The effect of slip surfaces on the laminar–turbulent separatrix of plane Poiseuille flow is studied by direct numerical simulation. In laminar flows, the inclusion of the slip surfaces results in a drag reduction of over 10 %, which is in good agreement with previous studies and the theory of laminar slip flows. Turbulence lifetimes, the likelihood that turbulence is sustained, is investigated for transitional flows with various slip lengths. We show that slip surfaces decrease the likelihood of sustained turbulence compared to the no-slip case, and the likelihood is further decreased as slip length is increased. A more deterministic analysis of the effects of slip surfaces on a transition to turbulence is performed by using nonlinear travelling-wave solutions to the Navier–Stokes equations, also known as exact coherent solutions. Two solution families, dubbed P3 and P4, are used since their lower-branch solutions are embedded on the boundary of the basin of attraction of laminar and turbulent flows (Park & Graham, J. Fluid Mech. , vol. 782, 2015, pp. 430–454). Additionally, they exhibit distinct flow structures – the P3 and P4 are denoted as core mode and critical-layer mode, respectively. Distinct effects of slip surfaces on the solutions are observed by the skin-friction evolution, linear growth rate and phase-space projection of transitional trajectories. The slip surface appears to modify the transition dynamics very little for the core mode, but quite considerably for the critical-layer mode. Most importantly, the slip surface promotes different transition dynamics – an early and bypass-like transition for the core mode and a delayed and H- or K-type-like transition for the critical-layer mode. We explain these distinct transition dynamics based on spatio-temporal and quadrant analyses. It is found that slip surfaces promote the prevalence of strong wall-toward motions (sweep-like events) near vortex cores close to the channel centre, inducing an early transition, while long sustained ejection events are present in the region of the $\unicode[STIX]{x1D6EC}$ -shaped vortex cores close to the critical layer, resulting in a delayed transition. This should motivate flow control strategies to fully exploit these distinct transition dynamics for transition to turbulence.
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Integrated Quadrant Analysis: A New Method for Analyzing Turbulent Coherent Structures
Integrated quadrant analysis is a novel technique to identify and to characterize the trajectory and strength of turbulent coherent structures in the atmospheric surface layer. By integrating the three-dimensional velocity field characterized by traditional quadrant analysis with respect to time, the trajectory history of individual coherent structures can be preserved with Eulerian turbulence measurements. We develop a method to identify the ejection phase of coherent structures based on turbulence kinetic energy (TKE). Identifying coherent structures within a time series using TKE performs better than identifying them with the streamwise and vertical velocity components because some coherent structures are dominated by the cross-stream velocity component as they pass the sensor. By combining this identification method with the integrated quadrant analysis, one can animate or plot the trajectory of individual coherent structures from high-frequency velocity measurements. This procedure links a coherent ejection with the subsequent sweep and quiescent period in time to visualize and quantify the strength and the duration of a coherent structure. We develop and verify the method of integrated quadrant analysis with data from two field studies: the Eclipse Boundary Layer Experiment (EBLE) in Corvallis, Oregon in August 2017 (grass field) and the Vertical Cherry Array Experiment (VACE) in Linden, California in November 2019 (cherry orchard). The combined TKE identification method and integrated quadrant analysis are promising additions to conditional sampling techniques and coherent structure characterization because the identify coherent structures and couple the sweep and ejection components in space. In an orchard (VACE), integrated quadrant analysis verifies each coherent structure is dominated by a sweep. Conversely, above the roughness sublayer (EBLE), each coherent structure is dominated by an ejection.
more » « less- Award ID(s):
- 1848019
- NSF-PAR ID:
- 10367209
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Boundary-Layer Meteorology
- Volume:
- 184
- Issue:
- 1
- ISSN:
- 0006-8314
- Page Range / eLocation ID:
- p. 45-69
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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