Very large structures in plane turbulent Couette flow

Komminaho, Jukka; Lundbladh, Anders; Johansson, A.

doi:10.1017/s0022112096007537

Cited by 181 publications

(190 citation statements)

References 16 publications

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“…However, the implication of the canonical scaling for the mean-flow correction and the relation to fully-turbulent mean profiles, whilst intriguing, is not pursued here. In fact the limiting form of the mean-flow correction agrees well with turbulent mean profiles for plane Couette flow; see for example Figure 2 of Komminaho et al (1996). It appears then that the basic shape for the mean flow correction in a turbulent boundary layer is driven by the large scale structures described here.…”

Section: Resultssupporting

confidence: 66%

“…The existence of such a minimum length for spot formation has been known by the computational community for some time; see for example Lundbladh and Johansson (1991), Komminaho et al (1996). If the result we find is indeed a predictor of the box length needed to allow spot formation to begin it is significant because for any high Reynolds number it tells us how long the computational box used must be in order to capture turbulent spots.…”

Section: Resultsmentioning

confidence: 62%

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

2013

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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.

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Section: Resultssupporting

confidence: 66%

Section: Resultsmentioning

confidence: 62%

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

2013

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“…It is well known 1,2 that such structures exist in the near wall region of turbulent boundary layers and channel flows where they scale in wall units with a mean spanwise spacing z + Ϸ 100. There is also evidence of the existence of large coherent streaky structures extending outside the near wall region in the turbulent boundary layer, 3,4 the turbulent Couette flow, 5 and the turbulent channel flow. 6 The size of these structures seems to scale in external units.…”

Section: Introductionmentioning

confidence: 99%

A note on optimal transient growth in turbulent channel flows

et al. 2009

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We compute the optimal transient growth of perturbations sustained by a turbulent channel flow following the same approach recently used by del Álamo and Jiménez ͓J. Fluid Mech. 559, 205 ͑2006͔͒. Contrary to this previous analysis, we use generalized Orr-Sommerfeld and Squire operators consistent with previous investigations of mean flows with variable viscosity. The optimal perturbations are streamwise vortices evolving into streamwise streaks. In accordance with del Álamo and Jiménez, it is found that for very elongated structures and for sufficiently large Reynolds numbers, the optimal energy growth presents a primary peak in the spanwise wavelength, scaling in outer units, and a secondary peak scaling in inner units and corresponding to z + Ϸ 100. Contrary to the previous results, however, it is found that the maximum energy growth associated with the primary peak increases with the Reynolds number. This growth, in a first approximation, scales linearly with an effective Reynolds number based on the centerline velocity, the channel half width and the maximum eddy viscosity associated. The optimal streaks associated with the primary peak have an optimal spacing of z =4h and scale in outer units in the outer region and in wall units in the near wall region, where they still have up to 50% of their maximum amplitude near y + = 10.

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“…Their refined (128×128×128)-grid, has a wallnormal grid spacing at the wall of y + ≈ 0.2, which is sufficiently small to resolve the steep velocity gradient in the viscous sublayer. Their streamwise and spanwise domain sizes L + ≈ 6600 and W + ≈ 1200, are large enough to capture not only the near-wall, vortical structures, but also the large, central structures (Komminaho, Lundbladh & Johansson 1996).…”

Section: Turbulent Single-phase Flowmentioning

confidence: 99%

“…It is known that Couette flow requires a very large separation distance x 10H, for the fluctuations to become fully uncorrelated, see e.g. Komminaho et al (1996). Owing to the use of cubic and homogeneous grids in the present numerical method, simulating on such large domains is unfeasible, requiring excessive amounts of grid nodes.…”

Section: Turbulence Modulationmentioning

confidence: 99%

Turbulent drag reduction using fluid spheres

Gillissen

2013

J. Fluid Mech.

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Using direct numerical simulations of turbulent Couette flow, we predict drag reduction in suspensions of neutrally buoyant fluid spheres, of diameter larger than the Kolmogorov length scale. The velocity fluctuations are enhanced in the streamwise direction, and reduced in the cross-stream directions, which is similar to the more studied case of drag reduction using polymers. Despite these similarities, the drag reduction mechanism is found to originate in the logarithmic region, while the buffer region contributes to a slight drag increase, which is opposite to polymer-induced drag reduction. Another striking difference is the reduction of the turbulent energy at the large scales and an enhancement at the small scales.

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Very large structures in plane turbulent Couette flow

Cited by 181 publications

References 16 publications

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

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

A note on optimal transient growth in turbulent channel flows

Turbulent drag reduction using fluid spheres

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