Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2006.00182

Turbulent boundary layers over streamwise-preferential porous materials

Christoph Efstathiou·Mitul Luhar
View original source ↗Read source document ↗Export metadata ↓

Abstract

Recent numerical simulations indicate that streamwise-preferential anisotropic porous materials have the potential to reduce skin friction in turbulent flows through a similar mechanism to riblets. This paper reports particle image velocimetry (PIV) measurements made in turbulent boundary layers at $Re_τ\approx 360$ over 3D-printed porous substrates exhibiting such streamwise-preferential permeability. The porous material has normalized streamwise permeability $\sqrt{K_{xx}^+}\approx 3.0$ and wall-normal and spanwise permeabilities $\sqrt{K_{yy}^+} = \sqrt{K_{zz}^+} \approx 1.1$. This material is flush-mounted into a cutout in the downstream half of a flat-plate boundary layer setup in a water channel facility. Measurements made at several locations along the porous substrate provide insight into boundary layer development. For fully-developed conditions, the mean profiles show the presence of a logarithmic region over the porous material with similar constants to those found over a smooth wall. A technique that estimates the mean profile at single-pixel resolution from the particle images suggests the presence of an interfacial slip velocity of $U_s^+ \approx \sqrt{K_{xx}^+}$ over the porous substrate. Friction velocity estimates obtained from outer layer fits to the mean profile suggest a marginal increase in drag over the porous substrate. PIV measurements show a decrease in the intensity of streamwise velocity fluctuations in the near-wall region and an increase in the intensity of wall-normal velocity fluctuations. These observations are consistent with simulation results, which suggest that materials with $\sqrt{K_{yy}^+} > 0.4$ are susceptible to the emergence of spanwise rollers similar to Kelvin-Helmholtz vortices that degrade drag reduction performance. Velocity spectra indicate that such structures emerge in the experiments as well.

Explore related subjects

physics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Christoph Efstathiou, Mitul Luhar. 2020-05-30. Turbulent boundary layers over streamwise-preferential porous materials. https://arxiv.org/abs/2006.00182

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Data-driven low-dimensional model for the onset of turbulence in plane Couette flow

We construct low-dimensional dynamical systems for low-Reynolds-number turbulence in plane Couette flow using Kernel Quantile Regression. Exploiting the finite-dimensional structure of attractors in dissipative systems, reduced-order models are learned from direct numerical simulation data using a small set of physically meaningful observables. The resulting discrete-time models accurately reproduce periodic and chaotic dynamics near the onset of turbulence. The minimum number of variables required for accurate prediction is found to be consistent with embedding theory based on the attractor dimension. For chaotic regimes, the models capture both short-term trajectory evolution and long-term statistical properties, including probability density functions. By incorporating the Reynolds number as an additional input variable, we further develop a parameter-dependent model that successfully reproduces the bifurcation structure over a range of Reynolds numbers, including bifurcations between training points. These results demonstrate the effectiveness of machine-learning-based reduced-order modeling for capturing the essential dynamics and statistics of weakly turbulent flows.

physics.flu-dyn↗
arXiv2026

Rapidly rotating internally heated convection: bounds on long-time averages

Convection on geophysical and astrophysical scales is subject to rapid rotation and strong heating from within the domain. In studying the long-time behaviour of the solutions for such a system, energy identities fail to capture the effects of rotation because the Coriolis force does no work, and rapid rotation can be prohibitive for direct numerical simulations. Instead, we derive an asymptotically reduced model for rapidly rotating convection driven by uniform internal heating between isothermal stress-free boundaries in a plane periodic layer. The main contribution is the proof of bounds on the mean temperature, and the mean vertical convective heat transport, in terms of the Rayleigh and Ekman numbers, in the limit of infinite Prandtl number. The first quantity represents the mixing of the flow, and the second the asymmetry in heat leaving the bottom and top boundaries due to convection, and unlike Rayleigh-Bénard convection, the two are not a priori related. We employ alternative estimation techniques to those used in previous studies (Grooms \& Whitehead, 2014 \textit{Nonlinearity}, 28, 29) and identify two distinct scaling behaviours for both quantities. Finally, our bounds are optimised, within the methodology, and provide a rigorous constraint for future studies of rotation-dominated internally heated convection.

physics.flu-dyn↗
arXiv2026

Baroclinic wave dynamics in the Ekman-free rotating rectangular annulus with localized forced plume

We report numerical simulations of a rotating rectangular annulus that isolates the Ekman-free bulk of the cylindrical baroclinic annulus, subjected to bi-directional temperature gradients imposed by a uniformly cooled inner wall and a localized forced heated plume at the outer bottom. The finite-volume OpenFOAM solver is employed across combinations of source Richardson number $Ri_0 = 99, 4, 1$ and Rossby number $Ro = 0.3, 0.1, 0.07$. A non-dimensional scaling of the governing equations identifies geostrophic-hydrostatic balance as the leading-order bulk state, a result confirmed a posteriori by the $x$ and $z-$momentum budgets. Baroclinic waves of mode $m=2$ at $Ro=0.3$ transition to $m=3$ as $Ro$ decreases, consistent with the contraction of the Eady deformation radius $L_ρ= NH/f$; Complex Empirical Orthogonal Function (CEOF) analysis characterizes the wave regime and detects a Hopf-bifurcated vacillating state at $Ri_0 = 99,~Ro = 0.1$. The plume morphology, classified through the Morton length scale and source flux-balance parameter, transitions from weak, laterally-swept structures at $Ri_0 = 99$ to sustained columnar plumes traversing the full baroclinic depth at $Ri_0 \leq 4$. The plume entrainment coefficient $Γ(z)$ shows opposite rotational sensitivities at low and high $Ri_0$, which we organize through a local plume Rossby number $Ro_p = w/(2Ωb)$. A mixing-length argument predicts a bulk turbulent heat flux $\overline{u'T'} \propto Ri_0^{-1/2}$, anticipating an order-of-magnitude enhancement from $Ri_0 = 99$ to $Ri_0 = 1$, in agreement with the simulations. A regime map in the $(Ri_0, Ro)$ plane reveals that, within the explored range, the plume-regime and wave-selection problems are approximately separable: $Ri_0$ sets the plume regime while $Ro$ selects the dominant baroclinic wave mode.

physics.flu-dyn↗