Improved assessment of the statistical stability of turbulent flows using extended Orr–Sommerfeld stability analysis

Markeviciute, Vilda K.; Kerswell, Rich R.

doi:10.1017/jfm.2022.963

Cited by 4 publications

(1 citation statement)

References 78 publications

(151 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(This principle has been somewhat controversial and was challenged by Reynolds & Tiederman (1967) within the context of stability theory. See a modern revisit of Malkus stability theory with statistical closures by Markeviciute & Kerswell (2022). ) Using the energy analysis formulated in our companion paper (Gomé, Tuckerman & Barkley 2023), we will associate the selected wavelength to a maximal dissipation observed for the large-scale flow along the bands.…”

Section: Introductionmentioning

confidence: 99%

Patterns in transitional shear turbulence. Part 2. Emergence and optimal wavelength

2023

View full text Add to dashboard Cite

Low Reynolds number turbulence in wall-bounded shear flows en route to laminar flow takes the form of oblique, spatially intermittent turbulent structures. In plane Couette flow, these emerge from uniform turbulence via a spatio-temporal intermittent process in which localised quasi-laminar gaps randomly nucleate and disappear. For slightly lower Reynolds numbers, spatially periodic and approximately stationary turbulent–laminar patterns predominate. The statistics of quasi-laminar regions, including the distributions of space and time scales and their Reynolds-number dependence, are analysed. A smooth, but marked transition is observed between uniform turbulence and flow with intermittent quasi-laminar gaps, whereas the transition from gaps to regular patterns is more gradual. Wavelength selection in these patterns is analysed via numerical simulations in oblique domains of various sizes. Via lifetime measurements in minimal domains, and a wavelet-based analysis of wavelength predominance in a large domain, we quantify the existence and nonlinear stability of a pattern as a function of wavelength and Reynolds number. We report that the preferred wavelength maximises the energy and dissipation of the large-scale flow along laminar–turbulent interfaces. This optimal behaviour is due primarily to the advective nature of the large-scale flow, with turbulent fluctuations playing only a secondary role.

show abstract

Section: Introductionmentioning

confidence: 99%

Patterns in transitional shear turbulence. Part 2. Emergence and optimal wavelength

2023

View full text Add to dashboard Cite

show abstract

Threshold transient growth as a criterion for turbulent mean profiles

Markeviciute,

Kerswell

2024

J. Fluid Mech.

View full text Add to dashboard Cite

Lozano-Duran et al. (J. Fluid Mech., vol. 914, 2021, p. A8) have recently identified the ability of streamwise-averaged turbulent streak fields ${\mathcal {U}}(y,z,t)\hat {\boldsymbol {x}}$ in minimal channels to produce short-term transient growth as the key linear mechanism needed to sustain turbulence at $Re_{\tau }=180$ . Here, in an attempt to extend this result to larger domains and higher $Re_{\tau }$ , we model this streak transient growth as a two-stage linear process by first selecting the dominant streak structure expected to emerge over the eddy turnover time on the turbulent mean profile $U(y)\hat {\boldsymbol {x}}$ , and then examining the secondary growth on this (frozen) streak field ${\mathcal {U}}(y,z)\hat {\boldsymbol {x}}$ . Choosing the mean streak amplitude and eddy turnover time consistent with simulations captures the growth thresholds found by Lozano-Duran et al. (2021) for sustained turbulence. In a larger domain at $Re_{\tau }=180$ , the most energetic near-wall streaks observed in simulations are close to the predicted optimal streaks. This most energetic streak spacing, approaches the optimal streak at $Re_{\tau }=550$ where the secondary growth possible on each also comes together. A key prediction from the model is that the threshold transient growth required to sustain turbulence decreases with increasing $Re_{\tau }$ . More fundamentally, the work of Lozano-Duran et al. (2021) and our results suggest a subtle but significant revision of Malkus's (J. Fluid Mech., vol. 1, 1956, pp. 521–539) classic hypothesis concerning realisable turbulent mean profiles. The key property for a realisable turbulent mean profile could be the ability to generate sufficient short-term transient growth rather than dependence on its (long-term) linear stability characteristics, which was Malkus's original idea.

show abstract

Statistical state dynamics-based study of the stability of the mean statistical state of wall-bounded turbulence

Farrell,

Ioannou

2024

Phys. Rev. Fluids

View full text Add to dashboard Cite

Improved assessment of the statistical stability of turbulent flows using extended Orr–Sommerfeld stability analysis

Cited by 4 publications

References 78 publications

Patterns in transitional shear turbulence. Part 2. Emergence and optimal wavelength

Patterns in transitional shear turbulence. Part 2. Emergence and optimal wavelength

Threshold transient growth as a criterion for turbulent mean profiles

Statistical state dynamics-based study of the stability of the mean statistical state of wall-bounded turbulence

Contact Info

Product

Resources

About