen, Lennaert van

doi:10.1146/annurev-fluid-120710-101228

Cited by 291 publications

(273 citation statements)

References 80 publications

Supporting

Mentioning

263

Contrasting

Order By: Relevance

“…Some of them are semi-empirical, based on observation of coherent structures [2] on canonical wall-bounded turbulent flows [3,4,5]. Some are time-periodic solutions of simpler wall-bounded flows [6], which can be related to the dynamics of fully turbulent flows [7]. In most of them, wall-attached vertical velocity (v) eddies (reminiscent of Townsend's attached eddies [8]) are of special significance from a dynamical point of view, driving the generation of elongated streaks of streamwise velocity (u) through a linear amplification process [9].…”

Section: Introductionmentioning

confidence: 99%

Wall-based identification of coherent structures in wall-bounded turbulence

Vila

Flores

2018

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Abstract. During the last decades, a number of reduced order models based on coherent structures have been proposed to describe wall-bounded turbulence. Many of these models emphasize the importance of coherent wall-normal velocity eddies (v-eddies), which drive the generation of the very long streamwise velocity structures observed in the logarithmic and outer region. In order to use these models to improve our ability to control wall-bounded turbulence in realistic applications, these v-eddies need to be identified from the wall in a non-intrusive way. In this paper, the possibility of using the pressure signal at the wall to identify these v-eddies is explored, analyzing the cross-correlation between the wall-normal velocity component and the pressure fluctuations at the wall in a DNS of a turbulent channel flow at Reτ = 939. The results show that the cross-correlation has a region of negative correlation upstream, and a region of positive correlation backwards. In the spanwise direction the correlation decays monotonously, except very close to the wall where a change of sign of the correlation coefficient is observed. Moreover, filtering the pressure fluctuations at the wall in space results in an increase of the region where the cross-correlation is strong, both for the positively and the negatively correlated regions. The use of a time filter for the pressure fluctuations at the wall yields different results, displacing the regions of strong correlation without changing much their sizes. The results suggest that space-filtering the pressure at the wall is a feasible way to identify v-eddies of different sizes, which could be used to trigger turbulent control strategies.

show abstract

Section: Introductionmentioning

confidence: 99%

Wall-based identification of coherent structures in wall-bounded turbulence

Vila

Flores

2018

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

show abstract

“…These states, which start to populate phase space at some critical Reynolds number and quickly proliferate as the Reynolds number increases, eventually produce a sufficiently tangled structure of stable and unstable manifolds in phase space to act as a scaffold for the observed complex dynamics (Kerswell 2005;Eckhardt et al 2007;Gibson and Cvitanović 2010;Kawahara et al 2012). These states (variously referred to as simple invariant solutions or Exact Coherent Structures (ECS) ), can either be embedded in the laminar-turbulent boundary (Wang et al 2007;Duguet et al 2008) or sit in the basin of attraction of the turbulent state with some buried in the turbulent attractor itself (Kerswell & Tutty 2007;Gibson et al 2008).…”

Section: Introductionmentioning

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

“…Indeed, a key feature of the NBCW invari-ant solution is that it captures structure commonly observed in shear flows in the form of wavy rolls that support alternating streaks of high and low streamwise velocity (see § 2.2 for further discussion). We refer the reader to the Kawahara et al (2012) review article for an excellent overview of research in this area.…”

Section: Introductionmentioning

confidence: 99%

Spanwise-localized solutions of planar shear flows

Gibson

Brand

2014

J. Fluid Mech.

View full text Add to dashboard Cite

We present several new spatially localized equilibrium and traveling-wave solutions of plane Couette and channel flows. The solutions exhibit strikingly concentrated regions of vorticity that are flanked on either side by high-speed streaks. For several traveling-wave solutions of channel flow, the concentrated vortex structures are confined to the nearwall region and form particularly isolated and elemental versions of coherent structures in the near-wall region of shear flows. The solutions are constructed by a variety of methods: application of windowing functions to previously known spatially periodic solutions, continuation from plane Couette to channel flow conditions, and from initial guesses obtained from turbulent simulation data. We show how the symmetries of localized solutions derive from the symmetries of their periodic counterparts, analyze the exponential decay of their tails, examine the scale separation and scaling of their streamwise Fourier modes, and show that they develop critical layers for large Reynolds numbers.

show abstract

The Significance of Simple Invariant Solutions in Turbulent Flows

Cited by 291 publications

References 80 publications

Wall-based identification of coherent structures in wall-bounded turbulence

Wall-based identification of coherent structures in wall-bounded turbulence

Exact coherent structures in stably stratified plane Couette flow

Spanwise-localized solutions of planar shear flows

Contact Info

Product

Resources

About