arXiv subjects

Geert Brethouwer

Publications and source records attributed to Geert Brethouwer.

8 recordsLinked to original sources

arXiv2025

Stability of plane Couette and Poiseuille flows rotating about the streamwise axis

We study the stability of plane Poiseuille flow (PPF) and plane Couette flow (PCF) subject to streamwise system rotation using linear stability analysis and direct numerical simulations. The linear stability analysis reveals two asymptotic regimes depending on the non-dimensional rotation rate ($Ro$): a low-$Ro$ and a high-$Ro$ regime. In the low-$Ro$ regime, the critical Reynolds number $Re_c$ and critical streamwise wavenumber $\alpha_c$ are proportional to $Ro$, while the critical spanwise wavenumber $\beta_c$ is constant. In the high-$Ro$ regime, as $Ro \rightarrow \infty$, we find $Re_c = 66.45$ and $\beta_c = 2.459$ for streamwise rotating PPF, and $Re_c = 20.66$ and $\beta_c = 1.558$ for streamwise rotating PCF, with $\alpha_c\propto 1/Ro$. Our results for streamwise rotating PPF match previous findings by Masuda et al. (2008). Interestingly, the critical values of $\beta_c$ and $Re_c$ at $Ro \rightarrow \infty$ in streamwise rotating PPF and PCF coincide with the minimum $Re_c$ reported by Lezius & Johnston (1976) and Wall & Nagata (2006) for spanwise rotating PPF at $Ro=0.3366$ and PCF at $Ro=0.5$. We explain this similarity through an analysis of the perturbation equations. Consequently, the linear stability of streamwise rotating PCF at large $Ro$ is closely related to that of spanwise rotating PCF and Rayleigh-Benard convection, with $Re_c = \sqrt{Ra_c}/2$, where $Ra_c$ is the critical Rayleigh number. To explore the potential for subcritical transitions, direct numerical simulations were performed. At low $Ro$, a subcritical transition regime emerges, characterized by large-scale turbulent-laminar patterns in streamwise rotating PPF and PCF. However, at higher $Ro$, subcritical transitions do not occur and the flow relaminarizes for $Re < Re_c$. Furthermore, we identify a narrow $Ro$-range where turbulent-laminar patterns develop under supercritical conditions.

physics.flu-dyn↗

arXiv2025

Turbulent heat transfer in open-channel flows with a thermally-conductive porous wall

Results of direct numerical simulations (DNS) of porous-wall turbulent flows in open channels with conjugate heat transfer are reported in this work. For the conductive porous walls considered here, the change in heat transfer is not monotonic. The heat flux initially decreases when going from a conductive smooth wall to slightly porous walls. In this initial porous-wall turbulence regime, the near-wall flow remains smooth-wall like and the heat transfer is dominated by molecular diffusion. As such, a reduction of the more favorably conducting solid material diminishes the overall heat transfer performance. Beyond a certain level of permeability however, the near-wall flow transitions to the K-H-like regime marked by the presence of cross-stream rollers, and the heat flux undergoes an increasing trend until it eventually surpasses that of smooth-wall turbulence. Neglecting the thermal behavior of the solid material can therefore result in overestimation of any gains in heat transfer. Additionally, thermal performance is assessed in terms of the Reynolds analogy breakdown, which is the disparity between the fractional increases in the Stanton number, $St$, and the fractional increases in the skin-friction coefficient, $C_f$, relative to smooth-wall flow. Similar to rough walls, the breakdown is unfavorable for porous walls. The unfavorable breakdown in Reynolds analogy is due to growing dissimilarities between the transfer of momentum and heat in the vicinity of the porous wall as it becomes more permeable. Turbulent sweep and ejection type events contribute more significantly to momentum transfer across the permeable surface than they do to heat transfer. However, unlike for rough walls, a saturation limit for heat transfer is not observed for the porous walls considered here. How much of a maximum increase in heat transfer can be achieved is something that remains to be determined.

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arXiv2021

Transitional Atmospheric Boundary Layer in the GABLS4 Experiment Modelled Using the Explicit Algebraic Reynolds-stress Model

A recently developed so-called explicit algebraic Reynolds-stress (EARS) model is applied to a transitioning atmospheric boundary layer (ABL). The simulation describes a diurnal cycle with a deep convective ABL during daytime and an extremely thin and stably stratified ABL during nighttime. The predictions of the EARS model are compared to large-eddy simulations (LES) of Couvreux \emph{et al.}~ (Bound Layer Meteorol 176:369-400, 2020). The model simulation is extended in time in order to study several consecutive diurnal cycles. The EARS model uses the same parametrization and model coefficients for stable and convective ABL and is applicable over a wide range of thermal stratifications. First-order statistics are shown to be well predicted by the model. We also show that the model can predict transitional effects such as residual turbulence as well as horizontal turbulent fluxes, which are an inherent part of the EARS model solution.

