High-Reynolds-number fractal signature of nascent turbulence during transition

Transition from laminar to turbulent flow occurring over a smooth surface is a particularly important route to chaos in fluid dynamics. It often occurs via sporadic inception of spatially localized patches (spots) of turbulence that grow and merge downstream to become the fully turbulent boundary layer. A long-standing question has been whether these incipient spots already contain properties of high-Reynolds-number, developed turbulence. In this study, the question is posed for geometric scaling properties of the interface separating turbulence within the spots from the outer flow. For high-Reynolds-number turbulence, such interfaces are known to display fractal scaling laws with a dimension D≈7/3, where the 1/3 excess exponent above 2 (smooth surfaces) follows from Kolmogorov scaling of velocity fluctuations. The data used in this study are from a direct numerical simulation, and the spot boundaries (interfaces) are determined by using an unsupervised machine-learning method that can identify such interfaces without setting arbitrary thresholds. Wide separation between small and large scales during transition is provided by the large range of spot volumes, enabling accurate measurements of the volume–area fractal scaling exponent. Measurements show a dimension of D=2.36±0.03 over almost 5 decades of spot volume, i.e., trends fully consistent with high-Reynolds-number turbulence. Additional observations pertaining to the dependence on height above the surface are also presented. Results provide evidence that turbulent spots exhibit high-Reynolds-number fractal-scaling properties already during early transitional and nonisotropic stages of the flow evolution.

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Enstrophy and dissipation must have the same scaling exponent in the high Reynolds number limit of fluid turbulence

Physics of Fluids ◽

10.1063/1.870081 ◽

1999 ◽

Vol 11 (8) ◽

pp. 2202-2204 ◽

Cited By ~ 32

Author(s):

Mark Nelkin

Keyword(s):

Reynolds Number ◽

High Reynolds Number ◽

Scaling Exponent ◽

Fluid Turbulence ◽

High Reynolds

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Scaling of the wall-normal turbulence component in high-Reynolds-number pipe flow

Journal of Fluid Mechanics ◽

10.1017/s0022112006004526 ◽

2007 ◽

Vol 576 ◽

pp. 457-473 ◽

Cited By ~ 33

Author(s):

RONGRONG ZHAO ◽

ALEXANDER J. SMITS

Keyword(s):

Reynolds Number ◽

Pipe Flow ◽

High Reynolds Number ◽

Reynolds Numbers ◽

Constant Region ◽

Intensity Data ◽

Number Range ◽

Outer Flow ◽

High Reynolds ◽

Wavenumber Region

Streamwise and wall-normal turbulence components are obtained in fully developed turbulent pipe over a Reynolds number range from 1.1 × 105to 9.8 × 106. The streamwise intensity data are consistent with previous measurements in the same facility. For the wall-normal turbulence intensity, a constant region inv'r.m.s.is found for the region 200 ≤ y+≤ 0.1R+for Reynolds numbers up to 1.0 × 106. An increase inv'r.m.s.is observed below abouty+∼ 100, although additional measurements will be required to establish its generality. The wall-normal spectra collapse in the energy-containing region with inner scaling, but for the low-wavenumber region ay/Rdependence is observed, which also indicates a continuing influence from the outer flow on the near-wall motions.

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Direct numerical simulation of complete H-type and K-type transitions with implications for the dynamics of turbulent boundary layers

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.142 ◽

2013 ◽

Vol 724 ◽

pp. 480-509 ◽

Cited By ~ 96

Author(s):

Taraneh Sayadi ◽

Curtis W. Hamman ◽

Parviz Moin

Keyword(s):