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arXiv2020

Much faster heat/mass than momentum transport in rotating Couette flows

Heat and mass transport is generally closely correlated to momentum transport in shear flows. This so-called Reynolds analogy between advective heat or mass transport and momentum transport hinders efficiency improvements in engineering heat and mass transfer applications. I show through direct numerical simulations that in plane Couette and Taylor-Couette flow rotation can strongly influence wall-to-wall passive tracer transport and make it much faster than momentum transport, clearly in violation of the Reynolds analogy. This difference between passive tracer transport, representative of heat/mass transport, and momentum transport is observed in steady flows with large counter-rotating vortices at low Reynolds numbers as well as in fully turbulent flows at higher Reynolds numbers. It is especially large near the neutral (Rayleigh's) stability limit. The rotation-induced Coriolis force strongly damps the streamwise/azimuthal velocity fluctuations when this limit is approached while tracer fluctuations are much less affected. Accordingly, momentum transport is much more reduced than tracer transport, showing that the Coriolis force breaks the Reynolds analogy. At higher Reynolds numbers this strong advective transport dissimilarity is accompanied by approximate limit cycle dynamics with intense low-frequency bursts of turbulence when approaching the neutral stability limit. The study demonstrates that simple body forces can cause clear dissimilarities between heat/mass and momentum transport in shear flows.

physics.flu-dyn↗

arXiv2017

Statistics and structure of spanwise rotating turbulent channel flow at moderate Reynolds numbers

A study of fully developed plane turbulent channel flow subject to spanwise system rotation through direct numerical simulations is presented. In order to study both the influence of the Reynolds number and spanwise rotation on channel flow, the Reynolds number $Re = U_b h/ν$ is varied from a low 3000 to a moderate $31\,600$ and the rotation number $Ro = 2 Ωh/U_b$ is varied from 0 to 2.7, where $U_b$ is the mean bulk velocity, $h$ the channel half gap and $Ω$ the system rotation rate. The mean streamwise velocity profile displays also at higher $Re$ the characteristic linear part with a slope near to $2 Ω$ and a corresponding linear part in the profiles of the production and dissipation rate of turbulent kinetic energy appears. With increasing $Ro$ a distinct unstable side with large spanwise and wall-normal Reynolds stresses and a stable side with much weaker turbulence develops in the channel. The flow starts to relaminarize on the stable side of the channel and persisting turbulent-laminar patterns appear at higher $Re$. If $Ro$ is further increased the flow on the stable side becomes laminar-like while at yet higher $Ro$ the whole flow relaminarizes, although the calm periods might be disrupted by repeating bursts of turbulence, as explained by Brethouwer (2016). The influence of the Reynolds number is considerable, in particular on the stable side of the channel where velocity fluctuations are stronger and the flow relaminarizes less quickly at higher $Re$. Visualizations and statistics show that at $Ro=0.15$ and 0.45 large-scale structures and large counter rotating streamwise roll cells develop on the unstable side. These become less noticeable and eventually vanish when $Ro$ raises, especially at higher $Re$. At high $Ro$, the largest energetic structures are larger at lower $Re$.

physics.flu-dyn↗

arXiv2017

Passive scalar transport in rotating turbulent channel flow

Passive scalar transport in turbulent channel flow subject to spanwise system rotation is studied by direct numerical simulations. The Reynolds number $Re = U_b h/ν$ is fixed at $20\,000$ and the rotation number $Ro = 2 Ωh/U_b$ is varied from 0 to 1.2, where $U_b$ is the bulk mean velocity, $h$ the half channel gap width and $Ω$ the rotation rate. The scalar value is constant but different at the two walls, leading to steady scalar transport across the channel. The rotation causes an unstable channel side with relatively strong turbulence and turbulent scalar transport, and a stable channel side with relatively weak turbulence or laminar-like flow, weak turbulent scalar transport but large scalar fluctuations and steep mean scalar gradients. The distinct turbulent-laminar patterns observed at certain $Ro$ on the stable channel side induce similar patterns in the scalar gradient field. The main conclusions of the study are that rotation reduces the similarity between the scalar and velocity field and that the Reynolds analogy for scalar-momentum transport does not hold for rotating turbulent channel flow. This is shown by a reduced correlation between velocity and scalar fluctuations, and a strongly reduced turbulent Prandtl number of less than 0.2 on the unstable channel side away from the wall at higher $Ro$. On the unstable channel side, scalar scales become larger than turbulence scales according to spectra and the turbulent scalar flux vector becomes more aligned with the mean scalar gradient owing to rotation. Budgets in the governing equations of the scalar energy and scalar fluxes are presented and discussed as well as other statistics relevant for turbulence modelling.

physics.flu-dyn↗

arXiv2014

Recurrent bursts via linear processes in turbulent environments

Large-scale instabilities occurring in the presence of small-scale turbulent fluctuations are frequently observed in geophysical or astrophysical contexts but are difficult to reproduce in the laboratory. Using extensive numerical simulations, we report here on intense recurrent bursts of turbulence in plane Poiseuille flow rotating about a spanwise axis. A simple model based on the linear instability of the mean flow can predict the structure and time scale of the nearly-periodic and self-sustained burst cycles. Rotating Poiseuille flow is suggested as a prototype for future studies of low-dimensional dynamics embedded in strongly turbulent environments.

physics.flu-dyn↗

arXiv2011

Hairpins et al. in Turbulent Boundary Layers

A new set of three-dimensional visualisations of a large-scale direct numerical simulations (DNS) of a turbulent boundary layer is presented. The Reynolds number ranges from $Re_θ=180$ to 4300, based on the momentum-loss thickness $θ$ and the free-stream velocity $U_\infty$. The focus of the present fluid dynamics video is on analysing the coherent vortical structures in the boundary layer: It is clearly shown that the initial phases are dominated by coherent so-called hairpin vortices which are characteristic remainders of the laminar-turbulent transition at lower Reynolds numbers. At higher $Re$ (say $Re_θ>2000$), these structures are no longer seen as being dominant; the coherence is clearly lost, both in the near-wall region as well as in the outer layer of the boundary layer. Note, however, that large-scale streaks in the streamwise velocity, which have their peak energy at about half the boundary-layer thickness, are unambiguously observed. In addition to visualisation with classical three-dimensional isosurfaces, the video is also rendered using stereoscopic views using red-cyan anaglyphs.

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