Reynolds Number ◽

Skin Friction ◽

Boundary Layers ◽

High Reynolds Number ◽

Reynolds Numbers ◽

Turbulent Boundary Layers ◽

Bypass Transition ◽

Hairpin Vortices ◽

Developed Turbulence ◽

High Reynolds

AbstractThe onset and development of turbulence from controlled disturbances in compressible ($\mathit{Ma}= 0. 2$), flat-plate boundary layers is studied by direct numerical simulation. We have validated the initial disturbance development, confirmed that H- and K-regime transitions were reproduced and, from these starting points, we carried these simulations beyond breakdown, past the skin-friction maximum and to higher Reynolds numbers than investigated before to evaluate how these two flow regimes converge towards turbulence and what transitional flow structures embody the statistics and mean dynamics of developed turbulence. We show that H- and K-type breakdowns both relax toward the same statistical structure typical of developed turbulence at high Reynolds number immediately after the skin-friction maximum. This threshold marks the onset of self-sustaining mechanisms of near-wall turbulence. At this point, computed power spectra exhibit a decade of Kolmogorov inertial subrange; this is further evidence of convergence to equilibrium turbulence at the late stage of transition. Here, visualization of the instantaneous flow structure shows numerous, tightly packed hairpin vortices (Adrian, Phys. Fluids, vol. 19, 2007, 041301). Strongly organized coherent hairpin structures are less perceptible farther downstream (at higher Reynolds numbers), but the flow statistics and near-wall dynamics are the same. These structurally simple hairpin-packet solutions found in the very late stages of H- and K-type transitions obey the statistical measurements of higher-Reynolds-number turbulence. Comparison with the bypass transition of Wu & Moin (Phys. Fluids, vol. 22, 2010, pp. 85–105) extends these observations to a wider class of transitional flows. In contrast to bypass transition, the (time- and spanwise-averaged) skin-friction maximum in both H- and K-type transitions overshoots the turbulent correlation. Downstream of these friction maxima, all three skin-friction profiles collapse when plotted versus the momentum-thickness Reynolds number, ${\mathit{Re}}_{\theta } $. Mean velocities, turbulence intensities and integral parameters collapse generally beyond ${\mathit{Re}}_{\theta } = 900$ in each transition scenario. Skin-friction maxima, organized hairpin vortices and the onset of self-sustaining turbulence found in controlled H- and K-type transitions are, in many dynamically important respects, similar to development of turbulent spots seen by Park et al. (Phys. Fluids, vol. 24, 2012, 035105). A detailed statistical comparison demonstrates that each of these different transition scenarios evolve into a unique force balance characteristic of higher-Reynolds-number turbulence (Klewicki, Ebner & Wu, J. Fluid Mech., vol. 682, 2011, pp. 617–651). We postulate that these dynamics of late-stage transition as manifested by hairpin packets can serve as a reduced-order model of high-Reynolds-number turbulent boundary layers.

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On drag reduction scaling and sustainability bounds of superhydrophobic surfaces in high Reynolds number turbulent flows

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.1027 ◽

2019 ◽

Vol 864 ◽

pp. 327-347 ◽

Cited By ~ 12

Author(s):

Amirreza Rastegari ◽

Rayhaneh Akhavan

Keyword(s):

Reynolds Number ◽

Turbulent Flow ◽

Drag Reduction ◽

Turbulent Flows ◽

High Reynolds Number ◽

Scaling Laws ◽

Base Flow ◽

Geometrical Parameters ◽

Pressure Stability ◽

High Reynolds

The drag reduction characteristics and sustainability bounds of superhydrophobic (SH) surfaces in high Reynolds number turbulent flows are investigated using results from direct numerical simulation (DNS) and scaling-law analysis. The DNS studies were performed, using lattice Boltzmann methods, in turbulent channel flows at bulk Reynolds numbers of $Re_{b}=3600$ ($Re_{\unicode[STIX]{x1D70F}_{0}}\approx 222$) and $Re_{b}=7860$ ($Re_{\unicode[STIX]{x1D70F}_{0}}\approx 442$) with SH longitudinal microgrooves or SH aligned microposts on the walls. Surface microtexture geometrical parameters corresponding to microgroove widths or micropost spacings of $4\lesssim g^{+0}\lesssim 128$ in base flow wall units and solid fractions of $1/64\leqslant \unicode[STIX]{x1D719}_{s}\leqslant 1/2$ were investigated at interface protrusion angles of $\unicode[STIX]{x1D703}_{p}=0^{\circ }$ and $\unicode[STIX]{x1D703}_{p}=-30^{\circ }$. Analysis of the governing equations and DNS results shows that the magnitude of drag reduction is not only a function of the geometry and size of the surface microtexture in wall units, but also the Reynolds number of the base flow. A Reynolds number independent measure of drag reduction can be constructed by parameterizing the magnitude of drag reduction in terms of the friction coefficient of the base flow and the shift, $(B-B_{0})$, in the intercept of a logarithmic law representation of the mean velocity profile in the flow with SH walls compared to the base flow, where $(B-B_{0})$ is Reynolds number independent. The scaling laws for $(B-B_{0})$, in terms of the geometrical parameters of the surface microtexture in wall units, are presented for SH longitudinal microgrooves and aligned microposts. The same scaling laws are found to also apply to liquid-infused (LI) surfaces as long as the viscosity ratios are large, $N\equiv \unicode[STIX]{x1D707}_{o}/\unicode[STIX]{x1D707}_{i}\gtrsim 10$. These scaling laws, in conjunction with the parametrization of drag reduction in terms of $(B-B_{0})$, allow for a priori prediction of the magnitude of drag reduction with SH or LI surfaces in turbulent flow at any Reynolds number. For the most stable of these SH surface microtextures, namely, longitudinal microgrooves, the pressure stability bounds of the SH surface under the pressure loads of turbulent flow are investigated. It is shown that the pressure stability bounds of SH surfaces are also significantly curtailed with increasing Reynolds number of the flow. Using these scaling laws, the narrow range of SH surface geometrical parameters which can yield large drag reduction as well as sustainability in high Reynolds number turbulent flows is identified.

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